bayesian analysis of dichotomous quantal response models abstract qualitative response models qrm s are analyzed from the bayesian point of view using diffuse and informative prior distributions exact finite sample bayesian and large sample bayesian and non bayesian estimation results are compared in addition the paper provides 1 plots and discussion of the properties of likelihood functions for qrm s 2 posterior distributions for logit models derivatives and elasticities 3 bayesian prediction procedures for qrm s 4 new estimates for the median and other fractiles of the logistic distribution 5 posterior odds ratios for model selection problems and 6 comparisons of two alternative monte carlo numerical integration procedures it is concluded that asymptotic approximations are not accurate for small to moderate sized samples even when only a single input variable is used and that operational bayesian methods are available for providing both exact small sample and large sample approximate inferences for drm s

some aspects of polya tree distributions for statistical modelling the definition and elementary properties of polya tree distributions are reviewed two theorems are presented showing that polya trees can be constructed to concentrate arbitrarily closely about any desired pdf and that polya tree priors can put positive mass in every relative entropy neighborhood of every positive density with finite entropy thereby satisfying a consistency condition such theorems are false for dirichlet processes models are constructed combining partially specified polya trees with other information such as monotonicity or unimodality it is shown how to compute bounds on posterior expectations over the class of all priors with the given specifications a numerical example is given a theorem of diaconis and freedman about dirichlet processes is generalized to polya trees allowing polya trees to be the models for errors in regression problems finally empirical bayes models using dirichlet processes are generalized to polya trees an example from berry and christensen is reanalyzed with a polya tree model

model averaging based on leave subject out cross validation this paper develops a frequentist model averaging method based on the leave subject out cross validation this method is applicable not only to averaging longitudinal data models but also to averaging time series models which can have heteroscedastic errors the resulting model averaging estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors both simulation study and empirical example show the superiority of the proposed estimators over their competitors

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

on the optimality of certainty equivalence for event triggered control systems digital control design is commonly constrained to time triggered control systems with periodic sampling the emergence of more and more complex and distributed systems urges the development of advanced triggering schemes that utilize communication computation and energy resources more efficiently this technical note addresses the question whether certainty equivalence is optimal for an event triggered control system with resource constraints the problem setting is an extension of the stochastic linear quadratic system framework where the joint design of the control law and the event triggering law minimizing a common objective is considered three differing variants are studied that reflect the resource constraints a penalty term to acquire the resource a limitation on the number of resource acquisitions and a constraint on the average number of resource acquisitions by reformulating the underlying optimization problem a characterization of the optimal control law is possible this characterization shows that the certainty equivalence controller is optimal for all three optimization problems

model averaged double robust estimation researchers estimating causal effects are increasingly challenged with decisions on how to best control for a potentially high dimensional set of confounders typically a single propensity score model is chosen and used to adjust for confounding while the uncertainty surrounding which covariates to include into the propensity score model is often ignored and failure to include even one important confounder will results in bias we propose a practical and generalizable approach that overcomes the limitations described above through the use of model averaging we develop and evaluate this approach in the context of double robust estimation more specifically we introduce the model averaged double robust ma dr estimators which account for model uncertainty in both the propensity score and outcome model through the use of model averaging the ma dr estimators are defined as weighted averages of double robust estimators where each double robust estimator corresponds to a specific choice of the outcome model and the propensity score model the ma dr estimators extend the desirable double robustness property by achieving consistency under the much weaker assumption that either the true propensity score model or the true outcome model be within a specified possibly large class of models using simulation studies we also assessed small sample properties and found that ma dr estimators can reduce mean squared error substantially particularly when the set of potential confounders is large relative to the sample size we apply the methodology to estimate the average causal effect of temozolomide plus radiotherapy versus radiotherapy alone on one year survival in a cohort of 1887 medicare enrollees who were diagnosed with glioblastoma between june 2005 and december 2009

shrinkage for categorical regressors abstract this paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e g categorical regressors quasi experimental data or panel data models the loss function is penalized by adding weighted squared l 2 norm differences between group location parameters and informative first stage estimates under quadratic loss the penalized estimation problem has a simple interpretable closed form solution that nests methods established in the literature on ridge regression discretized support smoothing kernels and model averaging methods we derive risk optimal penalty parameters and propose a plug in approach for estimation the large sample properties are analyzed in an asymptotic local to zero framework by introducing a class of sequences for close and distant systems of locations that is sufficient for describing a large range of data generating processes we provide the asymptotic distributions of the shrinkage estimators under different penalization schemes the proposed plug in estimator uniformly dominates the ordinary least squares estimator in terms of asymptotic risk if the number of groups is larger than three monte carlo simulations reveal robust improvements over standard methods in finite samples real data examples of estimating time trends in a panel and a difference in differences study illustrate potential applications

on the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem for standard eigenvalue problems closed form expressions for the condition numbers of a multiple eigenvalue are known in particular they are uniformly 1 in the hermitian case and generally take different values in the non hermitian case we consider the generalized eigenvalue problem and identify the condition numbers our main result is that a multiple eigenvalue generally has multiple condition numbers even in the hermitian definite case the condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors

efficient estimation of the partly linear additive cox model the partly linear additive cox model is an extension of the linear cox model and allows flexible modeling of covariate effects semiparametrically we study asymptotic properties of the maximum partial likelihood estimator of this model with right censored data using polynomial splines we show that with a range of choices of the smoothing parameter the number of spline basis functions required for estimation of the nonparametric components the estimator of the finite dimensional regression parameter is root n consistent asymptotically normal and achieves the semiparametric information bound rates of convergence for the estimators of the nonparametric components are obtained they are comparable to the rates in nonparametric regression implementation of the estimation approach can be done easily and is illustrated by using a simulated example

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

inference after model selection typical modeling strategies involve model selection which has a significant effect on inference of estimated parameters common practice is to use a selected model ignoring uncertainty introduced by the process of model selection this could yield overoptimistic inferences resulting in false discovery in this article we develop a general methodology via optimal approximation for estimating the mean and variance of complex statistics that involve the process of model selection this allows us to make approximately unbiased inferences taking into account the selection process we examine the operating characteristics of the proposed methodology via asymptotic analyses and simulations these results show that the proposed methodology yields correct inferences and outperforms common alternatives

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

least squares model averaging this paper considers the problem of selection of weights for averaging across least squares estimates obtained from a set of models existing model average methods are based on exponential akaike information criterion aic and bayesian information criterion bic weights in distinction this paper proposes selecting the weights by minimizing a mallows criterion the latter an estimate of the average squared error from the model average fit we show that our new mallows model average mma estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators in a simulation experiment we show that the mma estimator compares favorably with those based on aic and bic weights the proof of the main result is an application of the work of li 1987

analyzing nonstationary spatial data using piecewise gaussian processes in many problems in geostatistics the response variable of interest is strongly related to the underlying geology of the spatial location in these situations there is often little correlation in the responses found in different rock strata so the underlying covariance structure shows sharp changes at the boundaries of the rock types conventional stationary and nonstationary spatial methods are inappropriate because they typically assume that the covariance between points is a smooth function of distance in this article we propose a generic method for the analysis of spatial data with sharp changes in the underlying covariance structure our method works by automatically decomposing the spatial domain into disjoint regions within which the process is assumed to be stationary but the data are assumed independent across regions uncertainty in the number of disjoint regions their shapes and the model within regions is dealt with in a fully bayesian fashion we illustrate our approach on a previously

bayes model averaging with selection of regressors when a number of distinct models contend for use in prediction the choice of a single model can offer rather unstable predictions in regression stochastic search variable selection with bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors here we look at bayes model averaging incorporating variable selection for prediction this offers similar mean square errors of prediction but with a vastly reduced predictor space this can greatly aid the interpretation of the model it also reduces the cost if measured variables have costs the development here uses decision theory in the context of the multivariate general linear model in passing this reduced predictor space bayes model averaging is contrasted with single model approximations a fast algorithm for updating regressions in the markov chain monte carlo searches for posterior inference is developed allowing many more variables than observations to be contemplated we discuss the merits of absolute rather than proportionate shrinkage in regression especially when there are more variables than observations the methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution

james stein type estimators in large samples with application to the least absolute deviations estimator we explore the extension of james stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity instead of shrinking a base estimator toward a fixed point we shrink it toward a data dependent point we provide an analytic expression for the asymptotic risk and bias of james stein type estimators shrunk toward a data dependent point and prove that they have smaller asymptotic risk than the base estimator shrinking an estimator toward a data dependent point turns out to be equivalent to combining two random variables using the james stein rule we propose a general combination scheme that includes random combination the james stein combination and the usual nonrandom combination as special cases as an example we apply our method to combine the least absolute deviations estimator and the least squares estimator our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are dr

inference for deterministic simulation models the bayesian melding approach abstract deterministic simulation models are used in many areas of science engineering and policy making typically these are complex models that attempt to capture underlying mechanisms in considerable detail and they have many user specified inputs the inputs are often specified by some form of trial and error approach in which plausible values are postulated the corresponding outputs inspected and the inputs modified until plausible outputs are obtained here we address the issue of more formal inference for such models a probabilistic approach called bayesian synthesis was shown to suffer from the borel paradox according to which the results can depend on the parameterization of the model we propose a modified approach called bayesian melding which takes into full account information and uncertainty about both inputs and outputs to the model while avoiding the borel paradox this is done by recognizing the existence of two priors one implicit and one explicit on each input and output

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

a statistical concept to assess the uncertainty in bayesian model weights and its impact on model ranking bayesian model averaging bma ranks the plausibility of alternative conceptual models according to bayes theorem a prior belief about each model s adequacy is updated to a posterior model probability based on the skill to reproduce observed data and on the principle of parsimony the posterior model probabilities are then used as model weights for model ranking selection or averaging despite the statistically rigorous bma procedure model weights can become uncertain quantities due to measurement noise in the calibration data set or due to uncertainty in model input uncertain weights may in turn compromise the reliability of bma results we present a new statistical concept to investigate this weighting uncertainty and thus to assess the significance of model weights and the confidence in model ranking our concept is to resample the uncertain input or output data and then to analyze the induced variability in model weights in the special case of weighting uncertainty due to measurement noise in the calibration data set we interpret statistics of bayesian model evidence to assess the distance of a model s performance from the theoretical upper limit to illustrate our suggested approach we investigate the reliability of soil plant model selection following up on a study by wohling et al 2015 results show that the bma routine should be equipped with our suggested upgrade to 1 reveal the significant but otherwise undetected impact of measurement noise on model ranking results and 2 to decide whether the considered set of models should be extended with better performing alternatives

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

adaptive regression by mixing adaptation over different procedures is of practical importance different procedures perform well under different conditions in many practical situations it is rather hard to assess which conditions are approximately satisfied so as to identify the best procedure for the data at hand thus automatic adaptation over various scenarios is desirable a practically feasible method named adaptive regression by mixing arm is proposed to convexly combine general candidate regression procedures under mild conditions the resulting estimator is theoretically shown to perform optimally in rates of convergence without knowing which of the original procedures work the best simulations are conducted in several settings including comparing a parametric model with nonparametric alternatives comparing a neural network with a projection pursuit in multidimensional regression and combining bandwidths in kernel regression the results clearly support the theoretical property of arm the arm algorithm assigns we

frequentist model average estimators the traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance without acknowledging the additional uncertainty introduced by model selection this often means underreporting of variability and too optimistic confidence intervals we build a general large sample likelihood apparatus in which limiting distributions and risk properties of estimators post selection as well as of model average estimators are precisely described also explicitly taking modeling bias into account this allows a drastic reduction in complexity as competing model averaging schemes may be developed discussed and compared inside a statistical prototype experiment where only a few crucial quantities matter in particular we offer a frequentist view on bayesian model averaging methods and give a link to generalized ridge estimators our work also leads to new model selection criteria the methods are illustrated with real data applications

first order spectral perturbation theory of square singular matrix pencils abstract let h a 0 a 1 be a square singular matrix pencil and let 0 c be an eventually multiple eigenvalue of h it is known that arbitrarily small perturbations of h can move the eigenvalues of h anywhere in the complex plane i e the eigenvalues are discontinuous functions of the entries of a 0 and a 1 therefore it is not possible to develop an eigenvalue perturbation theory for arbitrary perturbations of h however if the perturbations are restricted to lie in an appropriate set then the eigenvalues change continuously we prove that this set of perturbations is generic i e it contains almost all pencils and present sufficient conditions for a pencil to be in this set in addition for perturbations in this set explicit first order perturbation expansions of 0 are obtained in terms of the perturbation pencil and bases of the left and right null spaces of h 0 both for simple and multiple eigenvalues infinite eigenvalues are also considered finally information on the eigenvectors of the generically regular perturbed pencil is presented we obtain as corollaries results for regular pencils that are also new

semiparametric model averaging prediction for dichotomous response abstract model averaging has attracted abundant attentions in the past decades as it emerges as an impressive forecasting device in econometrics social sciences and medicine so far most developed model averaging methods focus only on either parametric models or nonparametric models with a continuous response in this paper we propose a semiparametric model averaging prediction smap method for a dichotomous response the idea is to approximate the unknown score function by a linear combination of one dimensional marginal score functions the weight parameters involved in the approximation are obtained by first smoothing the nonparametric marginal scores and then applying the parametric model averaging via a maximum likelihood estimation the proposed smap provides greater flexibility than parametric models while being more stable than a fully nonparametric approach theoretical properties are investigated in two practical scenarios i covariates are conditionally independent given the response and ii the conditional independence assumption does not hold in the first scenario we show that smap puts weight one to the true model and hence the model averaging estimators are consistent in the second scenario in which a true model may not exist smap is shown to be asymptotically optimal in the sense that its kullback leibler loss is asymptotically identical to that of the best but infeasible model averaging estimator empirical evidences from simulation studies and a real data analysis are presented to support and illustrate our methods

stochastic complexity and modeling on demontre un theoreme fondamental qui donne une borne inferieure pour la longueur de code et donc pour les erreurs de prediction on definit les notions d information a priori et d information utile dans les donnees

model averaging by jackknife criterion in models with dependent data abstract the past decade witnessed a literature on model averaging by frequentist methods for the most part the asymptotic optimality of various existing frequentist model averaging estimators has been established under i i d errors recently hansen and racine hansen b e racine j 2012 jackknife model averaging journal of econometrics 167 38 46 developed a jackknife model averaging jma estimator which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors in this paper we broaden hansen and racine s scope of analysis to encompass models with i a non diagonal error covariance structure and ii lagged dependent variables thus allowing for dependent data we show that under these set ups the jma estimator is asymptotically optimal by a criterion equivalent to that used by hansen and racine a monte carlo study demonstrates the finite sample performance of the jma estimator in a variety of model settings

bayesian inference in a simultaneous equation model with limited dependent variables abstract this paper develops a bayesian approach for inference in a simultaneous equation model with limited dependent variables sldv by employing a combination of gibbs sampling and data augmentation we can draw from the exact posterior of this sldv model and avoid direct evaluation of the non trivial likelihood function a by product from our posterior simulation is the savage dickey density ratio which is used for computing the bayes factor the practicality and efficiency of the proposed method are illustrated through an example in corporate finance

semiparametric regression for clustered data using generalized estimating equations we consider estimation in a semiparametric generalized linear model for clustered data using estimating equations our results apply to the case where the number of observations per cluster is finite whereas the number of clusters is large the mean of the outcome variable is of the form g xt t where g is a link function x and t are covariates is an unknown parameter vector and t is an unknown smooth function kernel estimating equations proposed previously in the literature are used to estimate the infinite dimensional nonparametric function t and a profile based estimating equation is used to estimate the finite dimensional parameter vector we show that for clustered data this conventional profile kernel method often fails to yield a n consistent estimator of along with appropriate inference unless working independence is assumed or t is artificially undersmoothed in which case asymptotic inference is possible to gain insight into these results we derive the se

cluster synchronization of complex networks via event triggered strategy under stochastic sampling abstract this paper is concerned with the issue of mean square cluster synchronization of non identical nodes connected by a directed network suppose that the nodes possess nonlinear dynamics and split into several clusters then an event triggered control scheme is proposed for synchronization based on the information from stochastic sampling meanwhile an equilibrium is considered to be the synchronization state or the virtual leader for each cluster which can apply pinning control to the following nodes assume that a spanning tree exists in the subgraph consisting of the nodes belonging to the same cluster and the corresponding virtual leader and the instants for updating controllers are determined by the given event triggered strategy then some sufficient conditions for cluster synchronization are presented according to the lyapunov stability theory and linear matrix inequality technique finally a specific numerical example is shown to demonstrate the effectiveness of the theoretical results

the hierarchical logistic regression model for multilevel analysis abstract a hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable the group structure is defined by the presence of micro observations embedded within contexts macro observations and the specification is at both of these levels at the first micro level the usual logistic regression model is defined for each context the same regressors are used in each context but the micro regression coefficients are free to vary over contexts at the second level the micro coefficients are treated as functions of macro regressors an empirical bayes estimation procedure is proposed for estimating the micro and macro coefficients explicit formulas are provided that are computationally feasible for large scale data analyses these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within and between macro equation error variability the methodology is applied to world fertility survey data

model selection for estimating treatment effects summary researchers often believe that a treatment s effect on a response may be heterogeneous with respect to certain baseline covariates this is an important premise of personalized medicine several methods for estimating heterogeneous treatment effects have been proposed however little attention has been given to the problem of choosing between estimators of treatment effects models that best estimate the regression function may not be best for estimating the effect of a treatment therefore there is a need for model selection methods that are targeted to treatment effect estimation we demonstrate an application of the focused information criterion in this setting and develop a treatment effect cross validation aimed at minimizing treatment effect estimation errors theoretically treatment effect cross validation has a model selection consistency property when the data splitting ratio is properly chosen practically treatment effect cross validation has the flexibility to compare different types of models we illustrate the methods by using simulation studies and data from a clinical trial comparing treatments of patients with human immunodeficiency virus

maximum likelihood bayesian averaging of spatial variability models in unsaturated fractured tuff 1 hydrologic analyses typically rely on a single conceptual mathematical model yet hydrologic environments are open and complex rendering them prone to multiple interpretations and mathematical descriptions adopting only one of these may lead to statistical bias and underestimation of uncertainty bayesian model averaging bma hoeting et al 1999 provides an optimal way to combine the predictions of several competing models and to assess their joint predictive uncertainty however it tends to be computationally demanding and relies heavily on prior information about model parameters neuman 2002 2003 proposed a maximum likelihood version mlbma of bma to render it computationally feasible and to allow dealing with cases where reliable prior information is lacking we apply mlbma to seven alternative variogram models of log air permeability data from single hole pneumatic injection tests in six boreholes at the apache leap research site alrs in central arizona unbiased ml estimates of variogram and drift parameters are obtained using adjoint state maximum likelihood cross validation samper and neuman 1989a in conjunction with universal kriging and generalized least squares standard information criteria provide an ambiguous ranking of the models which does not justify selecting one of them and discarding all others as is commonly done in practice instead we eliminate some of the models based on their negligibly small posterior probabilities and use the rest to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes we then average these four projections and associated kriging variances using the posterior probability of each model as weight finally we cross validate the results by eliminating from consideration all data from one borehole at a time repeating the above process and comparing the predictive capability of mlbma with that of each individual model we find that mlbma is superior to any individual geostatistical model of log permeability among those we consider at the alrs

model averaging and weight choice in linear mixed effects models this article studies model averaging for linear mixed effects models we establish an unbiased estimator of the squared risk for the model averaging and use the estimator as a criterion for choosing weights the resulting model average estimator is proved to be asymptotically optimal under some regularity conditions simulation experiments show it is superior or comparable to estimators based on the final models selected by the commonly used methods and some existing averaging procedures the proposed procedure is applied to data from an aids clinic trial

multivariate logit copula model with an application to dental data applications of copulas for multivariate continuous data abound but there are only a few that treat multivariate binary data in the present paper we model multivariate binary data based on copulas using mixtures of max infinitely divisible copulas introduced by joe and hu j multivar anal 1996 57 2 240 265 when applying copulas to binary data the marginal distributions also contribute to the dependence measures we propose the use of covariate information in the copula parameters to obtain a direct effect of a covariate on dependence to deal with model uncertainty due to selecting among several candidate models we use a model averaging technique we apply the model to data from the signal tandmobiel dental study and in particular to four binary responses that refer to caries experience in the mandibular and maxillary left and right molars we aim to model kendall s tau associations between them and examine how covariate information affects these associations we found that there are systematically larger associations between the two mandibular and the two maxillary molars using covariates to model these associations more closely we found that the systematic fluoride and age of the children affect the associations note that such relationships could not have been revealed by methods that focus on the marginal models copyright 2008 john wiley sons ltd

optimal model averaging estimation for generalized linear models and generalized linear mixed effects models abstractconsidering model averaging estimation in generalized linear models we propose a weight choice criterion based on the kullback leibler kl loss with a penalty term this criterion is different from that for continuous observations in principle but reduces to the mallows criterion in the situation we prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions we further extend our concern to the generalized linear mixed effects model framework and establish associated theory numerical experiments illustrate that the proposed method is promising

on the harm that ignoring pretesting can cause in econometrics the same data set is typically used to select the model and to estimate the parameters in the selected model in applied econometrics practice however one typically acts as if the model had been given a priori thus ignoring the fact that the estimators are in fact pretest estimators hence one assumes incorrectly that the estimator is unbiased and that the reported variance conditional on the selected model is equal to its unconditional variance in this paper we nd the unconditional rst and second moments of the pretest estimator in fact of a more general estimator the wals estimator taking full account of the fact that model selection and estimation are an integrated procedure and show that the error in not reporting the correct moments can be large we also show that this error can vary substantially between di2erent model selection procedures finally we ask how the error increases when the number of auxiliary regressors increases

additive partial linear models with measurement errors we consider statistical inference for additive partial linear models when the linear covariate is measured with error we propose attenuation to correction and simex estimators of the parameter of interest it is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing this is an advantage of our estimator over existing backfitting based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component be root n consistent this feature stems from a decrease of the bias of the resulting estimator which is appropriately derived using a profile procedure a similar characteristic in semiparametric partially linear models was obtained by wang et al 2005 we also discuss the asymptotics of the proposed simex approach finite sample performance of the proposed estimators is assessed by simulation experiments the proposed methods are applied to a dataset from a semen study

eigenvalues pseudospectrum and structured perturbations we investigate the behavior of eigenvalues under structured perturbations we show that for many common structures such as complex symmetric toeplitz symmetric toeplitz circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations and prove similar results for real perturbations an exception are complex skewsymmetric matrices we also investigate componentwise complex and real perturbations here hermitian and skew hermitian matrices are exceptional for real perturbations furthermore we characterize the structured complex and real pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual unstructured pseudospectrum

stability of multivariable fractional polynomial models with selection of variables and transformations a bootstrap investigation sauerbrei and royston have recently described an algorithm based on fractional polynomials for the simultaneous selection of variables and of suitable transformations for continuous predictors in a multivariable regression setting they illustrated the approach by analyses of two breast cancer data sets here we extend their work by considering how to assess possible instability in such multivariable fractional polynomial models we first apply the algorithm repeatedly in many bootstrap replicates we then use log linear models to investigate dependencies among the inclusion fractions for each predictor and among the simplified classes of fractional polynomial function chosen in the bootstrap samples to further evaluate the results we define measures of instability based on a decomposition of the variability of the bootstrap selected functions in relation to a reference function from the original model for each data set we are able to identify large reasonably stable subsets of the bootstrap replications in which the functional forms of the predictors appear fairly stable despite the considerable flexibility of the family of fractional polynomials and the consequent risk of overfitting when several variables are considered we conclude that the multivariable selection algorithm can find stable models

sensitivity analysis and assessment of prior model probabilities in mlbma with application to unsaturated fractured tuff 1 previous application of maximum likelihood bayesian model averaging mlbma neuman 2002 2003 to alternative variogram models of log air permeability data in fractured tuff has demonstrated its effectiveness in quantifying conceptual model uncertainty and enhancing predictive capability ye et al 2004 a question remained how best to ascribe prior probabilities to competing models in this paper we examine the extent to which lead statistics of posterior log permeability predictions are sensitive to prior probabilities of seven corresponding variogram models we then explore the feasibility of quantifying prior model probabilities by 1 maximizing shannon s entropy h shannon 1948 subject to constraints reflecting a single analyst s or a group of analysts prior perception about how plausible each alternative model or a group of models is relative to others and 2 selecting a posteriori the most likely among such maxima corresponding to alternative prior perceptions of various analysts or groups of analysts another way to select among alternative prior model probability sets which however is not guaranteed to yield optimum predictive performance though it did so in our example and would therefore not be our preferred option is a minimum maximum approach according to which one selects a priori the set corresponding to the smallest value of maximum entropy whereas maximizing h subject to the prior perception of a single analyst or group maximizes the potential for further information gain through conditioning selecting the smallest among such maxima gives preference to the most informed prior perception among those of several analysts or groups we use the same variogram models and log permeability data as ye et al 2004 to demonstrate that our proposed approach yields the least amount of posterior entropy residual uncertainty after conditioning and enhances predictive model performance as compared to 1 the noninformative neutral case in which all prior model probabilities are set equal to each other and 2 an informed case that nevertheless violates the principle of parsimony

a copula based model for multivariate non normal longitudinal data analysis of a dose titration safety study on a new antidepressant a new model for multivariate non normal longitudinal data is proposed in a first step each longitudinal series of data corresponding to a given response is modelled separately using a copula to relate the marginal distributions of the response at each time of observation in a second step at each observation time the conditional on the past distributions of each response are related using another copula describing the relationship between the corresponding variables note that there is no need to consider the same family of distributions for these response variables the technique is illustrated in a dose titration safety study on a new antidepressant the haemodynamic effect on diastolic blood pressure systolic blood pressure and heart rate is studied these three responses are measured repeatedly over time on ten healthy volunteers during the dose escalation the available covariates are sex and the concentration of drug in the plasma at time of measurement

calibration based empirical probability probability forecasts for a sequence of uncertain events may be compared with the outcomes of those events by means of a natural criterion of empirical validity calibration it is shown that any two sequences of forecasts which both meet this criterion must be in asymptotic agreement these agreed values can then be considered as correct objective probability forecasts for the particular sequence of outcome results obtained however the objective forecasts vary with the extent of the information taken into account when they are formulated we thus obtain a general theory of empirical probability relative to an information base this theory does not require that such probabilities be interpreted in terms of repeated trials of the same event some implications of this theory are discussed

parsimonious model averaging with a diverging number of parameters model averaging generally provides better predictions than model selection but the existing model averaging methods cannot lead to parsimonious models parsimony is an especially important propert

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

on inclusion driven learning of bayesian networks two or more bayesian network structures are markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies therefore the search space of bayesian network structures may be organized in equivalence classes where each of them represents a different set of conditional independencies the collection of sets of conditional independencies obeys a partial order the so called inclusion order this paper discusses in depth the role that the inclusion order plays in learning the structure of bayesian networks in particular this role involves the way a learning algorithm traverses the search space we introduce a condition for traversal operators the inclusion boundary condition which when it is satisfied guarantees that the search strategy can avoid local maxima this is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph and the length of the sample is unbounded the previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the markov chain monte carlo method we carry out a set of experiments with synthetic and real world data that show empirically the benefit of striving for the inclusion order when learning bayesian networks from data

focused information criterion and model averaging for generalized additive partial linear models we study model selection and model averaging in generalized additive partial linear models gaplms polynomial spline is used to approximate nonparametric functions the corresponding estimators of the linear parameters are shown to be asymptotically normal we then develop a focused information criterion fic and a frequentist model average fma estimator on the basis of the quasi likelihood principle and examine theoretical properties of the fic and fma the major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability simulation experiments have provided evidence of the superiority of the proposed procedures the approach is further applied to a real world data example

eigenvalue condition numbers zero structured versus traditional we discuss questions of eigenvalue conditioning we study in some depth relationships between the classical theory of conditioning and the theory of the zero structured conditioning and we derive from the existing theory formulae for the mathematical objects involved then an algorithm to compare the zero structured individual condition numbers of a set of simple eigenvalues with the traditional ones is presented numerical tests are reported to highlight how the algorithm provides interesting information about eigenvalue sensitivity when the perturbations in the matrix have an arbitrarily assigned zero structure patterned matrices toeplitz and hankel will be investigated in a forthcoming paper eigenvalue patterned condition numbers toeplitz and hankel cases tech rep 3 mathematics department university of rome la sapienza 2005

model selection an integral part of inference we argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data we consider different philosophies for achieving this goal and suggest strategies for data analysis we illustrate our methods through three examples the first is a poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates the second is a line transect data set for which different models yield substantially different estimates of abundance the third is a simulated example in which truth is known

bayesian predictions of reynolds averaged navier stokes uncertainties using maximum a posteriori estimates computational fluid dynamics analyses of high reynolds number flows mostly rely on the reynolds averaged navier stokes equations the associated closure models are based on multiple simplifying ass

multimodel bayesian analysis of groundwater data worth we explore the way in which uncertain descriptions of aquifer heterogeneity and groundwater flow impact one s ability to assess the worth of collecting additional data we do so on the basis of maximum likelihood bayesian model averaging mlbma by accounting jointly for uncertainties in geostatistical and flow model structures and parameter hydraulic conductivity as well as system state hydraulic head estimates given uncertain measurements of one or both variables previous description of our approach was limited to geostatistical models based solely on hydraulic conductivity data here we implement the approach on a synthetic example of steady state flow in a two dimensional random log hydraulic conductivity field with and without recharge by embedding an inverse stochastic moment solution of groundwater flow in mlbma a moment equations based geostatistical inversion method is utilized to circumvent the need for computationally expensive numerical monte carlo simulations the approach is compatible with either deterministic or stochastic flow models and consistent with modern statistical methods of parameter estimation admitting but not requiring prior information about the parameters it allows but does not require approximating lead predictive statistical moments of system states by linearization while updating model posterior probabilities and parameter estimates on the basis of potential new data both before and after such data are actually collected

nonpathological sampling of switched linear systems we study the conservation of observability after sampling for the class of switched linear systems with no inputs and switching in the measurement equation only using van der waerden s theorem a classic result from ramsey theory we give a sufficient condition on the components of the resulting discretized switched linear system for it to be observable under arbitrary switching sequences this preliminary result then enables us to extend the kalman bertram criterion for nonpathological sampling to the class of switched linear systems under consideration

bayesian multivariate hierarchical transformation models for roc analysis a bayesian multivariate hierarchical transformation model bmhtm is developed for receiver operating characteristic roc curve analysis based on clustered continuous diagnostic outcome data with covariates two special features of this model are that it incorporates non linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed the mean variance and transformation components are all modelled parametrically enabling a wide range of inferences the general framework is illustrated by focusing on two problems 1 analysis of the diagnostic accuracy of a covariate dependent univariate test outcome requiring a box cox transformation within each cluster to map the test outcomes to a common family of distributions 2 development of an optimal composite diagnostic test using multivariate clustered outcome data in the second problem the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome the proposed methodology is illustrated on prostate cancer biopsy data from a multi centre clinical trial

quasi likelihood estimation in semiparametric models abstract suppose the expected value of a response variable y may be written h x t where x and t are covariates each of which may be vector valued is an unknown parameter vector is an unknown smooth function and h is a known function in this article we outline a method for estimating the parameter of this type of semiparametric model using a quasi likelihood function algorithms for computing the estimates are given and the asymptotic distribution theory for the estimators is developed the generalization of this approach to the case in which y is a multivariate response is also considered the methodology is illustrated on two data sets and the results of a small monte carlo study are presented

a bayesian method for combining results from several binomial experiments abstract the problem of combining information related to i binomial experiments each having a distinct probability of success i is considered instead of using a standard exchangeable prior for 1 i we propose a more flexible distribution that takes into account various degrees of similarity among the i s using ideas developed by malec and sedransk we consider a partition g of the experiments and take the i s belonging to the same partition subset to be exchangeable and the i s belonging to distinct subsets to be independent next we perform bayesian inference on conditional on g of course one is typically uncertain about which partition to use and so a prior distribution is assigned on a set of plausible partitions g the final inference on is obtained by combining the conditional inferences according to the posterior distribution of g the methodology adopted in this article offers a wide flexibility in structuring the dependence among the i s this allows the

distribution theory of the least squares averaging estimator this paper derives the limiting distributions of least squares averaging estimators for linear regression models in a local asymptotic framework we show that the averaging estimators with fixed weights are asymptotically normal and then develop a plug in averaging estimator that minimizes the sample analog of the asymptotic mean squared error we investigate the focused information criterion claeskens and hjort 2003 the plug in averaging estimator the mallows model averaging estimator hansen 2007 and the jackknife model averaging estimator hansen and racine 2012 we find that the asymptotic distributions of averaging estimators with data dependent weights are nonstandard and cannot be approximated by simulation to address this issue we propose a simple procedure to construct valid confidence intervals with improved coverage probability monte carlo simulations show that the plug in averaging estimator generally has smaller expected squared error than other existing model averaging methods and the coverage probability of proposed confidence intervals achieves the nominal level as an empirical illustration the proposed methodology is applied to cross country growth regressions

assessment and propagation of model uncertainty in most examples of inference and prediction the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model m that formalizes assumptions about how x and y are related m will typically have two parts structural assumptions s such as the form of the link function and the choice of error distribution in a generalized linear model and parameters whose meaning is specific to a given choice of s it is common in statistical theory and practice to acknowledge parametric uncertainty about given a particular assumed structure s it is less common to acknowledge structural uncertainty about s itself a widely used approach involves enlisting the aid of x to specify a plausible single best choice s for s and then proceeding as if s were known to be correct in general this approach fails to assess and propagate structural uncertainty fully and may lead to miscalibrated uncertainty assessments about y given x when miscalibration occurs it will often result in understatement of inferential or predictive uncertainty about y leading to inaccurate scientific summaries and overconfident decisions that do not incorporate sufficient hedging against uncertainty in this paper i discuss a bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible by virtue of recent computational advances and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the us space shuttle

malmem model averaging in linear measurement error models we develop model averaging estimation in the linear regression model where some covariates are subject to measurement error the absence of the true covariates in this framework makes the calculation of the standard residual based loss function impossible we take advantage of the explicit form of the parameter estimators and construct a weight choice criterion it is asymptotically equivalent to the unknown model average estimator minimizing the loss function when the true model is not included in the set of candidate models the method achieves optimality in terms of minimizing the relative loss whereas when the true model is included the method estimates the model parameter with root n rate simulation results in comparison with existing bayesian information criterion and akaike information criterion model selection and model averaging methods strongly favour our model averaging method the method is applied to a study on health

the cost of generalizing logistic regression abstract binary response regression models in which the link function is a family defined by one or more unknown shape parameters are considered detailed attention is given to the two single parameter families proposed by aranda ordaz 1981 that incorporate the logistic linear and complementary log log link functions as special cases one model is a symmetric family of alternatives to the logistic shape and the second model is an asymmetric family the increase in variance of quantities of interest due to the addition of an extra parameter is calculated using asymptotic methods this inflation in variance is interpreted as the cost of adding an additional parameter to the model in considering the seriousness of this cost the reduction in bias due to the estimation of the additional parameter should also be taken into account three quantities of interest predicted probabilities for a fixed value of the explanatory variable predicted value of the explanatory variable to obtain a specific probability

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

first order structured perturbation theory for multiple zero eigenvalues of skew adjoint matrices abstract given a matrix belonging to some class of structured matrices we consider the question of comparing the sensitivity of its eigenvalues under two different kinds of perturbations either unstructured i e arbitrary or structured i e those belonging to the same class of matrices as the unperturbed one in a previous paper kressner et al 2009 13 the authors compared the structured and unstructured condition numbers of possibly multiple eigenvalues for several different matrix and pencil structures only one case was left out of the analysis namely the one where the asymptotic order of perturbed eigenvalues under structured perturbations is different from the asymptotic order under unstructured ones this is precisely the case we consider in the present paper given a matrix which is skew adjoint with respect to a symmetric scalar product and has a zero eigenvalue with a certain jordan structure first order expansions are obtained for the perturbed eigenvalues under structured perturbation as well as bounds on the structured condition number similar results are obtained for structured perturbations of symmetric skew symmetric and palindromic matrix pencils

robust bayes and empirical bayes analysis with _ epsilon contaminated priors on considere deux directions dans l analyse bayesienne robuste la premiere consiste a determiner l etendue des probabilites a posteriori d un ensemble la seconde consiste a selectionner une bonne distribution a priori

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

a note on structured pseudospectra in this note we study the notion of structured pseudospectra we prove that for toeplitz circulant hankel and symmetric structures the structured pseudospectrum equals the unstructured pseudospectrum we show that this is false for hermitian and skew hermitian structures we generalize the result to pseudospectra of matrix polynomials indeed we prove that the structured pseudospectrum equals the unstructured pseudospectrum for matrix polynomials with toeplitz circulant hankel and symmetric structures we conclude by giving a formula for structured pseudospectra of real matrix polynomials the particular type of perturbations used for these pseudospectra arise in control theory

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

self triggering under state independent disturbances this note extends the prior work in l2 stability of self triggered feedback systems where the next task release time and finishing time are predicted based on the sampled states a self triggering scheme is proposed which relaxes the assumption in the prior work that the magnitude of the process noise is bounded by a linear function of the norm of the system state we show that the sample periods generated by this scheme are always greater than a positive constant we also provide state based deadlines for delays and propose a way that may enlarge those deadlines without breaking l2 stability

information theory and mixing least squares regressions for gaussian regression we develop and analyze methods for combining estimators from various models for squared error loss an unbiased estimator of the risk of the mixture of general estimators is developed special attention is given to the case that the component estimators are least squares projections into arbitrary linear subspaces such as those spanned by subsets of explanatory variables in a given design we relate the unbiased estimate of the risk of the mixture estimator to estimates of the risks achieved by the components this results in simple and accurate bounds on the risk and its estimate in the form of sharp and exact oracle inequalities that is without advance knowledge of which model is best the resulting performance is comparable to or perhaps even superior to what is achieved by the best of the individual models furthermore in the case that the unknown parameter has a sparse representation our mixture estimator adapts to the underlying sparsity simulations show that the performance of these mixture estimators is better than that of a related model selection estimator which picks a model with the highest weight also the connection between our mixtures with bayes procedures is discussed

can one estimate the conditional distribution of post model selection estimators we consider the problem of estimating the conditional distribution of a post model selection estimator where the conditioning is on the selected model the notion of a post model selection estimator here refers to the combined procedure resulting from first selecting a model e g by a model selection criterion such as aic or by a hypothesis testing procedure and then estimating the parameters in the selected model e g by least squares or maximum likelihood all based on the same data set we show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically in particular we show that no estimator for this distribution can be uniformly consistent not even locally this follows as a corollary to local minimax lower bounds on the performance of estimators for this distribution similar impossibility results are also obtained for the conditional distribution of linear functions e g predictors of the post model selection estimator

a numerically stable structure preserving method for computing the eigenvalues of real hamiltonian or symplectic pencils a new method is presented for the numerical computation of the generalized eigenvalues of real hamiltonian or symplectic pencils and matrices the method is numerically backward stable and preserves the structure i e hamiltonian or symplectic in the case of a hamiltonian matrix the method is closely related to the square reduced method of van loan but in contrast to that method which may suffer from a loss of accuracy of order sqrt varepsilon where varepsilon is the machine precision the new method computes the eigenvalues to full possible accuracy

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

clinical heterogeneity in random effect meta analysis between study boundary estimate problem random effect meta analysis is commonly applied to estimate overall effects with unexplained heterogeneity across studies however standard methods including restricted maximum likelihood ml or reml frequently produce near zero estimates for between study variance parameters consequently these methods are reduced to simple and unrealistic fixed effect models resulting in an ignorance of the substantial clinical heterogeneity and sometimes leading to incorrect conclusions to solve the boundary estimate problem we propose 1 an adjusted maximum likelihood method for the between study variance that maximizes a likelihood defined as a product of a standard likelihood and a gaussian class of adjustment factor and 2 a framework using sensitivity analysis by developing a new criterion to check for the occurrence of the boundary estimate although the adjustment introduces bias to the overall effects to ensure strictly positive estimates of the between study variance when the number of studies k is small the bias asymptotically approaches zero resulting in the same estimates derived from the reml method moreover the adjusted maximum likelihood estimator of the between study variance is consistent for large k and interestingly the reml method and our method are equivalent in terms of mean squared error criterion up to o k 1 we illustrate our approach with a motivating example to examine the controversial result of a meta analysis for 24 randomized controlled trials of human albumin numerical evaluations show that our approach produces no boundary estimates but similar synthesized results with the standard maximum likelihood methods as those produced by conventional methods especially with a small number of studies

predictive rans simulations via bayesian model scenario averaging the turbulence closure model is the dominant source of error in most reynolds averaged navier stokes simulations yet no reliable estimators for this error component currently exist here we develop a stochastic a posteriori error estimate calibrated to specific classes of flow it is based on variability in model closure coefficients across multiple flow scenarios for multiple closure models the variability is estimated using bayesian calibration against experimental data for each scenario and bayesian model scenario averaging bmsa is used to collate the resulting posteriors to obtain a stochastic estimate of a quantity of interest qoi in an unmeasured prediction scenario the scenario probabilities in bmsa are chosen using a sensor which automatically weights those scenarios in the calibration set which are similar to the prediction scenario the methodology is applied to the class of turbulent boundary layers subject to various pressure gradients for all considered prediction scenarios the standard deviation of the stochastic estimate is consistent with the measurement ground truth furthermore the mean of the estimate is more consistently accurate than the individual model predictions

semiparametric regression in likelihood based models abstract a weighted likelihood is used to estimate the parameters in a semiparametric model involving two covariates and allowing an association between the covariates the development is for arbitrary but specified densities of the observations the estimators are consistent and asymptotically normal hypothesis testing of the parametric component can be performed using a wald test simulations and analysis of data with bernoulli observations demonstrate the estimators application speckman developed kernel estimators where the conditional density of the observations is normal with p parametric covariates speckman s estimators and the new estimators are asymptotically equivalent with the bias of speckman s estimators being smaller as an example we study the relationship between a binary response indicating the occurrence of an intraoperative cardiac complication icc in vascular surgery patients and two risk factors duration of the operation or and asa score which is an evaluation of the patien

self triggered output feedback control of linear plants in the presence of unknown disturbances this note addresses the control of linear time invariant plants in the presence of unknown bounded disturbances when the output of the plant is only measured at sampling instants determined by a self triggered strategy in a self triggered scenario the controller is allowed to choose when the next sampling time should occur and does so based on available measurements and on a priori knowledge about the plant the proposed solution is a cascade interconnection of a state observer and a self triggered state feedback controller we focus our attention on state observers that are only updated at sampling times and that are input to state stable iss with respect to disturbances due to the cascade structure of the closed loop system and the fact that self triggered control strategies presented in the literature are iss with respect to observation errors and exogenous disturbances we conclude that the closed loop is rendered iss with respect to exogenous disturbances

the dimensionality reduction principle for generalized additive models soit x y une paire de variables aleatoires telles que x x 1 x j s etende sur c 0 1 j la distribution conditionnelle de y etant donne x x est supposee appartenir a une famille exponentielle appropriee ayant pour parametre r f x denote la dependance de vis a vis de x et f l approximation additive de f ayant la log vraisemblance esperee maximum possible

parameterization and bayesian modeling progress in statistical computation often leads to advances in statistical modeling for example it is surprisingly common that an existing model is reparameterized solely for computational purposes but then this new configuration motivates a new family of models that is useful in applied statistics one reason why this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood in a bayesian framework however a transformation of parameters typically suggests a new family of prior distributions we discuss examples in censored and truncated data mixture modeling multivariate imputation stochastic processes and multilevel models