model inconsistency illustrated by the cox proportional hazards model we consider problems involving the comparison of two or more treatments where we have the opportunity to adjust for relevant covariates either conditionally in a regression model or implicitly in repeated measures data for example in crossover trials it is seen that for data arising from non normal distributions there is the possibility that models adjusting for covariates and those not adjusting for covariates will be inconsistent that is at most one of the models can be valid alternatively even if conditional and unconditional models are valid parameters in each model may have different interpretations we note that this presents difficulties for the specification and interpretation of the analysis it is also clear that model validation is critical specific attention is paid to survival data analysed by the cox proportional hazards model

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

internal deformation of lie algebroids and symplectic realizations given a lie algebroid and a bundle over its base which is endowed with a localizable poisson structure and a flat connection we construct an extended bundle whose dual is endowed with an almost poisson structure that is a quadratic poisson structure when a certain compatibility property is satisfied this new formalism on lie algebroids describes systems with internal degrees of freedom

semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

non parametric analysis of covariance for confirmatory randomized clinical trials to evaluate dose response relationships in confirmatory randomized clinical trials that are designed to compare multiple doses of a test treatment with a control group and with one another there are often statistical issues regarding compound hypotheses and multiple comparisons which need to be considered in most cases the analysis plan needs a clear specification for the proposed order for conducting statistical tests or for managing the overall significance level which statistical methods will be used and whether adjustment for covariates will be performed there are several benefits of specifying non parametric analysis of covariance ancova for performing the primary confirmatory analyses only minimal assumptions are needed beyond randomization in the study design whereas regression model based methods have assumptions about model fit for which departures may require modifications that are incompatible with a fully prespecified analysis plan non parametric methods provide traditionally expected results of ancova namely a typically small adjustment to the estimate for a treatment comparison so as to account for random imbalance of covariates between treatment groups and variance reduction for this estimate when covariates are strongly correlated with the response of interest the application of non parametric ancova is illustrated for two randomized clinical trials the first has a 3 x 4 factorial response surface design for the comparison of 12 treatments that is combinations of three doses of one drug and four doses of a second drug for change in blood pressure and the second example addresses the comparison of three doses of test treatment and placebo for time to disease progression this clinical trial has comparisons among treatments made for a dichotomous criterion wilcoxon rank scores and averages of cumulative survival rates in each example the non parametric covariance method provides variance reduction relative to its unadjusted counterpart

the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

on the differential geometry of the euler lagrange equations and the inverse problem of lagrangian dynamics the conditions for a system of second order differential equations to be derivable from a lagrangian the conditions of self adjointness in the terminology of santilli 1978 and others are related in the time independent case to the differential geometry of the tangent bundle of configuration space these conditions are simply expressed in terms of the horizontal distribution which is associated with any vector field representing a system of second order differential equations necessary and sufficient conditions for such a vector field to be derivable from a lagrangian may be stated as the existence of a two form with certain properties it is interesting that it is a deduction not an assumption that this two form is closed and thus defines a symplectic structure some other differential geometric properties of euler lagrange second order differential equations are described

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

contractions nijenhuis and saletan tensors for general algebraic structures we study generalizations in many directions of the contraction procedure for lie algebras introduced by saletan we consider products of an arbitrary nature not necessarily lie brackets and we generalize to infinite dimension considering a modification of the approach by nijenhuis tensors to bilinear operations on sections of finite dimensional vector bundles we apply our general procedure to lie algebras lie algebroids and poisson brackets we also present results on contractions of n ary products and coproducts

graphical models for statistical inference and data assimilation in data assimilation for a system which evolves in time one combines past and current observations with a model of the dynamics of the system in order to improve the simulation of the system as well as any future predictions about it from a statistical point of view this process can be regarded as estimating many random variables which are related both spatially and temporally given observations of some of these variables typically corresponding to times past we require estimates of several others typically corresponding to future times graphical models have emerged as an efiective formalism for assisting in these types of inference tasks particularly for large numbers of random variables graphical models provide a means of representing dependency structure among the variables and can provide both intuition and e ciency in estimation and other inference computations we provide an overview and introduction to graphical models and describe how they can be used to represent statistical dependency and how the resulting structure can be used to organize computation the relation between statistical inference using graphical models and optimal sequential estimation algorithms such as kalman flltering is discussed we then give several additional examples of how graphical models can be applied to climate dynamics speciflcally estimation using multi resolution models of large scale data sets such as satellite imagery and learning hidden markov models to capture rainfall patterns in space and time

brief paper estimation of the disturbance structure from data using semidefinite programming and optimal weighting designing a state estimator for a linear state space model requires knowledge of the characteristics of the disturbances entering the states and the measurements in odelson b j rajamani m r rawlings j b 2006 a new autocovariance least squares method for estimating noise covariances automatica 42 2 303 308 the correlations between the innovations data were used to form a least squares problem to determine the covariances for the disturbances in this paper we present new and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates we also formulate the optimal weighting to be used in the least squares objective in the covariance estimation problem to ensure minimum variance in the estimates a modification to the above technique is then presented to estimate the number of independent stochastic disturbances affecting the states this minimum number of disturbances is usually unknown and must be determined from data a semidefinite optimization problem is solved to estimate the number of independent disturbances entering the system and their covariances

an optimal design problem in rhythmometry a trigonometric regression model is assumed for a problem involving circadian rhythm exhibited by peak expiratory flow experimental designs are sought with a view to estimating a particular nonlinear function of the parameters both optimal and nonoptimal but more practicable designs are derived and their relative efficiencies are established

survival analysis with time varying regression effects using a tree based approach nonproportional hazards often arise in survival analysis as is evident in the data from the international non hodgkin s lymphoma prognostic factors project a tree based method to handle such survival data is developed for the assessment and estimation of time dependent regression effects under a cox type model the tree method approximates the time varying regression effects as piecewise constants and is designed to estimate change points in the regression parameters a fast algorithm that relies on maximized score statistics is used in recursive segmentation of the time axis following the segmentation a pruning algorithm with optimal properties similar to those of classification and regression trees cart is used to determine a sparse segmentation bootstrap resampling is used in correcting for overoptimism due to split point optimization the piecewise constant model is often more suitable for clinical interpretation of the regression parameters than the more flexible spline models the utility of the algorithm is shown on the lymphoma data where we further develop the published international risk index into a time varying risk index for non hodgkin s lymphoma

unobserved covariates in the two sample comparison of survival times a maximin efficiency robust test in analysing a clinical trial with the logrank test the hazards between the two groups are usually assumed to be proportional nevertheless this hypothesis is no longer valid with unobserved covariates as a consequence there is a loss of power of the logrank test for testing the null hypothesis h 0 of no treatment effect we propose a test suited for taking into account unobserved covariates the proposed approach is based on a proportional hazard frailty model whereby the omitted covariates are considered as an unobserved frailty variable the procedure is as follows in a first step the weighted logrank test optimal for testing h 0 against a general proportional hazard frailty model is obtained and its specialization for a gamma frailty variable is derived in a second step the proposed test is obtained by combining the maximin efficiency robustness principle and the gamma frailty distribution properties simulation studies investigate the power properties of the test for different frailty distributions a breast cancer clinical trial is analysed as an example the proposed test might be recommended rather than the logrank for practical situations in which one expects heterogeneity related to omitted covariates

probabilistic index models summary we present a semiparametric statistical model for the probabilistic index which can be defined as p y y a where y and y a are independent random response variables associated with covariate patterns x and x a respectively a link function defines the relationship between the probabilistic index and a linear predictor asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory the model is illustrated with several examples and the estimation theory is validated in a simulation study

the impact of covariate adjustment at randomization and analysis for binary outcomes understanding differences between superiority and noninferiority trials the question of when to adjust for important prognostic covariates often arises in the design of clinical trials and there remain various opinions on whether to adjust during both randomization and analysis at randomization alone or at analysis alone furthermore little is known about the impact of covariate adjustment in the context of noninferiority ni designs the current simulation based research explores this issue in the ni setting as compared with the typical superiority setting by assessing the differential impact on power type i error and bias in the treatment estimate as well as its standard error in the context of logistic regression under both simple and covariate adjusted permuted block randomization algorithms in both the superiority and ni settings failure to adjust for covariates that influence outcome in the analysis phase regardless of prior adjustment at randomization results in treatment estimates that are biased toward zero with standard errors that are deflated however as no treatment difference is approached under the null hypothesis in superiority and under the alternative in ni this results in decreased power and nominal or conservative deflated type i error in the context of superiority but inflated power and type i error under ni results from the simulation study suggest that regardless of the use of the covariate in randomization it is appropriate to adjust for important prognostic covariates in analysis as this yields nearly unbiased estimates of treatment as well as nominal type i error

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

effect of frailty on marginal regression estimates in survival analysis unexplained heterogeneity in univariate survival data and association in multivariate survival can both be modelled by the inclusion of frailty effects this paper investigates the consequences of ignoring frailty in analysis fitting misspecified cox proportional hazards models to the marginal distributions regression coefficients are biased towards 0 by an amount which depends in magnitude on the variability of the frailty terms and the form of frailty distribution the bias is reduced when censoring is present fitted marginal survival curves can also differ substantially from the true marginals

observability of discretized partial differential equations the situation in which one cannot solve a numerical initial value problem for lack of complete initial data is arising ever more frequently in applied sciences and engineering the procedure of estimating the evolving solution by inserting incomplete data into a numerical model as they become available at different instants of time is called data assimilation or filtering we show that if data generated by a linear system of partial differential equations pde are inserted properly then complete observability of the discrete numerical model is necessary and sufficient for asymptotic stability of the data assimilation process this complete observability means that if the data had been generated by the discrete model rather than by the pde system then the data would define the state of the model uniquely after some finite time simple observability criteria for discretizations of linear constant coefficient pde on periodic domains are formulated in terms of properties of the symbol of the numerical schem

a new reduced order adaptive filter for state estimation in high dimensional systems a simple reduced order adaptive filter optimal in the sense of minimum prediction error is proposed for estimating the state of high dimensional systems in which the process and observation noise statistics are unknown it is shown that implementation of this adaptive filter requires the solution of only two linear difference equations the dimensions of which are the dimensions of the full and reduced states respectively and that no solution of either an algebraic riccati equation or a lyapunov equation is needed in addition substantial gain in computer memory and cpu time is obtained by parametrization of the filter gain in the form of the product of two matrices one of which is a prescribed projection from the reduced space onto the full space a twin experiment on data assimilation with a quasi geostrophic ocean model shows the efficiency of the proposed approach

adaptive error covariances estimation methods for ensemble kalman filters this paper presents a computationally fast algorithm for estimating both the system and observation noise covariances of nonlinear dynamics that can be used in an ensemble kalman filtering framework the new method is a modification of belanger s recursive method to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large when we use only product of innovation processes up to one lag the computational cost is indeed comparable to a recently proposed method by berry sauer s however our method is more flexible since it allows for using information from product of innovation processes of more than one lag extensive numerical comparisons between the proposed method and both the original belanger s and berry sauer s schemes are shown in various examples ranging from low dimensional linear and nonlinear systems of sdes and 40 dimensional stochastically forced lorenz 96 model our numerical results suggest that the proposed scheme is as accurate as the original belanger s scheme on low dimensional problems and has a wider range of more accurate estimates compared to berry sauer s method on l 96 example

reduction techniques for infinite dimensional hamiltonian systems some ideas and applications in the language of tensor analysis on differentiable manifolds we present a reduction method of integrability structures and apply it to recover some well known hierarchies of integrable nonlinear evolution equations

experimental design for binary data abstract models for binary data are usually such that the information matrix depends on the unknown parameters thus the standard criteria for optimality in regression experiments cannot be applied without modification methods of going around this difficulty include the use of initial point estimates sequential methods and bayesian analysis this article is mainly concerned with the robustness and the number of design points for methods involving initial estimates and for sequential methods in a small number of stages a final section discusses the criterion of constant information for models involving one or two parameters and summarizes recent results in this field

algebraic constructions in the category of lie algebroids the aim of this paper is to give the first general and abstract treatment of the algebraic properties of lie algebroids the concept of lie algebroid was introduced in 1967 by pradines ls as the basic infinitesimal invariant of a differentiable groupoid the construction of the lie algebroid of a differentiable groupoid is a direct generalization of the construction of the lie algebra of a lie group and 183 described a full lie theory for differentiable groupoids and lie algebroids encompassing many phenomena in the foundations of differential geometry a more detailed account and further references are given in 13 however at this stage the algebraic properties of lie algebroids were not pursued in 13 iii section 2 iv section 11 one of us gave a fairly detailed account of the abstract algebra of lie algebroids over a fixed base lie algebroids are vector bundles with several additional structures and a category of lie algebroids on a given base and morphisms which preserve that base has properties similar to those of the category of lie algebras using this algebra it was demonstrated in 13 that the lie theory of a category of locally trivial differentiable lie groupoids over a fixed base and the corresponding category of transitive lie algebroids over that base is coextensive with the standard theory of connections in principal bundles we now propose to show that the lie functor from the category of all differentiable groupoids over arbitrary bases and arbitrary smooth morphisms to the category of all lie algebroids preserves the basic algebraic constructions known to be possible in the category of differentiable groupoids the main work is to give abstract formulations of the corresponding lie algebroid concepts the groupoid results with which we

a hierarchical bayes ensemble kalman filter abstract a new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested the filter relies on the conditional gaussian distribution of the state given the model error and predictability error covariance matrices the latter are treated as random matrices and updated in a hierarchical bayes scheme along with the state the hyper prior distribution of the covariance matrices is assumed to be inverse wishart the new hierarchical bayes ensemble filter hbef assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances the actual probability distribution of the ensemble members is allowed to be different from the true one an approximation that leads to a practicable analysis algorithm is proposed the new filter is studied in numerical experiments with a doubly stochastic one variable model of truth the model permits the assessment of the variance of the truth and the true filtering error variance at each time instance the hbef is shown to outperform the enkf and the henkf by myrseth and omre 2010 in a wide range of filtering regimes in terms of performance of its primary and secondary filters

tangent bundle geometry lagrangian dynamics various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined and the results applied to time independent lagrangian dynamics it is shown that a certain type 1 1 tensor field which is part of the intrinsic geometry of a tangent bundle being a tensorial equivalent of the projection map of tangent vectors plays a role in lagrangian theory scarcely less important than that of the canonical one form on a cotangent bundle in hamiltonian theory recent results in lagrangian theory are interpreted from this new viewpoint

erosion of regression effect in a survival study lack of persistence or erosion of the regression effect is an alternative to proportional hazards of particular interest in many medical applications such a departure from proportional hazards is often the most likely direction in which the model may be inadequate questions such as is the effect of treatment only transitory or to what extent does an initially measured prognostic variable maintain its impact frequently arise in the context of a simple changepoint model we propose a test of the null hypothesis of proportional hazards against the specific alternative of erosion of the regression effect the particular changepoint model used can be viewed as a first approximation to a more complex reality an approximation that enables us to avoid specifically modeling the functional form that any erosion might take practical guidelines for carrying out the test are provided the approach is illustrated in the context of a study on risk factors for breast cancer survival

lagrangian submanifolds and dynamics on lie algebroids in some previous papers a geometric description of lagrangian mechanics on lie algebroids has been developed in this topical review we give a hamiltonian description of mechanics on lie algebroids in addition we introduce the notion of a lagrangian submanifold of a symplectic lie algebroid and we prove that the lagrangian hamiltonian dynamics on lie algebroids may be described in terms of lagrangian submanifolds of symplectic lie algebroids the lagrangian hamiltonian formalism on lie algebroids permits us to deal with lagrangian hamiltonian functions not defined necessarily on tangent cotangent bundles thus we may apply our results to the projection of lagrangian hamiltonian functions which are invariant under the action of a symmetry lie group as a consequence we obtain that lagrange poincare hamilton poincare equations are the euler lagrange hamilton equations associated with the corresponding atiyah algebroid moreover we prove that lagrange poincare hamilton poincare equations are the local equations defining certain lagrangian submanifolds of symplectic atiyah algebroids

linear theory for filtering nonlinear multiscale systems with model error in this paper we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes in particular the analysis assumes the availability of continuous time noisy observations of all components of the slow variables mathematically this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure in particular we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables given noisy observation of the slow variables alone from the mathematical analysis we learn that for a continuous time linear model with gaussian noise there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed moreover these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system and as a consequence they can be estimated offline from the equilibrium statistics of the true signal by examining a nonlinear test model we show that the linear theory extends in this non gaussian nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model however when the stochastic parametrization model is inappropriate parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa this finding is based on analytical and numerical results on our nonlinear test model and the two layer lorenz 96 model finally even when the correct stochastic ansatz is given it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates in numerical experiments on the two layer lorenz 96 model we find that the parameters estimated online as part of a filtering procedure simultaneously produce accurate filtering and equilibrium statistical prediction in contrast an offline estimation technique based on a linear regression which fits the parameters to a training dataset without using the filter yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed this finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline

design of measurement difference autocovariance method for estimation of process and measurement noise covariances abstract the paper deals with the estimation of the process and measurement noise covariance matrices of a system described by the linear time varying state space model in particular the stress is laid on the correlation methods and a novel method the measurement difference autocovariance method is designed the proposed method is based on the statistical analysis of an augmented measurement prediction error leading to a system of linear matrix equations for the elements of the noise covariance matrices compared to other correlation methods the proposed method provides unbiased estimates even for a finite number of measurements the theoretical results are discussed and illustrated in a numerical example

tangent lie algebroids this paper shows that a lie algebroid structure on a smooth vector bundle a to pi over q gives rise to a lie algebroid structure on the bundle ta to t pi over tq called the tangent lie algebroid the analysis uses global arguments a lie algebroid a is equivalent to a certain poisson structure on a and the tangent bundle of any poisson manifold has a tangent poisson structure the tangent poisson structure on ta is then dualized to produce the tangent lie algebroid structure on ta local calculations are used and formulae for local brackets are given

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

effect of misspecification of regression models in the analysis of survival data the accelerated life and proportional hazards families of models are widely used in the analysis of survival data we examine the question if interest lies in the qualitative effect on failure of various explanatory variables how critical is the choice of model family in assessing the relative importance of the explanatory variables we consider small effects when censoring is independent of the explanatory variables to first order the regression parameters are proportional under the alternative models this is not true when the censoring varies appreciably with the explanatory variables some higherorder theory is examined for the special case of the two sample problem

efficient design of experiments in the monod model summary estimation and experimental design in a non linear regression model that is used in microbiology are studied the monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics water research pharmacokinetics and plant physiology it is proved that least squares estimates are asymptotically unbiased and normally distributed the asymptotic covariance matrix of the estimator is the basis for the construction of efficient designs of experiments in particular locally d e and c optimal designs are determined and their properties are studied theoretically and by simulation if certain intervals for the non linear parameters can be specified locally optimal designs can be constructed which are robust with respect to a misspecification of the initial parameters and which allow efficient parameter estimation parameter variances can be decreased by a factor of 2 by simply sampling at optimal times during the experiment

a distributional model for repeated failure time measurements summary a standard model for repeated measurements is based on the multivariate normal distribution with equicorrelated variables a corresponding analysis is developed for weibull failure times the resulting distribution has some attractive properties for practical application to multivariate failure times

an efficient algorithm for estimating noise covariances in distributed systems we present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems such systems arise typically by discretizing distributed parameter systems and their size renders computational efficiency a major consideration our adaptive filtering algorithm is based on the ideas of belanger and is algebraically equivalent to his algorithm the earlier algorithm however has computational complexity proportional to p6 where p is the number of observations of the system state while the new algorithm has complexity proportional to only p3 furthermore our formulation of noise covariance estimation as a secondary filter analogous to state estimation as a primary filter suggests several generalizations of the earlier algorithm the performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction

two stage residual inclusion for survival data and competing risks an instrumental variable approach with application to seer medicare linked data instrumental variable is an essential tool for addressing unmeasured confounding in observational studies two stage predictor substitution 2sps estimator and two stage residual inclusion 2sri are two commonly used approaches in applying instrumental variables recently 2sps was studied under the additive hazards model in the presence of competing risks of time to events data where linearity was assumed for the relationship between the treatment and the instrument variable this assumption may not be the most appropriate when we have binary treatments in this paper we consider the 2sri estimator under the additive hazards model for general survival data and in the presence of competing risks which allows generalized linear models for the relation between the treatment and the instrumental variable we derive the asymptotic properties including a closed form asymptotic variance estimate for the 2sri estimator we carry out numerical studies in finite samples and apply our methodology to the linked surveillance epidemiology and end results seer medicare database comparing radical prostatectomy versus conservative treatment in early stage prostate cancer patients

a multivariate distribution with weibull connections a simple form of multivariate distribution is defined which for certain parameter values has weibull marginals the distribution has a single parameter governing association between the variates which may be positive negative or zero the simple forms for marginal and conditional distributions hazard functions and densities make it attractive for practical application and interpretation

reduced models of atmospheric low frequency variability parameter estimation and comparative performance abstract low frequency variability lfv of the atmosphere refers to its behavior on time scales of 10 100 days longer than the life cycle of a mid latitude cyclone but shorter than a season this behavior is still poorly understood and hard to predict the present study compares various model reduction strategies that help in deriving simplified models of lfv three distinct strategies are applied here to reduce a fairly realistic high dimensional quasi geostrophic 3 level qg3 atmospheric model to lower dimensions i an empirical dynamical method which retains only a few components in the projection of the full qg3 model equations onto a specified basis and finds the linear deterministic and the stochastic corrections empirically as in selten 1995 5 ii a purely dynamics based technique employing the stochastic mode reduction strategy of majda et al 2001 62 and iii a purely empirical multi level regression procedure which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in kravtsov et al 2005 3 the empirical dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi level regression models the extended kalman filter was used for the parameter estimation overall the reduced models perform better when more statistical information is used in the model construction thus the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full qg3 model s lfv i e its autocorrelations and spectra as well as the nonlinear properties i e the persistent flow regimes that induce non gaussian features in the model s probability density function the empirical dynamical models capture the basic statistical properties of the full model s lfv such as the variance and integral correlation time scales of the leading lfv modes as well as some of the regime behavior features but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical dynamical models but do much less well on the full qg3 model s nonlinear dynamics these results are discussed in terms of their implications for a better understanding and prediction of lfv

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

an ensemble kalman filter for statistical estimation of physics constrained nonlinear regression models a central issue in contemporary science is the development of nonlinear data driven statistical dynamical models for time series of noisy partial observations from nature or a complex model it has been established recently that ad hoc quadratic multi level regression models can have finite time blow up of statistical solutions and or pathological behavior of their invariant measure recently a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior here a new finite ensemble kalman filtering algorithm is developed for estimating the state the linear and nonlinear model coefficients the model and the observation noise covariances from available partial noisy observations of the state several stringent tests and applications of the method are developed here in the most complex application the perfect model has 57 degrees of freedom involving a zonal east west jet two topographic rossby waves and 54 nonlinearly interacting rossby waves the perfect model has significant non gaussian statistics in the zonal jet with blocked and unblocked regimes and a non gaussian skewed distribution due to interaction with the other 56 modes we only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation numerically we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion including the skew non gaussian distribution and autocorrelation decay on the other hand a similar stochastic model with zero memory levels fails to capture the crucial non gaussian behavior of the zonal jet from the perfect 57 mode model