Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Statistics for Spatial Data.

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the stan- d ardWaldconfid ence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that the chaotic coverage properties of the Waldinter- val are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects andcannot be trusted . This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and con- text. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equal- tailedJeffreys prior interval for small n andthe interval suggestedin Agresti andCoull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.

/pdf/interval-estimation-for-a-binomial-proportion-3t1vha8pn0.pdf

Interval Estimation for a Binomial Proportion

List of Figures. List of Tables. Foreword. Preface. 1. Introduction. What is a Small Area? Demand for Small Area Statistics. Traditional Indirect Estimators. Small Area Models. Model-Based Estimation. Some Examples. 2. Direct Domain Estimation. Introduction. Design-based Approach. Estimation of Totals. Domain Estimation. Modified Direct Estimators. Design Issues. Proofs. 3. Traditional Demographic Methods. Introduction. Symptomatic Accounting Techniques. Regression Symptomatic Procedures. Dual-system Estimation of Total Population. Derivation of Average MSEs. 4. Indirect Domain Estimation. Introduction. Synthetic Estimation. Composite Estimation. James-Stein Method. Proofs. 5. Small Area Models. Introduction. Basic Area Level (Type A) Mode l. Basic Unit Level (Type B) Model. Extensions: Type A Models. Extensions: Type B Models. Generalized Linear Mixed Models. 6. Empirical Best Linear Unbiased Prediction: Theory. Introduction. General Linear Mixed Model. Block Diagonal Covariance Structure. Proofs. 7. EBLUP: Basic Models. Basic Area Level Model. Basic Unit Level Model. 8. EBLUP: Extensions. Multivariate Fay-Herriot Model. Correlated Sampling Errors. Time Series and Cross-sectional Models. Spatial Models. Multivariate Nested Error Regression Model. Random Error Variances Linear Model. Two-fold Nested Error Regression Model. Two-level Model. 9. Empirical Bayes (EB) Method. Introduction. Basic Area Level Model. Linear Mixed Models. Binary Data. Disease Mapping. Triple-goal Estimation. Empirical Linear Bayes. Constrained LB. Proofs. 10. Hierarchical Bayes (HB) Method. Introduction. MCMC Methods. Basic Area Level Model. Unmatched Sampling and Linking Area Level Models. Basic Unit Level Model. General ANOVA Model. Two-level Models. Time Series and Cross-sectional Models. Multivariate Models. Disease Mapping Models. Binary Data. Exponential Family Models. Constrained HB. Proofs. References. Author Index. Subject Index.

Small Area Estimation

Introduction and the Shrinkage Argument.- Matching Priors for Posterior Quantiles.- Matching Priors for Distribution Functions.- Matching Priors for Highest Posterior Density Regions.- Matching Priors for Other Credible Regions.- Matching Priors for Prediction.

/pdf/probability-matching-priors-higher-order-asymptotics-3wkd5suala.pdf

Probability Matching Priors: Higher Order Asymptotics

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 measuring the variability of small area estimators under a basic area level model

This article focuses primarily on a comparison between the reference priors of Berger and Bernardo and the reverse reference priors suggested by J. K. Ghosh. Sufficient conditions are given that provide agreement between the two classes of priors. Several examples are given showing the agreement or disagreement between the two. In addition, these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real-valued parametric function to match a nominal level with a remainder of O(n −1), where n denotes the sample size. The latter priors, first introduced by Welch and Peers, are obtained by solving a differential equation due to Peers. Finally, in the presence of several parameters of interest, a general class of priors that satisfies the matching criterion separately for each parameter is constructed, and examples are given to illustrate how reference or reverse reference priors fit within this class of priors.

Some remarks on noninformative priors

various noninformative priors have been proposed in the literature. This article explores the invariance (or lack thereof) of some of these noninformative priors including the reference prior of Berger and Bernardo, the reverse reference prior of J. K. Ghosh and the probabilitymatching prior of Peers and Stein under reparameterization. Berger and Bernardo's m-group ordered reference prior is shown to remain invariant under a special type of reparameterization. The reverse reference prior of J. K. Ghosh is shown not to remain invariant under reparameterization. However, the probability-matching prior is shown to remain invariant under any reparameterization. Also for spherically symmetric distributions, certain noninformative priors are derived using the principle of group invariance.

/pdf/on-the-invariance-of-noninformative-priors-1buhgsazqf.pdf

On the invariance of noninformative priors

This paper introduces a hierarchical Bayes (HB) approach for prediction in general mixed linear models. The results find application in small area estimation. Our model unifies and extends a number of models previously considered in this area. Computational formulas for obtaining the Bayes predictors and their standard errors are given in the general case. The methods are applied to two actual data sets. Also, in a special case, the HB predictors are shown to possess some interesting frequentist properties.

/pdf/bayesian-prediction-in-linear-models-applications-to-small-1a4806z0z0.pdf

Gauri Sankar Datta

Papers

Probability Matching Priors: Higher Order Asymptotics

On measuring the variability of small area estimators under a basic area level model

Some remarks on noninformative priors

On the invariance of noninformative priors

Bayesian Prediction in Linear Models: Applications to Small Area Estimation