seismic data restoration via data driven tight frame restoration interpolation of missing traces plays a crucial role in the seismic data processing pipeline efficient restoration methods have been proposed based on sparse signal representation in a transform domain such as fourier wavelet curvelet and shearlet transforms most existing methods are based on transforms with a fixed basis we considered an adaptive sparse transform for restoration of data with complex structures in particular we evaluated a data driven tight frame based sparse regularization method for seismic data restoration the main idea of the data driven tight frame tf is to adaptively learn a set of framelet filters from the currently interpolated data under which the data can be more sparsely represented hence the sparsity promoting l1 norm spl1 minimization methods can produce better restoration results by using the learned filters a split inexact uzawa algorithm which can be viewed as a generalization of the alternating direction of multiplier method admm was applied to solve the presented spl1 model numerical tests were performed on synthetic and real seismic data for restoration of randomly missing traces over a regular data grid our experiments showed that our proposed method obtains the state of the art restoration results in comparison with the traditional fourier based projection onto convex sets the tight frame based method and the recent shearlet regularization admm method

interpolation and denoising of high dimensional seismic data by learning a tight frame abstractsparse transforms play an important role in seismic signal processing steps such as prestack noise attenuation and data reconstruction analytic sparse transforms so called implicit dictionaries such as the fourier radon and curvelet transforms are often used to represent seismic data there are situations however in which the complexity of the data requires adaptive sparse transform methods whose basis functions are determined via learning methods we studied an application of the data driven tight frame ddtf method to noise suppression and interpolation of high dimensional seismic data rather than choosing a model beforehand for example a family of lines parabolas or curvelets to fit the data the ddtf derives the model from the data itself in an optimum manner the process of estimating the basis function from the data can be summarized as follows first the input data are divided into small blocks to form training sets then the ddtf algorithm is applied on the training set

simplified bayesian sensitivity analysis for mismeasured and unobserved confounders we examine situations where interest lies in the conditional association between outcome and exposure variables given potential confounding variables concern arises that some potential confounders may not be measured accurately whereas others may not be measured at all some form of sensitivity analysis might be employed to assess how this limitation in available data impacts inference a bayesian approach to sensitivity analysis is straightforward in concept a prior distribution is formed to encapsulate plausible relationships between unobserved and observed variables and posterior inference about the conditional exposure disease relationship then follows in practice though it can be challenging to form such a prior distribution in both a realistic and simple manner moreover it can be difficult to develop an attendant markov chain monte carlo mcmc algorithm that will work effectively on a posterior distribution arising from a highly nonidentified model in this article a simple prior distribution for acknowledging both poorly measured and unmeasured confounding variables is developed it requires that only a small number of hyperparameters be set by the user moreover a particular computational approach for posterior inference is developed because application of mcmc in a standard manner is seen to be ineffective in this problem

evidence factors in observational studies some experiments involve more than one random assignment of treatments to units an analogous situation arises in certain observational studies although randomization is not used so each assignment may be biased if each assignment is suspect it is natural to ask whether there are separate pieces of information dependent upon different assumptions and perhaps whether conclusions about treatment effects are not critically dependent upon one or another suspect assumption the design of an observational study contains evidence factors if it permits several statistically independent tests of the same null hypothesis about treatment effects where these tests rely on different assumptions about treatment assignments at several levels of assignment two designs and two empirical examples are considered one example of each design in the dose control design there are matched pairs of a treated subject and an untreated control and doses of treatment vary between pairs for treated subjects this yields two evidence factors in the varied intensity design there are matched sets with two treated subjects and one or more untreated controls where the two treated subjects within the same matched set receive different doses of treatment and in a technically different way the design yields two evidence factors

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

multistep autoregressive reconstruction of seismic records linear prediction filters in the f x domain are widely used to interpolate regularly sampled data we study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters we propose a two stage algorithm first we reconstruct the unaliased part of the data spectrum using a fourier method minimum weighted norm interpolation then prediction filters for all the frequencies are extracted from the reconstructed low frequencies the latter is implemented via a multistep autoregressive msar algorithm finally these prediction filters are used to reconstruct the complete data in the f x domain the applicability of the proposed method is examined using synthetic and field data examples

simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis we present a rank reduction algorithm that permits simultaneous reconstruction and random noise attenuation of seismic records we based our technique on multichannel singular spectrum analysis mssa the technique entails organizing spatial data at a given temporal frequency into a block hankel matrix that in ideal conditions is a matrix of rank k where k is the number of plane waves in the window of analysis additive noise and missing samples will increase the rank of the block hankel matrix of the data consequently rank reduction is proposed as a means to attenuate noise and recover missing traces we present an iterative algorithm that resembles seismic data reconstruction with the method of projection onto convex sets in addition we propose to adopt a randomized singular value decomposition to accelerate the rank reduction stage of the algorithm we apply mssa reconstruction to synthetic examples and a field data set synthetic examples were used to assess the performance of the method in two

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

testing one hypothesis twice in observational studies in a matched observational study of treatment effects a sensitivity analysis asks about the magnitude of the departure from random assignment that would need to be present to alter the conclusions of an analysis that assumes that matching for measured covariates removes all bias the reported degree of sensitivity to unmeasured biases depends on both the process that generated the data and the chosen methods of analysis so a poor choice of method may lead to an exaggerated report of sensitivity to bias this suggests the possibility of performing more than one analysis with a correction for multiple inference say testing one null hypothesis using two or three different tests in theory and in an example it is shown that in large samples the gains from testing twice will often be large because testing twice has the larger of the two design sensitivities of the component tests and the losses due to correcting for two tests will often be small because two tests of one hypothesis will typically be highly correlated so a correction for multiple testing that takes this into account will be small an illustration uses data from the u s national health and nutrition examination survey concerning lead in the blood of cigarette smokers copyright 2012 oxford university press

seismic data interpolation and denoising in the frequency wavenumber domain i introduce a unified approach for denoising and interpolation of seismic data in the frequency wavenumber f k domain first an angular search in the f k domain is carried out to identify a sparse number of dominant dips not only using low frequencies but over the whole frequency range then an angular mask function is designed based on the identified dominant dips the mask function is utilized with the least squares fitting principle for optimal denoising or interpolation of data the least squares fit is directly applied in the time space domain the proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid synthetic and real data examples are provided to examine the performance of the proposed method

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

bahadur efficiency of sensitivity analyses in observational studies an observational study draws inferences about treatment effects when treatments are not randomly assigned as they would be in a randomized experiment the naive analysis of an observational study assumes that adjustments for measured covariates suffice to remove bias from nonrandom treatment assignment a sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of the naive analysis say leading to the acceptance of a null hypothesis rejected in the naive analysis observational studies vary greatly in their sensitivity to unmeasured biases but a poor choice of test statistic can lead to an exaggerated report of sensitivity to bias the bahadur efficiency of a sensitivity analysis is introduced calculated and connected to established concepts such as the power of a sensitivity analysis and the design sensitivity the bahadur slope equals zero when the sensitivity parameter equ

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

fundamental concepts of qualitative probabilistic networks abstract graphical representations for probabilistic relationships have recently received considerable attention in ai qualitative probabilistic networks abstract from the usual numeric representations by encoding only qualitative relationships which are inequality constraints on the joint probability distribution over the variables although these constraints are insufficient to determine probabilities uniquely they are designed to justify the deduction of a class of relative likelihood conclusions that imply useful decision making properties two types of qualitative relationship are defined each a probabilistic form of monotonicity constraint over a group of variables qualitative influences describe the direction of the relationship between two variables qualitative synergies describe interactions among influences the probabilistic definitions chosen justify sound and efficient inference procedures based on graphical manipulations of the network these procedures answer queries about qualitative relationships among variables separated in the network and determine structural properties of optimal assignments to decision variables

inconsistent treatment estimates from mis specified logistic regression analyses of randomized trials when the difference between treatments in a clinical trial is estimated by a difference in means then it is well known that randomization ensures unbiassed estimation even if no account is taken of important baseline covariates however when the treatment effect is assessed by other summaries for example by an odds ratio if the outcome is binary then bias can arise if some covariates are omitted regardless of the use of randomization for treatment allocation or the size of the trial we present accurate closed form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression we compare this approximation with ones in the literature and derive more convenient forms for some of these existing results the expressions give insight into the form of the bias which simulations show is usable for distributions other than the normal the key result applies even when there are additional binary covariates in the model

fourier reconstruction of nonuniformly sampled aliased seismic data there are numerous methods for interpolating uniformly sampled aliased seismic data but few can handle the combination of nonuniform sampling and aliasing we combine the principles of fourier reconstruction of nonaliased nonuniformly sampled data with the ideas of frequency wavenumber f k interpolation of aliased uniformly sampled data in a new two step algorithm in the first step we estimate the fourier coefficients at the lower nonaliased temporal frequencies from the nonuniformly sampled data the coefficients are then used in the second step as an a priori model to distinguish between aliased and nonaliased energy at the higher aliased temporal frequencies by using a nonquadratic model penalty in the inversion both the artifacts in the fourier domain from nonuniform sampling and the aliased energy are suppressed the underlying assumption is that events are planar therefore the algorithm is applied to seismic data in overlapping spatiotemporal windows

assessing the sensitivity of regression results to unmeasured confounders in observational studies this paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variable after adjusting for measured covariates the proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders one can use the corresponding reduced model that omits the unmeasured confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed groups along with the effects of the unmeasured confounder on the outcome variable under certain conditions there exists a simple algebraic relationship between the true exposure effect in the full model and the apparent exposure effect in the reduced model one can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports the proposed method handles both binary response and censored survival time data accommodates any study design and allows the unmeasured confounder to be discrete or normally distributed we describe applications on two major medical studies

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

a tensor higher order singular value decomposition for prestack seismic data noise reduction and interpolation a patch of prestack data depends on four spatial dimensions x y midpoints and x y offsets and frequency the spatial data at one temporal frequency can be represented by a fourth order tensor in ideal conditions of high signal to noise ratio and complete sampling one can assume that the seismic data can be approximated via a low rank fourth order tensor missing samples were recovered by reinserting data obtained by approximating the original noisy and incomplete data volume with new observations obtained via the rank reduction process the higher order singular value decompostion was used to reduce the rank of the prestack seismic tensor synthetic data demonstrated the ability of the proposed seismic data completion algorithm to reconstruct events with curvature the synthetic example allowed to quantify the quality of the reconstruction for different levels of noise and survey sparsity we also provided a real data example from the western canadian sedimentary basin

context specific sign propagation in qualitative probabilistic networks qualitative probabilistic networks are qualitative abstractions of probabilistic networks summarising probabilistic influences by qualitative signs as qualitative networks model influences at the level of variables knowledge about probabilistic influences that hold only for specific values cannot be expressed the results computed from a qualitative network as a consequence can be weaker than strictly necessary and may in fact be rather uninformative we extend the basic formalism of qualitative probabilistic networks by providing for the inclusion of context specific information about influences and show that exploiting this information upon reasoning has the ability to forestall unnecessarily weak results

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

augmented lagrangian approach to design of structured optimal state feedback gains we consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers these constraints are in the form of sparsity requirements for the feedback matrix implying that each controller has access to information from only a limited number of subsystems the minimizer of this constrained optimal control problem is sought using the augmented lagrangian method notably this approach does not require a stabilizing structured gain to initialize the optimization algorithm motivated by the structure of the necessary conditions for optimality of the augmented lagrangian we develop an alternating descent method to determine the structured optimal gain we also utilize the sensitivity interpretation of the lagrange multiplier to identify favorable communication architectures for structured optimal design examples are provided to illustrate the effectiveness of the developed method

beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data we propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform in a first pass the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data the aforementioned coefficients are divided into two groups of scales alias free and alias contaminated scales the alias free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias contaminated scale coefficients the mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data once the alias free coefficients are determined the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions the proposed method can be used to reconstruct regularly and irregularly sampled seismic data we believe that our exposition leads to a clear unifying thread between f x and f k beyond alias interpo

an alternate numerical solution to the linear quadratic problem this note proposes a new method based on convex programming for solving the linear quadratic problem lqp directly on the parameter space generated by the feedback control gain all stabilizing controllers are mapped into a convex set the problem is then formulated as a minimization of a linear function over this convex set its optimal solution furnishes under certain conditions the same feedback control gain obtained from the classical riccati equation generalizations to decentralized control and output feedback control design are included the theory is illustrated by some numerical examples

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

adjusting for unmeasured confounding due to either of two crossed factors with a logistic regression model motivated by an investigation of the effect of surface water temperature on the presence of vibrio cholerae in water samples collected from different fixed surface water monitoring sites in haiti in different months we investigated methods to adjust for unmeasured confounding due to either of the two crossed factors site and month in the process we extended previous methods that adjust for unmeasured confounding due to one nesting factor such as site which nests the water samples from different months to the case of two crossed factors first we developed a conditional pseudolikelihood estimator that eliminates fixed effects for the levels of each of the crossed factors from the estimating equation using the theory of u statistics for independent but non identically distributed vectors we show that our estimator is consistent and asymptotically normal but that its variance depends on the nuisance parameters and thus cannot be easily estimated consequently we apply our estimator in conjunction with a permutation test and we investigate use of the pigeonhole bootstrap and the jackknife for constructing confidence intervals we also incorporate our estimator into a diagnostic test for a logistic mixed model with crossed random effects and no unmeasured confounding for comparison we investigate between within models extended to two crossed factors these generalized linear mixed models include covariate means for each level of each factor in order to adjust for the unmeasured confounding we conduct simulation studies and we apply the methods to the haitian data copyright 2016 john wiley sons ltd

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

f x adaptive seismic trace interpolation we use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency space f x seismic interpolation adaptive prediction filters can model signals where the dominant wavenumbers vary in space this concept leads to an f x interpolation method that does not require windowing strategies for optimal results in other words adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips the interpolation method s performance depends on two parameters filter length and forgetting factor we pay particular attention to selection of the forgetting factor because it controls the algorithm s adaptability to changes in local dip finally we use synthetic and real data examples to illustrate the performance of the proposed adaptive f x interpolation method

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

seismic trace interpolation in the fourier transform domain a data adaptive interpolation method is designed and applied in the fourier transform domain f k or f kx ky for spatially aliased data the method makes use of fast fourier transforms and their cyclic properties thereby offering a significant cost advantage over other techniques that interpolate aliased data the algorithm designs and applies interpolation operators in the f k or f kx ky domain to fill zero traces inserted in the data in the t x or t x y domain at locations where interpolated traces are needed the interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data this operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies and corresponds to the f k or f kx ky domain version of the well known f x or f x y domain trace interpolators the method is applicable to 2d and 3d data recorded sparsely in a horizontal plane the most comm

5d seismic data completion and denoising using a novel class of tensor decompositions abstractwe have developed a novel strategy for simultaneous interpolation and denoising of prestack seismic data most seismic surveys fail to cover all possible source receiver combinations leading to missing data especially in the midpoint offset domain this undersampling can complicate certain data processing steps such as amplitude variation with offset analysis and migration data interpolation can mitigate the impact of missing traces we considered the prestack data as a 5d multidimensional array or otherwise referred to as a 5d tensor using synthetic data sets we first found that prestack data can be well approximated by a low rank tensor under a recently proposed framework for tensor singular value decomposition tsvd under this low rank assumption we proposed a complexity penalized algorithm for the recovery of missing traces and data denoising in this algorithm the complexity regularization was controlled by tuning a single regularization parameter using a statistical test we tested t

multidimensional interpolation using a model constrained minimum weighted norm interpolation abstractfourier based minimum weighted norm interpolation mwni has been widely used to regularize land seismic data however it has difficulty interpolating regular missing data that are spatially aliased minimizing the aliasing artifacts is still a technical challenge in mwni i have developed a novel method to address the aliasing problem in mwni using a prior model as constraints the prior model was constructed by a linear interpolation along dominant dips to produce a fully regular initial model the spectral weights derived from this initial model are typically not aliased and can be used to constrain the least squares inversion in mwni frequency by frequency to overcome the aliasing artifacts this new interpolation scheme expands the capability of conventional mwni to handle spatially aliased data that are often associated with steeply dipping structures and it reconstructs more reliable interpolation results decimation tests of a simple 2d synthetic data set and a complex 3d synthetic sal

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided

properties of monotonic effects on directed acyclic graphs various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations counterexamples are provided to show that the results do not hold under less restrictive conditions monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification the theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator hypercholesterolemia and the outcome cardiovascular disease

fourier reconstruction of marine streamer data in four spatial coordinates many methods exist for interpolation of seismic data in one and two spatial dimensions but few can interpolate properly in three or four spatial dimensions marine multi streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled we approach the problem of interpolation of marine streamer data in four spatial dimensions by splitting the problem into a 1d interpolation along the densely sampled streamers and a 3d fourier reconstruction for the remaining spatial coordinates in fourier reconstruction the fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least squares inversion the method is computationally efficient requires no subsurface information and can handle uniform grids with missing data as well as nonuniform grids or random sampling the output grid of the 1d interpolation in the first step is arbitrary when the output grid has uniform inline midpoints spacing the 3d fourier reconstruction in the second step is performed in the crossline midpoint absolute offset and azimuth coordinates when the first step outputs to uniform absolute offset the 3d fourier reconstruction handles the crossline inline midpoint and the azimuth coordinates in both cases the main innovation is the inclusion of the azimuthal coordinate in the fourier reconstruction the azimuth multiplicity must be increased for the method to be successful which means that overlap shooting is required we have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3d multiple prediction and regularization to reduce sampling related differences in processing of time lapse data

constrained stochastic lqc a tractable approach despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems such an approach is limited by its inability to tractably deal with even simple constraints in this paper we present an alternative approach based on results from robust optimization to solve the stochastic linear quadratic control slqc problem in the unconstrained case the problem may be formulated as a semidefinite optimization problem sdp we show that we can reduce this sdp to optimization of a convex function over a scalar variable followed by matrix multiplication in the current state thus yielding an approach that is amenable to closed loop control and analogous to the riccati equation in our framework we also consider a tight second order cone socp approximation to the sdp that can be solved much more efficiently when the problem has additional constraints both the sdp and socp are tractable in the presence of control and state space constraints moreover compared to the riccati approach they provide much greater control over the stochastic behavior of the cost function when the noise in the system is distributed normally

directed acyclic graphs with edge specific bounds we give a definition of a bounded edge within the causal directed acyclic graph framework a bounded edge generalizes the notion of a signed edge and is defined in terms of bounds on a ratio of survivor probabilities we derive rules concerning the propagation of bounds bounds on causal effects in the presence of unmeasured confounding are also derived using bounds related to specific edges on a graph we illustrate the theory developed by an example concerning estimating the effect of antihistamine treatment on asthma in the presence of unmeasured confounding

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

strong control of the familywise error rate in observational studies that discover effect modification by exploratory methods an effect modifier is a pretreatment covariate that affects the magnitude of the treatment effect or its stability when there is effect modification an overall test that ignores an effect modifier may be more sensitive to unmeasured bias than a test that combines results from subgroups defined by the effect modifier if there is effect modification one would like to identify specific subgroups for which there is evidence of effect that is insensitive to small or moderate biases in this paper we propose an exploratory method for discovering effect modification and combine it with a confirmatory method of simultaneous inference that strongly controls the familywise error rate in a sensitivity analysis despite the fact that the groups being compared are defined empirically a new form of matching strength k matching permits a search through more than k covariates for effect modifiers in such a way that no pairs are lost provided that at most k covariates are selected to group the pairs in a strength k match each set of k covariates is exactly balanced although a set of more than k covariates may exhibit imbalance we apply the proposed method to study the effects of the earthquake that struck chile in 2010

the computational complexity of probabilistic inference using bayesian belief networks research note abstract bayesian belief networks provide a natural efficient method for representing probabilistic dependencies among a set of variables for these reasons numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks more general classes of belief networks however have eluded efforts to develop efficient inference algorithms we show that probabilistic inference using belief networks is np hard therefore it seems unlikely that an exact algorithm can be developed to perform probabilistic inference efficiently over all classes of belief networks this result suggests that research should be directed away from the search for a general efficient probabilistic inference algorithm and toward the design of efficient special case average case and approximation algorithms

brief the infinite time near optimal decentralized regulator problem for singularly perturbed systems a convex optimization approach this paper presents lq decentralized pole location for singularly perturbed systems the poles are located in a sector included in the left half complex plane the singular perturbation method is used to define reduced and well behaved problems it is shown that the lq control problem with pole location in a sector can be solved using the lmi tool the associated parametrical optimization problem involves a linear cost objective under lmi constraints the decentralized control problem is then solved in the reduced slow system by just introducing structure constraints on the matrix variables constraints that do not destroy the linearity and then the convexity of the problem

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

asymptotic separability in sensitivity analysis summary in an observational study in which each treated subject is matched to several untreated controls by using observed pretreatment covariates a sensitivity analysis asks how hidden biases due to unobserved covariates might alter the conclusions the bounds required for a sensitivity analysis are the solution to an optimization problem in general this optimization problem is not separable in the sense that one cannot find the needed optimum by performing a separate optimization in each matched set and combining the results we show however that this optimization problem is asymptotically separable so that when there are many matched sets a separate optimization may be performed in each matched set and the results combined to yield the correct optimum with negligible error this is true when the wilcoxon rank sum test or the hodgeslehmann aligned rank test is applied in matching with multiple controls numerical calculations show that the asymptotic approximation performs well with as few as 10 matched sets in the case of the rank sum test a table is given containing the separable solution with this table only simple arithmetic is required to conduct the sensitivity analysis the method also supplies estimates such as the hodges lehmann estimate and confidence intervals associated with rank tests the method is illustrated in a study of dropping out of us high schools and the effects on cognitive test scores

identification of treatment effects under conditional partial independence conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption we derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional independence assumption these deviations are defined via a conditional treatment assignment probability which makes it straightforward to interpret our results can be used to assess the robustness of empirical conclusions obtained under the baseline conditional independence assumption

probability intervals over influence diagrams a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point valued probabilities is described procedures for operations corresponding to conditional expectation and bayesian conditioning in influence diagrams are derived where lower bounds on probabilities are stored at each node the resulting bounds for the transformed diagram are shown to be the tightest possible within the class of constraints on probability distributions that can be expressed exclusively as lower bounds on the component probabilities of the diagram sequences of these operations can be performed to answer probabilistic queries with indeterminacies in the input and for performing sensitivity analysis on an influence diagram the storage requirements and computational complexity of this approach are comparable to those for point valued probabilistic inference mechanisms

reconstruction of structurally incomplete matrices with reweighted low rank and sparsity priors most matrix reconstruction methods assume that missing entries randomly distribute in the incomplete matrix and the low rank prior or its variants are used to well pose the problem however in practical applications missing entries are structurally rather than randomly distributed and cannot be handled by the rank minimization prior individually to remedy this this paper introduces new matrix reconstruction models using double priors on the latent matrix named reweighted low rank and sparsity priors relasp in the proposed relasp models the matrix is regularized by a low rank prior to exploit the inter column and inter row correlations and its columns rows are regularized by a sparsity prior under a dictionary to exploit intra column row correlations both the low rank and sparse priors are reweighted on the fly to promote low rankness and sparsity respectively numerical algorithms to solve our relasp models are derived via the alternating direction method under the augmented lagrangian multiplier framework results on synthetic data image restoration tasks and seismic data interpolation show that the proposed relasp models are quite effective in recovering matrices degraded by highly structural missing and various types of noise complementing the classic matrix reconstruction models that handle random missing only

a comparison of bayesian and monte carlo sensitivity analysis for unmeasured confounding bias from unmeasured confounding is a persistent concern in observational studies and sensitivity analysis has been proposed as a solution in the recent years probabilistic sensitivity analysis using either monte carlo sensitivity analysis mcsa or bayesian sensitivity analysis bsa has emerged as a practical analytic strategy when there are multiple bias parameters inputs bsa uses bayes theorem to formally combine evidence from the prior distribution and the data in contrast mcsa samples bias parameters directly from the prior distribution intuitively one would think that bsa and mcsa ought to give similar results both methods use similar models and the same prior probability distributions for the bias parameters in this paper we illustrate the surprising finding that bsa and mcsa can give very different results specifically we demonstrate that mcsa can give inaccurate uncertainty assessments e g 95 intervals that do not reflect the data s influence on uncertainty about unmeasured confounding using a data example from epidemiology and simulation studies we show that certain combinations of data and prior distributions can result in dramatic prior to posterior changes in uncertainty about the bias parameters this occurs because the application of bayes theorem in a non identifiable model can sometimes rule out certain patterns of unmeasured confounding that are not compatible with the data consequently the mcsa approach may give 95 intervals that are either too wide or too narrow and that do not have 95 frequentist coverage probability based on our findings we recommend that analysts use bsa for probabilistic sensitivity analysis copyright 2017 john wiley sons ltd

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

large sample learning of bayesian networks is np hard in this paper we provide new complexity results for algorithms that learn discrete variable bayesian networks from data our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest structure for which the model is able to represent the generative distribution exactly our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset we show that identifying high scoring structures is np hard even when any combination of one or more of the following hold the generative distribution is perfect with respect to some dag containing hidden variables we are given an independence oracle we are given an inference oracle we are given an information oracle we restrict potential solutions to structures in which each node has at most k parents for all k 3 our proof relies on a new technical result that we establish in the appendices in particular we provide a method for constructing the local distributions in a bayesian network such that the resulting joint distribution is provably perfect with respect to the structure of the network

bias testing bias correction and confounder selection using an instrumental variable model instrumental variable iv analysis can be used to address bias due to unobserved confounding when estimating the causal effect of a treatment on an outcome of interest however if a proposed iv is correlated with unmeasured confounders and or weakly correlated with the treatment the standard iv estimator may be more biased than an ordinary least squares ols estimator several methods have been proposed that compare the bias of the iv and ols estimators relying on the belief that measured covariates can be used as proxies for the unmeasured confounder despite these developments there is lack of discussion about approaches that can be used to formally test whether the iv estimator may be less biased than the ols estimator thus we have developed a testing framework to compare the bias and a criterion to select informative measured covariates for bias comparison and regression adjustment we also have developed a bias correction method which allows one to use an invalid iv to correct the bias of the ols or iv estimator numerical studies demonstrate that the proposed methods perform well with realistic sample sizes

interpolation with fourier radial adaptive thresholding many interpolation methods are effective with regularly sampled or randomly sampled data whereas the spatial sampling of seismic reflectivity data is typically neither regular nor random fourier radial adaptive thresholding frat is a sparsity promoting method in which the interpolated result is sparse in the frequency wavenumber domain and is coherent in a manner consistent with that of a collection of unaliased plane waves the sparsity and the desired pattern in the f k domain are promoted by iterative soft thresholding and adaptive weighting data in the f k domain are transformed to polar coordinates and then low pass filtered along the radial axis to generate the nonlinear weight frat interpolates data that are randomly sampled and aliased i e where the minimum distance between adjacent traces is greater than the nyquist sampling interval a conventional approach to solving this problem is to apply a cascade of two procedures first a sparsity based method such as projection onto convex sets

a logic to reason about likelihood abstract we present a logic ll which uses a modal operator l to help capture the notion of being likely despite the fact that likelihood is not assigned quantitative values through probabilities ll captures many of the properties of likelihood in an intuitively appealing way we give a possible worlds style semantics to ll and using standard techniques of modal logic we give a complete axiomatization for ll and show that satisfiability of ll formulas can be decided in exponential time we discuss how the logic might be used in areas such as medical diagnosis where decision making in the face of uncertainties is crucial we conclude by using ll to give a formal proof of correctness of some aspects of a protocol for exchanging secrets

multidimensional de aliased cadzow reconstruction of seismic records abstractwe tested a strategy for beyond alias interpolation of seismic data using cadzow reconstruction the strategy enables cadzow reconstruction to be used for interpolation of regularly sampled seismic records first in the frequency space f x domain we generated a hankel matrix from the spatial samples of the low frequencies to perform interpolation at a given frequency the spatial samples were interlaced with zero samples and another hankel matrix was generated from the zero interlaced data next the rank reduced eigen decomposition of the hankel matrix at low frequencies was used for beyond alias preconditioning of the hankel matrix at a given frequency finally antidiagonal averaging of the conditioned hankel matrix produced the final interpolated data in addition the multidimensional extension of the proposed algorithm was explained the proposed method provides a unifying thread between reduced rank cadzow reconstruction and beyond alias f x prediction error interpolation synthetic an

static output feedback controllers stability and convexity the main objective of this paper is to solve the following stabilizing output feedback control problem given matrices a b sub 2 c sub 2 with appropriate dimensions find if one exists a static output feedback gain l such that the closed loop matrix a b sub 2 lc sub 2 is asymptotically stable it is known that the existence of l is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs hence this paper provides a new sufficient but not necessary condition for the solvability of the above stabilizing output feedback control problem as a natural extension we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index some examples borrowed from the literature are solved to illustrate the theoretical results

estimation of the causal effect of a time varying exposure on the marginal mean of a repeated binary outcome abstract we provide sufficient conditions for estimating from longitudinal data the causal effect of a time dependent exposure or treatment on the marginal probability of response for a dichotomous outcome we then show how one can estimate this effect under these conditions using the g computation algorithm of robins we also derive the conditions under which some current approaches to the analysis of longitudinal data such as the generalized estimating equations gee approach of zeger and liang the feedback model techniques of liang and zeger and within subject conditional methods can provide valid tests and estimates of causal effects we use our methods to estimate the causal effect of maternal stress on the marginal probability of a child s illness from the mothers stress and children s morbidity data and compare our results with those previously obtained by zeger and liang using a gee approach

bagged one to one matching for efficient and robust treatment effect estimation observational studies present challenges due to bias from imbalance in baseline confounders one to one matching oom a popular cohort construction technique for observational studies reduces bias and provides a compelling basis for inference but generally leads to at least some loss of efficiency due to the exclusion of potentially informative subjects we introduce the bagged one to one matching boom estimator which combines the bias reducing properties of oom with the variance reducing properties of bootstrap aggregation bagging we describe the boom algorithm in detail provide r code for its implementation and investigate its performance in simulation studies and a case study in the simulation studies under different types of model misspecification we compare the boom estimator s performance in terms of mean squared error bias variance accuracy of standard error estimation and coverage of nominal 95 confidence intervals to that of oom and to that of ordinary least squares estimation inverse probability weighting and targeted maximum likelihood estimation all on the full unmatched cohort in our simulations the boom estimator achieves as much bias reduction as the estimator based on oom while having much lower variance in all of the settings examined in the simulations the boom s mean squared error is comparable to or better than that of the comparison methods in the case study boom yields estimates similar to those from the established methods with narrower 95 confidence intervals

some approximate evidence factors in observational studies an observational study or nonrandomized experiment has exact evidence factors if it permits several statistically independent tests of the same null hypothesis h0 of no treatment effect where these several tests depend upon different assumptions about bias from nonrandom treatment assignment in an observational study we are typically uncertain about what assumptions truly describe treatment assignment if independent tests each reject h0 and if each of these tests is valid under assumptions about treatment assignment that would invalidate the others then rejection of h0 does not depend upon the truth of any one of these assumptions although exact evidence factors do exist the requirement of exact independence may limit the class of test statistics in ways that reduce pitman efficiency and design sensitivity so one might wish to be free of these limitations a much larger class of statistics permits approximate evidence factors which are not independent but which preserve some of the important con

signed directed acyclic graphs for causal inference formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality specifically the notions of a monotonic effect a weak monotonic effect and a signed edge are introduced results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables the incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables it is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data is missing on confounding variables

interpolation and extrapolation using a high resolution discrete fourier transform we present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra this approach minimizes a cost function derived from bayes theorem the method is suitable for line spectra since a long tailed distribution is used to model the prior distribution of spectral amplitudes since the data themselves are used as constraints phase information can also be recovered and used to extend the data outside the original window the objective function is formulated in terms of hyperparameters that control the degree of fit and spectral resolution noise rejection can also be achieved by truncating the number of iterations spectral resolution and extrapolation length are controlled by a single parameter when this parameter is large compared with the spectral powers the algorithm leads to zero extrapolation of the data and the estimated fourier transform yields the periodogram when the data are sampled at a constant rate the algorithm uses one levinson recursion per iteration for irregular sampling the algorithm uses one cholesky decomposition per iteration the performance of the algorithm is illustrated with three different problems that arise in geophysical data 1 harmonic retrieval from a time series contaminated with noise 2 linear event detection from a finite aperture array of receivers 3 interpolation extrapolation of gapped data the performance of the algorithm as a spectral estimator is tested with the kay and marple 1981 data set

on sampling functions and fourier reconstruction methods random sampling can lead to algorithms in which the fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band limited conversely regular sampling often hampers the fourier data recovery methods however 2d signals that are band limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well sampled signal and aliasing artifacts this concept can be easily extended to higher dimensions and used to define potential strategies for acquisition guided fourier reconstruction the wavenumber response of various sampling operators is derived and sampling conditions for optimal fourier reconstruction are investigated using synthetic and real data examples

lmi relaxations for reduced order robust cal h _ infty control of continuous time uncertain linear systems this technical note is concerned with the problem of reduced order robust h dynamic output feedback control design for uncertain continuous time linear systems the uncertain time invariant parameters belong to a polytopic domain and affect all the system matrices the search for a reduced order controller is converted in a problem of static output feedback control design for an augmented system to solve the problem a two stage linear matrix inequality lmi procedure is proposed at the first step a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined this parameter dependent state feedback controller is used at the second stage which synthesizes the robust parameter independent output feedback h dynamic controller a homogeneous polynomially parameter dependent lyapunov function of arbitrary degree is used to assess closed loop stability with a prescribed h attenuation level as illustrated by numerical examples the proposed method provides better results than other lmi based conditions from the literature

tensor completion based on nuclear norm minimization for 5d seismic data reconstruction abstractmany standard seismic data processing and imaging techniques require regularly sampled data prestack seismic data are multidimensional signals that can be represented via low rank fourth order tensors in the frequency space f x domain we propose to adopt tensor completion strategies to recover unrecorded observations and to improve the signal to noise ratio of prestack seismic volumes tensor completion can be posed as an inverse problem and solved by minimizing a convex objective function the objective function contains two terms a data misfit and a nuclear norm the data misfit measures the proximity of the reconstructed seismic data to the observations the nuclear norm constraints the reconstructed data to be a low rank tensor in essence we solve the prestack seismic reconstruction problem via low rank tensor completion the cost function of the problem is minimized using the alternating direction method of multipliers we present synthetic examples to illustrate the behavior of the al

minimal sufficient causation and directed acyclic graphs notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs this in turn provides a clear theoretical link between two major conceptualizations of causality one counterfactual based and the other based on a more mechanistic understanding of causation the theory developed can be used to draw conclusions about the sign of the conditional covariances among variables

doubly misspecified models estimation bias arising from local model uncertainty and incomplete data has been studied by copas eguchi 2005 under the assumption of a correctly specified marginal model we extend the approach to allow additional local uncertainty in the assumed marginal model arguing that this is almost unavoidable for nonlinear problems we present a general bias analysis and sensitivity procedure for such doubly misspecified models and illustrate the breadth of application through three examples logistic regression with a missing confounder measurement error for binary responses and survival analysis with frailty we show that a double the variance rule is not conservative under double misspecification the ideas are brought together in a meta analysis of studies of rehabilitation rates for juvenile offenders copyright 2012 oxford university press

a fast reduced rank interpolation method for prestack seismic volumes that depend on four spatial dimensions rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization we present a fast version of cadzow reduced rank reconstruction method cadzow reconstruction is implemented by embedding 4d spatial data into a level four block toeplitz matrix rank reduction of this matrix via the lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise the computational cost of the lanczos bidiagonalization is dominated by the cost of multiplying a level four block toeplitz matrix by a vector this is efficiently implemented via the 4d fast fourier transform the proposed algorithm significantly decreases the computational cost of rank reduction methods for multidimensional seismic data denoising and reconstruction synthetic and field prestack data examples are used to examine the effectiveness of the proposed method

a bayesian finite mixture of bivariate regression model for causal mediation analyses building on the work of schwartz et al joint bayesian analysis of birthweight and censored gestational age using finite mixture models in statistics in medicine we propose a bayesian finite mixture of bivariate regression model for causal mediation analyses using an identifiability condition within each component of the mixture we express the natural direct and indirect effects of the exposure on the outcome as functions of the component specific regression coefficients on the basis of simulated data we examine the behavior of the model for estimating these effects in situations where the associations between exposure mediator and outcome are confounded or not additionally we demonstrate that this mixture model can be used to account for heterogeneity arising through unmeasured binary or categorical mediator outcome confounders considering gestational age as a potential mediator we then illustrate our mediation mixture model to estimate the natural direct and indirect effects of exposure to inhaled corticosteroids during pregnancy on birthweight using a cohort of asthmatic women from the province of quebec canada

low order controller design for siso systems using coprime factors and lmi this paper develops a low order controller design method for linear continuous time invariant single input single output systems requiring only the solution of a convex optimization problem the technique integrates several well known results in control theory an important step is the use of coprime factors so that based on strictly positive real functions feedback stabilization using low order controllers becomes a zero placement problem which is convex from this result we develop algorithms to solve two optimal control problems

seismic trace interpolation in the f x y domain seismic trace interpolation is implemented as a 2 d x y spatial prediction performed separately on each frequency f slice this so called f x y domain trace interpolation method is based on the relation that the linear prediction lp operator estimated at a given frequency may be used to predict data at a higher frequency but a smaller trace spacing the relationship originally given for thef x domain trace interpolation is successfully extended to the f x y domain the extension is achieved by masking the data samples selectively from the input frequency slice to design the lp operators two interpolation algorithms using the full step and the fractional step predictions respectively are developed both methods use an all azimuth prediction in the x y domain but the fractional step prediction method is computationally more efficient while the interpolation method can be applied to a common offset cube of 3 d seismic it can also be applied to 2 d seismic traces for prestack data processing sy

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size