approximate maximum entropy joint feature inference consistent with arbitrary lower order probability constraints application to statistical classification we propose a new learning method for discrete space statistical classifiers similar to chow and liu 1968 and cheeseman 1983 we cast classification inference within the more general framework of estimating the joint probability mass function p m f for the feature vector class label pair cheeseman s proposal to build the maximum entropy me joint p m f consistent with general lower order probability constraints is in principle powerful allowing general dependencies between features however enormous learning complexity has severely limited the use of this approach alternative models such as bayesian networks bns require explicit determination of conditional independencies these may be difficult to assess given limited data here we propose an approximate me method which like previous methods incorporates general constraints while retaining quite tractable learning the new method restricts joint p m f support during learning to a small subset of the full feature space classification gains are realized over dependence trees tree augmented naive bayes networks bns trained by the kutato algorithm and multilayer perceptrons extensions to more general inference problems are indicated we also propose a novel exact inference method when there are several missing features

on the global well posedness theory for a class of pde models for criminal activity abstract we study a class of reaction advection diffusion system of partial differential equations which can be taken as basic models for criminal activity this class of models are based on routine activity theory and other theories such as the repeat and near repeat victimization effect and were first introduced in short et al 2008 11 in these models the criminal density is advected by a velocity field that depends on a scalar field which measures the appeal to commit a crime we refer to this scalar field as the attractiveness field we prove local well posedness of solutions for the general class of models furthermore we prove global well posedness of solutions to a fully parabolic system with a velocity field that depends logarithmically on the attractiveness field our final result is the global well posedness of solutions the fully parabolic system with velocity field that depends linearly on the attractiveness field for small initial mass

critic driven ensemble classification we develop new rules for combining the estimates obtained from each classifier in an ensemble in order to address problems involving multiple 2 classes a variety of techniques have been previously suggested including averaging probability estimates from each classifier as well as hard 0 1 voting schemes in this work we introduce the notion of a critic associated with each classifier whose objective is to predict the classifier s errors since the critic only tackles a two class problem its predictions are generally more reliable than those of the classifier and thus can be used as the basis for improved combination rules several such rules are suggested here while previous techniques are only effective when the individual classifier error rate is p 0 5 the new approach is successful as proved under an independence assumption even when this condition is violated in particular so long as p q 1 with q the critic s error rate more generally critic driven combining is found to achieve significant performance gains over alternative methods on a number of benchmark data sets we also propose a new analytical tool for modeling ensemble performance based on dependence between experts this approach is substantially more accurate than the analysis based on independence that is often used to justify ensemble methods

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

robust estimation of mean squared error of small area estimators abstract a well known model due to fay and herriot for estimating small area domain means i is considered given i s it is assumed that the survey estimators y i are independent with means i and known variances di i 1 t further the i s are assumed to be independent with means x i and unknown variance a where x i is a vector of benchmark variables related to i and is a vector of regression parameters an empirical best linear unbiased prediction eblup estimator or an empirical linear bayes estimator t i y of i is obtained it is shown that an estimator of mean squared error mse of t t y derived by prasad and rao under normality of i and y i given i is robust with respect to nonnormality of the i s specifically it is shown that the prasad rao estimator of mse is correct to terms of order o t 1 for large t assuming only certain moment conditions on the i s and normally distributed survey errors results of a simulation study on the accur

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

on measuring the variability of small area estimators under a basic area level model summary in this paper based on a basic area level model we obtain second order accurate approxi mations to the mean squared error of model based small area estimators using the fay herriot 1979 iterative method of estimating the model variance based on weighted residual sum of squares we also obtain mean squared error estimators unbiased to second order based on simulations we compare the finite sample performance of our mean squared error estimators with those based on method of moments maximum likelihood and residual maximum likelihood estimators of the model variance our results suggest that the fay herriot method performs better in terms of relative bias of mean squared error estimators than the other methods across different combinations of number of areas pattern of sampling variances and distribution of small area effects we also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second order unbiased for the mean squared error the posterior variance based on such a prior possesses both bayesian and frequentist interpretations

on parametric bootstrap methods for small area prediction summary the particularly wide range of applications of small area prediction e g in policy making decisions has meant that this topic has received substantial attention in recent years the problems of estimating mean squared predictive error of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers although existing methodology is still restricted to a narrow range of models to overcome this difficulty we develop new bootstrap based methods which are applicable in very general settings for constructing bias corrected estimators of mean squared error and for computing prediction regions unlike existing techniques which are based largely on taylor expansions our bias corrected mean squared error estimators do not require analytical calculation they also have the property that they are non negative our prediction intervals have a high degree of coverage accuracy o n 3 where n is the number of areas if double bootstrap methods are employed the techniques do not depend on the form of the small area estimator and are applicable to general two level small area models where the variables at either level can be discrete or continuous and in particular can be non normal most importantly the new methods are simple and easy to apply

nonparametric estimation of mean squared prediction error in nested error regression models nested error regression models are widely used for analyzing clustered data for example they are often applied to two stage sample surveys and in biology and econometrics prediction is usually the main goal of such analyses and mean squared prediction error is the main way in which prediction performance is measured in this paper we suggest a new approach to estimating mean squared prediction error we introduce a matched moment double bootstrap algorithm enabling the notorious underestimation of the naive mean squared error estimator to be substantially reduced our approach does not require specific assumptions about the distributions of errors additionally it is simple and easy to apply this is achieved through using monte carlo simulation to implicitly develop formulae which in a more conventional approach would be derived laboriously by mathematical arguments

a fast procedure for model search in multidimensional contingency tables summary a procedure to select the simplest acceptable models for a multidimensional contingency table is proposed it is based on two rules first that if a model is accepted then all models that include it are considered to be accepted and secondly that if a model is rejected then all its submodels are considered to be rejected two versions are described one for the class of graphical models and the other for the class of hierarchical log linear models application of both versions to a six dimensional table is illustrated the procedure can be regarded as an alternative to fitting all possible models made computationally feasible by application of the two rules it is a generalization of the procedure proposed by havr anek 1984 but is in many cases considerably faster

estimation of finite population domain means a model assisted empirical best prediction approach in this article we introduce a general methodology for producing a model assisted empirical best predictor ebp of a finite population domain mean using data from a complex survey our method improves on the commonly used design consistent survey estimator by using a suitable mixed model such a model combines information from related sources such as census and administrative data unlike a purely model based ebp the proposed model assisted ebp converges in probability to the customary design consistent estimator as the domain and sample sizes increase the convergence in probability is shown to hold with respect to the sampling design irrespective of the assumed mixed model a property commonly known as design consistency this property ensures robustness of the proposed predictor against possible model failures in addition the convergence in probability is shown to be valid with respect to the assumed mixed model model consistency a new mean squared prediction error mspe estimator is proposed

robust empirical bayes estimation of means from stratified samples abstract this article considers simultaneous estimation of means from several strata where each stratum contains a finite number of elements for example quite often estimates of annual incomes unemployment rates and so forth must be made simultaneously for many areas our results find application in small area estimation where very few samples are available from an individual area and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas ghosh and meeden 1986 considered empirical bayes estimation of the finite population mean assuming a normal superpopulation model their estimators generalize automatically when one estimates a vector of stratum means this article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations this is the so called posterior linearity property as described in ericson 1

small area estimation with uncertain random effects random effects models play an important role in model based small area estimation random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables in a recent article datta hall and mandal showed that if the random effects can be dispensed with via a suitable test then the model parameters and the small area means may be estimated with substantially higher accuracy the work of datta hall and mandal is most useful when the number of small areas m is moderately large for large m the null hypothesis of no random effects will likely be rejected rejection of the null hypothesis is usually caused by a few large residuals signifying a departure of the direct estimator from the synthetic regression estimator as a flexible alternative to the fay herriot random effects model and the approach in datta hall and mandal in this article we consider a mixture model for random effects it is reasonably expected that small areas wit

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

existence and asymptotics of solutions for a parabolic elliptic system with nonlinear no flux boundary conditions u x 0 u c 2 0 3 from which d x 0 is determined via la and 2b the systems of this type appear in the theory of semiconductors l 4 or in electrochemistry where u or rather ut u2 for more general systems involving several unknown functions u are the densities of charge carriers electrons holes ions and in groundwater flow problems 5 61 where u is the density of a fluid in a porous medium the parabolic equation la is flux conservative and the boundary condition 2a is the physically relevant no flux condition hence the total charge or mass according to the physical interpretation

stationary solutions of chemotaxis systems the keller segel model is a system of partial differential equations modelling a mutual attraction of amoebae caused by releasing a chemical substance chemotaxis this paper analyzes the stationary solutions of the system with general nonlinearities via bifurcation techniques and gives a criterion for bifurcation of stable nonhomogeneous aggregation patterns examples are discussed with various kinds of nonlinearities modelling the sensitivity of the chemotaxis response

bayesian versus frequentist measures of error in small area estimation summary this paper compares analytically and empirically the frequentist and bayesian measures of error in small area estimation the model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables when the variance components are known then under a uniform prior for the regression coefficients and normality of the error terms the frequentist and the bayesian approaches yield the same predictors and prediction mean squared errors mses defined accordingly when the variance components are unknown it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors so that the resulting empirical predictors remain the same under the two approaches the use of this paradigm requires however modifications to the expressions of the prediction mse to account for the extra variability induced by the need to estimate the variance components the main focus of this paper is to review and compare the modifications to prediction mses proposed in the literature under the two approaches with special emphasis on the orders of the bias of the resulting approximations to the true mses some new approximations based on monte carlo simulation are also proposed and compared with the existing methods the advantage of these approximations is their simplicity and generality finite sample frequentist properties of the various methods are explored by a simulation study the main conclusions of this study are that the use of second order bias corrections generally yields better results in terms of the bias of the mse approximations and the coverage properties of confidence intervals for the small area means the bayesian methods are found to have good frequentist properties but they can be inferior to the frequentist methods the second order approximations under both approaches have however larger variances than the corresponding first order approximations which in most cases result in higher mses of the mse approximations

general statistical inference for discrete and mixed spaces by an approximate application of the maximum entropy principle we propose a method for learning a general statistical inference engine operating on discrete and mixed discrete continuous feature spaces such a model allows inference on any of the discrete features given values for the remaining features applications are e g to medical diagnosis with multiple possible diseases fault diagnosis information retrieval and imputation in databases bayesian networks bns are versatile tools that possess this inference capability however bns require explicit specification of conditional independencies which may be difficult to assess given limited data alternatively cheeseman 1983 proposed finding the maximum entropy me joint probability mass function pmf consistent with arbitrary lower order probability constraints this approach is in principle powerful and does not require explicit expression of conditional independence however until now the huge learning complexity has severely limited the use of this approach here we propose an approximate me method which also encodes arbitrary low order constraints but while retaining quite tractable learning our method uses a restriction of joint pmf support during learning to a subset of the feature space results on the university of california irvine repository reveal performance gains over several bn approaches and over multilayer perceptrons

monte carlo comparison of anova mivque reml and ml estimators of variance components for the one way classification random model with unbalanced data we compare five estimators of 2 a and 2 e the among and within treatments variance components analysis of variance anova maximum likelihood ml restricted maximum likelihood reml and two minimum variance quadratic unbiased mivque estimators mivque 0 is mivque with a priori values 0 and 1 mivque a is mivque with the anova estimates used as a priori s we enforce nonnegativity for all estimators setting any negative estimate to zero in accord with usual practice the estimators are compared through their biases and mse s estimated by monte carlo simulation our results indicate that the anova estimators perform well except with seriously unbalanced data when 2 a 2 e 1 ml is excellent when 2 a 2 e 0 5 and mivque a is adequate further iteration to the reml estimates is unnecessary when 2 a 2 e 1 mivque 0 the default for sass procedure varcomp is poor for estimating 2 a and very poor for 2 e

vector quantization by deterministic annealing a deterministic annealing approach is suggested to search for the optimal vector quantizer given a set of training data the problem is reformulated within a probabilistic framework no prior knowledge is assumed on the source density and the principle of maximum entropy is used to obtain the association probabilities at a given average distortion the corresponding lagrange multiplier is inversely related to the temperature and is used to control the annealing process in this process as the temperature is lowered the system undergoes a sequence of phase transitions when existing clusters split naturally without use of heuristics the resulting codebook is independent of the codebook used to initialize the iterations

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

confidence sets centered at james stein estimators a surprise concerning the unknown variance case abstract we compare the confidence set centered at a james stein point estimator to the usual f confidence set for the p regression parameters of a linear model previous studies usually focused on the known variance case and typically concluded that whatever holds in the known variance case also holds in the unknown variance case when the variance is replaced by its best linear estimator based on s 2 where s 2 is the sum of squarred residuals we are surprised that this is not entirely the scenario we observe here in fact in many situations involving unknown variance the range of the shrinkage factor a for the associated confidence set to have uniformly higher coverage probabilities than its f counterpart can be ten times bigger than 2 p 2 the expected upper bound in the known variance case this is true especially when the degrees of freedom are small our numerical studies also show that to gain substantial improvement one has to use a much larger a especially when the degrees of freedom of the residuals are small application to an economic data set is also included

a random effects regression model for meta analysis many meta analyses use a random effects model to account for heterogeneity among study results beyond the variation associated with fixed effects a random effects regression approach for the synthesis of 2 x 2 tables allows the inclusion of covariates that may explain heterogeneity a simulation study found that the random effects regression method performs well in the context of a meta analysis of the efficacy of a vaccine for the prevention of tuberculosis where certain factors are thought to modify vaccine efficacy a smoothed estimator of the within study variances produced less bias in the estimated regression coefficients the method provided very good power for detecting a non zero intercept term representing overall treatment efficacy but low power for detecting a weak covariate in a meta analysis of 10 studies we illustrate the model by exploring the relationship between vaccine efficacy and one factor thought to modify efficacy the model also applies to the meta analysis of continuous outcomes when covariates are present

model selection by testing for the presence of small area effects and application to area level data the models used in small area inference often involve unobservable random effects while this can significantly improve the adaptivity and flexibility of a model it also increases the variability of both point and interval estimators if we could test for the existence of the random effects and if the test were to show that they were unlikely to be present then we would arguably not need to incorporate them into the model and thus could significantly improve the precision of the methodology in this article we suggest an approach of this type we develop simple bootstrap methods for testing for the presence of random effects applicable well beyond the conventional context of the natural exponential family if the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small area means such estimators can be substantially more effective for example because they enjoy much fa

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

vector quantization with complexity costs vector quantization is a data compression method by which a set of data points is encoded by a reduced set of reference vectors the codebook a vector quantization strategy is discussed that jointly optimizes distortion errors and the codebook complexity thereby determining the size of the codebook a maximum entropy estimation of the cost function yields an optimal number of reference vectors their positions and their assignment probabilities the dependence of the codebook density on the data density for different complexity functions is investigated in the limit of asymptotic quantization levels how different complexity measures influence the efficiency of vector quantizers is studied for the task of image compression the wavelet coefficients of gray level images are quantized and the reconstruction error is measured the approach establishes a unifying framework for different quantization methods like k means clustering and its fuzzy version entropy constrained vector quantization or topological feature maps and competitive neural networks

standard errors of prediction in generalized linear mixed models abstract the unconditional mean squared error of prediction umsep is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model but the umsep is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data when the random effects describe variation between independent small domains and domain specific prediction is of interest we propose a conditional mean squared error of prediction cmsep as a general measure of prediction variance the cmsep is shown to be the sum of the conditional variance and a positive correction that accounts for the sampling variability of parameter estimates we derive a second order correct estimate of the cmsep that consists of three components a a plug in estimate of the conditional variance b a plug in estimate of a taylor series approximation to the correction term and c a bootstrap estimate of

mean squared error estimation in transformed fay herriot models summary the problem of accurately estimating the mean squared error of small area estimators within a fay herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable for bias corrected empirical best linear unbiased predictor small area point estimators mean squared error formulae and estimators are provided with biases of smaller order than the reciprocal of the number of small areas the performance of these mean squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the us census bureau s on going small area income and poverty estimation project

regression analysis with linked data record linkage or exact matching can be used to join together two files that contain information on the same individuals but lack unique personal identification codes the possibility of errors in linkage causes problems for estimating the relationships between variables on the two files the effect is analogous to the impact of measurement error a model of a linear regression relationship between variables in linked files is proposed assuming the probabilities that pairs of records are links are known an unbiased estimator of the regression coefficients is derived methods for estimating the linkage probabilities by using mixture models are discussed a consistent estimator of the covariance matrix of the proposed estimator is proposed a bootstrap estimator is used to reflect the impact of the uncertainty in record linkage model parameters on the estimators of the regression parameters a simulation study compares the performance of the proposed estimator and alternatives

empirical likelihood for small area estimation abstract small areaestimation has become a topic of growingimportance inrecent years due to increasing demand for small area statistics fromboth the public and private sectors the current methodologies inthis area with possibly a handful of exceptions are all parametric be it bayesian or frequentist even the so called nonparamet ric procedures based on empirical best linear unbiased predictors eblup assume linearity of the estimators of small area means resampling methods like jacknife and bootstrap are used mostlyfor mean squared error estimation in this paper we propose analternative bayesian approach based on empirical likelihood whichdoes not require the assumption of either a parametric likelihoodor linearity of estimators the proposed method can also handleboth discrete and continuous data in a uni ed manner empiricallikelihood for both area and unit level models are introduced theimproved performance of our estimator is illustrated through twoexamples involving both discrete and continuous data key words and phrases area level exponentially tilted t prior unit level

global well posedness and uniform boundedness of urban crime models one dimensional case abstract in this paper we study a pde system which was proposed by short et al 2008 42 to describe the spatial temporal dynamics in urban criminal activity by establishing a user friendly integral inequality we prove the global existence uniqueness and uniform boundedness of the classical solution to this system in one dimension space our result extends the local well posedness by rodriguez and bertozzi 2010 38 to global

pattern mixture models for multivariate incomplete data consider a random sample on variables x1 xv with some values of xv missing selection models specify the distribution of x1 xv over respondents and nonrespondents to xv and the conditional distribution that xv is missing given x1 xv in contrast pattern mixture models specify the conditional distribution of x 1 xv given that xv is observed or missing respectively and the marginal distribution of the binary indicator for whether or not xv is missing for multivariate data with a general pattern of missing values the literature has tended to adopt the selection modeling approach see for example little and rubin here pattern mixture models are proposed for this more general problem pattern mixture models are chronically underidentified in particular for the case of univariate nonresponse mentioned above there are no data on the distribution of xv given x1 xv 1 in the stratum with xv missing thus the models require restrictions or prior information to identify the paramet

a sample reuse method for accurate parametric empirical bayes confidence intervals abstract parametric empirical bayes methods of point estimation for a vector of unknown parameters date to the landmark paper of james and stein 1961 the usual approach is to use the mean of the estimated posterior distribution of each parameter where the estimation of the prior parameters hyperparameters is accomplished through the marginal distribution of the data while point estimates computed this way usually perform well interval estimates based on the estimated posterior called naive eb intervals are not they fail to account for the variability in the estimation of the hyperparameters generally resulting in sub nominal coverage probability in the eb sense defined in morris 1983a in this paper we extend the work of carlin and gelfand 1989 who proposed a conditional bias correction method for developing eb intervals which corrects the deficiencies in the naive intervals we show how bias correction can be implemented in general via a type iii parametric bootstrap procedure a sample reuse method first employed by laird and louis 1987

transductive methods for the distributed ensemble classification problem we consider ensemble classification for the case where there is no common labeled training data for jointly designing the individual classifiers and the function that aggregates their decisions this problem which we call distributed ensemble classification applies when individual classifiers operate perhaps remotely on different sensing modalities and when combining proprietary or legacy classifiers the conventional wisdom in this case is to apply fixed rules of combination such as voting methods or rules for aggregating probabilities alternatively we take a transductive approach optimizing the combining rule for an objective function measured on the unlabeled batch of test data we propose maximum likelihood ml objectives that are shown to yield well known forms of probabilistic aggregation albeit with iterative expectation maximization based adjustment to account for mismatch between class priors used by individual classifiers and those reflected in the new data batch these methods are extensions for the ensemble case of the work of saerens latinne and decaestecker 2002 we also propose an information theoretic method that generally outperforms the ml methods better handles classifier redundancies and addresses some scenarios where the ml methods are not applicable this method also well handles the case of missing classes in the test batch on uc irvine benchmark data all our methods give improvements in classification accuracy over the use of fixed rules when there is prior mismatch

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

frequentist accuracy of bayesian estimates in the absence of relevant prior experience popular bayesian estimation techniques usually begin with some form of uninformative prior distribution intended to have minimal inferential influence bayes rule will still produce nice looking estimates and credible intervals but these lack the logical force attached to experience based priors and require further justification this paper concerns the frequentist assessment of bayes estimates a simple formula is shown to give the frequentist standard deviation of a bayesian point estimate the same simulations required for the point estimate also produce the standard deviation exponential family models make the calculations particularly simple and bring in a connection to the parametric bootstrap

a standard error for the estimated state vector of a state space model abstract this paper motivates an estimate of the variance of the estimated state vector x t in a state space model when the vector of parameters characterizing system dynamics must be estimated from the data

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

the mean squared error of small area predictors constructed with estimated area variances in the small area estimation literature the sampling error variances are customarily assumed to be known or to depend on a finite number of parameters we consider the empirical best linear unbiased predictor eblup obtained by using the individual directly estimated variance for each small area an approximation for the mean squared error mse of the eblup that recognizes the impact on the predictors of estimation of the variance components is derived simulation studies show that the theoretical expressions are good approximations for the mse of the predictors unless the between area variance component is very small relative to the within area variance an improved estimator of the mse is developed that has smaller overestimation than the original estimator when the between area variance component is small the robustness of the mse estimator is studied and predictors for nonnormal sampling errors are proposed an example from the national resources inventory that motivated the development of the t

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

a james stein type estimator for combining unbiased and possibly biased estimators abstract we present a method for combining unbiased sample data with possibly biased auxiliary information the estimator we derive is similar in spirit to the james stein estimator we prove that the estimator dominates the sample mean under quadratic loss when the auxiliary information is unbiased our estimator has risk slightly greater than the usual combined estimator as the bias increases however the risk of the usual estimator is unbounded while the risk of our estimator is bounded by the risk of the sample mean we show how our estimator can be considered an approximation to the best linear combination of the sample data and the auxiliary information allude to how it can be derived as an empirical bayes estimator and suggest a method for constructing confidence sets finally the performance of our estimator is compared to that of the sample mean and the usual combined estimator using real forestry data

global and exploding solutions for nonlocal quadratic evolution problems nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered the inertial type nonlinearity is quadratic and nonlocal while the diffusive term also nonlocal is anomalous and fractal i e represented by a fractional power of the laplacian conditions for global in time existence versus finite time blow up are studied self similar solutions are constructed for certain homogeneous initial data

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

a model for incorporating historical controls into a meta analysis a method is presented for estimating the treatment effect in a meta analysis when some of the studies are comparative studies and the rest are noncomparative historical control studies a random effects model is used in which the baseline effect in each study is random but the treatment effect is constant with this model the appropriate contribution of the historical studies can be determined extensions of the model are developed to accommodate preliminary tests for bias and for the possibility that the treatment effect is heterogeneous

a semi bayes approach to the analysis of correlated multiple associations with an application to an occupational cancer mortality study thomas et al presented the application of empirical bayes methods to the problem of multiple inference in epidemiologic studies one limitation of their approach which they noted was the need to assume exchangeable log relative risk parameters and independent relative risk estimates numerical integration was also required here i generalize their approach to allow for non exchangeable parameters and non independent estimates the resulting method is bayesian in so far as some feature of the prior distribution are specified from prior information but is empirical bayes in so far as some explicit parameters in the prior distribution are estimated from the data estimation is based on approximations to the posterior distribution this allows one to implement the approach with standard software packages for matrix algebra the method is illustrated in an occupational mortality study of 84 exposure cancer associations

maximum entropy and learning theory we derive the learning theory recently reported by tishby levin and solla tls directly from the principle of maximum entropy instead of statistical mechanics the theory generally applies to any problem of modeling data we analyze an elementary example for which we find the predictions consistent with intuition and conventional statistical results and we numerically examine the more realistic problem of training a competitive net to learn a one dimensional probability density from samples the tls theory is useful for predicting average training behavior

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due