Scholars@Duke
James O. Berger

James O. Berger

Arts and Sciences Distinguished Professor Emeritus of Statistics
Statistical Science
berger@stat.duke.edu
Box 90251, Durham, NC 27708-0251
221 Old Chemistry, Durham, NC 27708

Selected Publications

Learning Statistics From Counterexamples

Journal Article Sankhya A · November 1, 2024 The title of this article is (essentially) the same as the famous paper Basu (2011b). Basu often opined that counterexamples were the best way to learn limitations of theories or methods and I have followed his directive in my own teaching. A number of cou ... Full text Cite

On the prevalence of information inconsistency in normal linear models

Journal Article Test · March 1, 2021 Informally, ‘information inconsistency’ is the property that has been observed in some Bayesian hypothesis testing and model selection scenarios whereby the Bayesian conclusion does not become definitive when the data seem to become definitive. An example ... Full text Cite

Volcanic Hazard Assessment for an Eruption Hiatus, or Post-eruption Unrest Context: Modeling Continued Dome Collapse Hazards for Soufrière Hills Volcano

Journal Article Frontiers in Earth Science · December 16, 2020 Effective volcanic hazard management in regions where populations live in close proximity to persistent volcanic activity involves understanding the dynamic nature of hazards, and associated risk. Emphasis until now has been placed on identification and fo ... Full text Cite

Bayesian analysis of the covariance matrix of a multivariate normal distribution with a new class of priors

Journal Article Annals of Statistics · August 1, 2020 Bayesian analysis for the covariance matrix of a multivariate normal distribution has received a lot of attention in the last two decades. In this paper, we propose a new class of priors for the covariance matrix, including both inverse Wishart and referen ... Full text Cite

An objective prior for hyperparameters in normal hierarchical models

Journal Article Journal of Multivariate Analysis · July 1, 2020 Hierarchical models are the workhorse of much of Bayesian analysis, yet there is uncertainty as to which priors to use for hyperparameters. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule approach or reference prior approach, ar ... Full text Cite

Frequentist properties of bayesian multiplicity control for multiple testing of normal means

Journal Article Sankhya: The Indian Journal of Statistics · January 1, 2020 We consider the standard problem of multiple testing of normal means, ob-taining Bayesian multiplicity control by assuming that the prior inclusion probability (the assumed equal prior probability that each mean is nonzero) is unknown and assigned a prior ... Full text Cite

Restricted Type II Maximum Likelihood Priors on Regression Coefficients

Journal Article Bayesian Analysis · January 1, 2020 In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to undesirable behavior ... Full text Cite

Comparison of Bayesian and Frequentist Multiplicity Correction for Testing Mutually Exclusive Hypotheses Under Data Dependence

Journal Article Bayesian Analysis · January 1, 2020 The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test statistic dependence ... Full text Cite

Larry Brown's contributions to parametric inference, decision theory and foundations: A survey

Journal Article Statistical Science · November 1, 2019 This article gives a panoramic survey of the general area of parametric statistical inference, decision theory and foundations of statistics for the period 1965-2010 through the lens of Larry Brown's contributions to varied aspects of this massive area. Th ... Full text Cite

RobustGaSP: Robust gaussian stochastic process emulation in R

Journal Article R Journal · June 1, 2019 Gaussian stochastic process (GaSP) emulation is a powerful tool for approximating computationally intensive computer models. However, estimation of parameters in the GaSP emulator is a challenging task. No closed-form estimator is available and many numeri ... Full text Cite

Corrigendum to “Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses” (Journal of Mathematical Psychology (2016) 72 (90–103), (S002224961600002X) (10.1016/j.jmp.2015.12.007))

Journal Article Journal of Mathematical Psychology · April 1, 2019 The following list provides a description of the corrections to the publication since the original version was printed. Page 94: In the fifth paragraph the following sentence appears: “For the control group, the mean is 0, while for the treatment group, th ... Full text Cite

Three Recommendations for Improving the Use of p-Values

Journal Article American Statistician · March 29, 2019 Researchers commonly use p-values to answer the question: How strongly does the evidence favor the alternative hypothesis relative to the null hypothesis? p-Values themselves do not directly answer this question and are often misinterpreted in ways that le ... Full text Cite

On the statistical formalism of uncertainty quantification

Journal Article Annual Review of Statistics and Its Application · March 7, 2019 The use of models to try to better understand reality is ubiquitous. Models have proven useful in testing our current understanding of reality; for instance, climate models of the 1980s were built for science discovery, to achieve a better understanding of ... Full text Cite

Prior-based Bayesian information criterion

Journal Article Statistical Theory and Related Fields · January 2, 2019 We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood fun ... Full text Cite

Redefine statistical significance.

Journal Article Nature human behaviour · January 2018 Full text Open Access Cite

Robust Gaussian stochastic process emulation

Journal Article Annals of Statistics · January 1, 2018 We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through ... Full text Cite

Coupling computer models through linking their statistical emulators

Journal Article SIAM-ASA Journal on Uncertainty Quantification · January 1, 2018 Direct coupling of computer models is often difficult for computational and logistical reasons. We propose coupling computer models by linking independently developed Gaussian process emulators (GaSPs) of these models. Linked emulators are developed that a ... Full text Cite

Parallel partial Gaussian process emulation for computer models with massive output

Journal Article Annals of Applied Statistics · September 1, 2016 We consider the problem of emulating (approximating) computer models (simulators) that produce massive output. The specific simulator we study is a computer model of volcanic pyroclastic flow, a single run of which produces up to 109 outputs over a space–t ... Full text Cite

Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses.

Journal Article Journal of mathematical psychology · June 2016 Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over 50 years ... Full text Cite

Estimating shape constrained functions using Gaussian processes

Journal Article SIAM-ASA Journal on Uncertainty Quantification · January 1, 2016 Gaussian processes are a popular tool for nonparametric function estimation because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. Often, the function is known to be in a shape-constrained class, ... Full text Cite

Overall objective priors

Journal Article Bayesian Analysis · March 1, 2015 In multi-parameter models, reference priors typically depend on the parameter or quantity of interest, and it is well known that this is necessary to produce objective posterior distributions with optimal properties. There are, however, many situations whe ... Full text Cite

Probabilistic quantification of hazards: A methodology using small ensembles of physics-based simulations and statistical surrogates

Journal Article International Journal for Uncertainty Quantification · January 1, 2015 This paper presents a novel approach to assessing the hazard threat to a locale due to a large volcanic avalanche. The methodology combines: (i) mathematical modeling of volcanic mass flows; (ii) field data of avalanche frequency, volume, and runout; (iii) ... Full text Cite

The Effective Sample Size

Journal Article Econometric Reviews · February 1, 2014 Model selection procedures often depend explicitly on the sample size n of the experiment. One example is the Bayesian information criterion (BIC) criterion and another is the use of Zellner-Siow priors in Bayesian model selection. Sample size is well-defi ... Full text Cite

A Bayesian approach to subgroup identification.

Journal Article Journal of biopharmaceutical statistics · January 2014 This article discusses subgroup identification, the goal of which is to determine the heterogeneity of treatment effects across subpopulations. Searching for differences among subgroups is challenging because it is inherently a multiple testing problem wit ... Full text Cite

Automating emulator construction for geophysical hazard maps

Journal Article SIAM-ASA Journal on Uncertainty Quantification · January 1, 2014 This paper describes an efficient and systematic process for using geophysical computer model simulations to guide efforts in probabilistic hazard mapping. The framework being proposed requires the simultaneous construction of many (102–104) statistical em ... Full text Cite

Conditioning is the issue

Chapter · January 1, 2014 The importance of conditioning in statistics and its implementation are highlighted through the series of examples that most strongly affected my understanding of the issue. The examples range from “oldies but goodies” to new examples that illustrate the i ... Cite

Bayesian analysis of dynamic item response models in educational testing

Journal Article Annals of Applied Statistics · March 1, 2013 Item response theory (IRT) models have been widely used in educational measurement testing. When there are repeated observations available for individuals through time, a dynamic structure for the latent trait of ability needs to be incorporated into the m ... Full text Cite

Objective priors for discrete parameter spaces

Journal Article Journal of the American Statistical Association · August 2, 2012 This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development-such as the reference prior approach-often result in a constant prior for a discrete parameter, which is questionab ... Full text Cite

Criteria for bayesian model choice with application to variable selection

Journal Article Annals of Statistics · June 1, 2012 In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most g ... Full text Cite

Preface

Chapter · January 19, 2012 Full text Cite

Bayesian Statistics 9

Conference Bayesian Statistics 9 · January 19, 2012 The Valencia International Meetings on Bayesian Statistics - established in 1979 and held every four years - have been the forum for a definitive overview of current concerns and activities in Bayesian statistics. These are the edited Proceedings of the Ni ... Full text Cite

Bayesian Nonparametric Shrinkage Applied to Cepheid Star Oscillations.

Journal Article Statistical science : a review journal of the Institute of Mathematical Statistics · January 2012 Bayesian nonparametric regression with dependent wavelets has dual shrinkage properties: there is shrinkage through a dependent prior put on functional differences, and shrinkage through the setting of most of the wavelet coefficients to zero through Bayes ... Full text Cite

Bayesian methods for analysis and adaptive scheduling of exoplanet observations

Journal Article Statistical Methodology · January 1, 2012 We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work a ... Full text Cite

Statistical interpretation of the RV144 HIV vaccine efficacy trial in Thailand: a case study for statistical issues in efficacy trials.

Journal Article The Journal of infectious diseases · April 2011 Recently, the RV144 randomized, double-blind, efficacy trial in Thailand reported that a prime-boost human immunodeficiency virus (HIV) vaccine regimen conferred ∼30% protection against HIV acquisition. However, different analyses seemed to give conflictin ... Full text Cite

Incoherent phylogeographic inference.

Journal Article Proceedings of the National Academy of Sciences of the United States of America · October 2010 Full text Cite

Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

Journal Article Annals of Statistics · October 1, 2010 This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish th ... Full text Open Access Cite

Modularization in Bayesian analysis, with emphasis on analysis of computer models

Journal Article Bayesian Analysis · December 1, 2009 Bayesian analysis incorporates different sources of information into a single analysis through Bayes theorem. When one or more of the sources of information are suspect (e.g., if the model assumed for the information is viewed as quite possibly being signi ... Full text Cite

Statistical and applied mathematical sciences institute

Journal Article Wiley Interdisciplinary Reviews: Computational Statistics · December 1, 2009 The Statistical and Applied Mathematical Sciences Institute (SAMSI) is a national institute in the USA devoted to forging a synthesis of the statistical sciences and the applied mathematical sciences with disciplinary science to confront the very hardest a ... Full text Cite

Using statistical and computer models to quantify volcanic hazards

Journal Article Technometrics · November 1, 2009 Risk assessment of rare natural hazards, such as large volcanic block and ash or pyroclastic flows, is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A comput ... Full text Cite

Special issue on computer modeling

Journal Article Technometrics · November 1, 2009 Full text Cite

Predicting vehicle crashworthiness: Validation of computer models for functional and hierarchical data

Journal Article Journal of the American Statistical Association · October 14, 2009 The CRASH computer model simulates the effect of a vehicle colliding against different barrier types. If it accurately represents real vehicle crashworthiness, the computer model can be of great value in various aspects of vehicle design, such as the setti ... Full text Cite

The formal definition of reference priors

Journal Article Annals of Statistics · April 1, 2009 Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-t ... Full text Cite

Natural induction: An objective bayesian approach

Journal Article Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas · January 1, 2009 The statistical analysis of a sample taken from a finite population is a classic problem for which no generally accepted objective Bayesian results seem to exist. Bayesian solutions to this problem may be very sensitive to the choice of the prior, and ther ... Full text Cite

Rejoinder on: Natural Induction: An Objective Bayesian Approach

Journal Article Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas · January 1, 2009 Full text Cite

A comparison of testing methodologies

Journal Article PHYSTAT LHC Workshop on Statistical Issues for LHC Physics, PHYSTAT 2007 - Proceedings · December 1, 2008 This is a mostly philosophical discussion of approaches to statistical hypothesis testing, including p-values, classical frequentist testing, Bayesian testing, and conditional frequentist testing. We also briefly discuss the issue of multiplicity, an issue ... Cite

A Bayesian analysis of the thermal challenge problem

Journal Article Computer Methods in Applied Mechanics and Engineering · May 1, 2008 A major question for the application of computer models is Does the computer model adequately represent reality? Viewing the computer models as a potentially biased representation of reality, Bayarri et al. [M. Bayarri, J. Berger, R. Paulo, J. Sacks, J. Ca ... Full text Cite

Objective priors for the bivariate normal model

Journal Article Annals of Statistics · April 1, 2008 Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., B ... Full text Cite

Mixtures of g-priors for Bayesian Variable Selection

Journal Article Journal of the American Statistical Association · 2008 Zellner's g prior remains a popular conventional prior for use in Bayesian variable selection, despite several undesirable consistency issues. In this article we study mixtures of g priors as an alternative to default g priors that resolve many of the prob ... Full text Link to item Cite

Computer model validation with functional output

Journal Article Annals of Statistics · October 1, 2007 A key question in evaluation of computer models is Does the computer model adequately represent reality? A six-step process for computer model validation is set out in Bayarri et al. [Technometrics 49 (2007) 138-154] (and briefly summarized below), based o ... Full text Cite

A framework for validation of computer models

Journal Article Technometrics · May 1, 2007 We present a framework that enables computer model evaluation oriented toward answering the question: Does the computer model adequately represent reality? The proposed validation framework is a six-step procedure based on Bayesian and likelihood methodolo ... Full text Cite

Incorporating uncertainties into traffic simulators

Conference Recent Advances in Modeling and Simulation Tools for Communication Networks and Services · January 1, 2007 It is possible to incorporate uncertainty in model inputs into analyses of traffic simulators, and incorporating this uncertainty can significantly improve the predictions made with these simulators. CORSIM is a microsimulator for vehicular traffic, and is ... Full text Cite

A statistician's perspective on Astrostatistics

Conference STATISTICAL CHALLENGES IN MODERN ASTRONOMY IV · January 1, 2007 Link to item Cite

Current challenges in Bayesian model choice

Journal Article Statistical Challenges in Modern Astronomy IV · 2007 Link to item Cite

The case for objective Bayesian analysis

Journal Article Bayesian Analysis · December 1, 2006 Bayesian statistical practice makes extensive use of versions of objective Bayesian analysis. We discuss why this is so, and address some of the criticisms that have been raised concerning objective Bayesian analysis. The dangers of treating the issue too ... Full text Cite

Rejoinder

Journal Article Bayesian Analysis · December 1, 2006 Full text Cite

An exploration of aspects of Bayesian multiple testing

Journal Article Journal of Statistical Planning and Inference · July 1, 2006 There has been increased interest of late in the Bayesian approach to multiple testing (often called the multiple comparisons problem), motivated by the need to analyze DNA microarray data in which it is desired to learn which of potentially several thousa ... Full text Cite

Statistical inverse analysis for a network microsimulator

Journal Article Technometrics · November 1, 2005 CORSIM, a microsimulator for vehicular traffic, is being studied with respect to its ability to successfully model and predict behavior of traffic in a 36-block section of Chicago. Inputs to the simulator include information about street configuration, dri ... Full text Cite

Some Bayesian predictive approaches to model selection

Journal Article Statistics and Probability Letters · July 15, 2005 A variety of pseudo-Bayes factors have been proposed, based on using part of the data to update an improper prior, and using the remainder of the data to compute the Bayes factor. A number of these approaches are of a bootstrap or cross-validation nature, ... Full text Cite

Posterior propriety and admissibility of hyperpriors in normal hierarchical models

Journal Article Annals of Statistics · April 1, 2005 Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably inferior perform ... Full text Cite

Posterior model probabilities via path-based pairwise priors

Journal Article Statistica Neerlandica · February 1, 2005 We focus on Bayesian model selection for the variable selection problem in large model spaces. The challenge is to search the huge model space adequately, while accurately approximating model posterior probabilities for the visited models. The issue of cho ... Full text Cite

Optimal predictive model selection

Journal Article Annals of Statistics · June 1, 2004 Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is ... Full text Cite

Training samples in objective Bayesian model selection

Journal Article Annals of Statistics · June 1, 2004 Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them ... Full text Cite

The interplay of Bayesian and frequentist analysis

Journal Article Statistical Science · February 1, 2004 Statistics has struggled for nearly a century over the issue of whether the Bayesian or frequentist paradigm is superior. This debate is far from over and, indeed, should continue, since there are fundamental philosophical and pedagogical issues at stake. ... Full text Cite

Assessing uncertainties in traffic simulation : A key component in model calibration and validation

Journal Article Transportation Research Record · January 1, 2004 Calibrating and validating a traffic simulation model for use on a transportation network depend on field data that are often limited but essential for determining inputs to the model and for assessing its reliability. Quantification and systemization of t ... Full text Cite

Some recent developments in Bayesian variable selection

Conference BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING · January 1, 2004 Link to item Cite

Space-time modeling of vertical ozone profiles

Journal Article Environmetrics · September 1, 2003 Ozonesondes collect data relevant to ozone level at various altitudes. Modeling these data involves a combination of spatial and temporal modeling. The spatial component can be conveniently modeled as a four component mixture of normal distributions. The ( ... Full text Cite

A Bayesian analysis of the cepheid distance scale

Journal Article Astrophysical Journal · July 20, 2003 We develop and describe a Bayesian statistical analysis to solve the surface brightness equations for Cepheid distances and stellar properties. Our analysis provides a mathematically rigorous and objective solution to the problem, including immunity from L ... Full text Cite

Approximations and consistency of Bayes factors as model dimension grows

Journal Article Journal of Statistical Planning and Inference · March 1, 2003 Stone (J. Roy. Statist. Soc. Ser. B 41 (1979) 276) showed that BIC can fail to be asymptotically consistent. Note, however, that BIC was developed as an asymptotic approximation to Bayes factors between models, and that the approximation is valid only unde ... Full text Cite

Could Fisher, Jeffreys and Neyman have agreed on testing?

Journal Article Statistical Science · February 1, 2003 Ronald Fisher advocated testing using p-values, Harold Jeffreys proposed use of objective posterior probabilities of hypotheses and Jerzy Neyman recommended testing with fixed error probabilities. Each was quite critical of the other approaches. Most troub ... Full text Cite

Could Fisher, Jeffreys and Neyman have agreed on testing? Comment

Journal Article STATISTICAL SCIENCE · February 1, 2003 Link to item Cite

Unified conditional frequentist and Bayesian testing of composite hypotheses

Journal Article Scandinavian Journal of Statistics · January 1, 2003 Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities, error pr ... Full text Cite

Expected-posterior prior distributions for model selection

Journal Article Biometrika · December 1, 2002 We consider the problem of comparing parametric models using a Bayesian approach. A new method of developing prior distributions for the model parameters is presented, called the expected-posterior prior approach. The idea is to define the priors for all m ... Full text Cite

Unified Bayesian and conditional frequent testing of composite hypoetheses

Journal Article Scandinavian Journal of Statistics · 2002 Cite

Objective bayesian analysis of spatially correlated data

Journal Article Journal of the American Statistical Association · December 1, 2001 Spatially varying phenomena are often modeled using Gaussian random fields, specified by their mean function and covariance function. The spatial correlation structure of these models is commonly specified to be of a certain form (e.g., spherical, power ex ... Full text Cite

Intervals for posttest probabilities: a comparison of 5 methods.

Journal Article Medical decision making : an international journal of the Society for Medical Decision Making · November 2001 BackgroundSeveral medical articles discuss methods of constructing confidence intervals for single proportions and the likelihood ratio, but scant attention has been given to the systematic study of intervals for the posterior odds, or the positiv ... Full text Cite

Why should clinicians care about Bayesian methods?

Journal Article Journal of Statistical Planning and Inference · March 2001 Full text Cite

Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives

Journal Article Journal of the American Statistical Association · March 1, 2001 Testing the fit of data to a parametric model can be done by embedding the parametric model in a nonparametric alternative and computing the Bayes factor of the parametric model to the nonparametric alternative. Doing so by specifying the nonparametric alt ... Full text Cite

Calibration of p values for testing precise null hypotheses

Journal Article American Statistician · February 1, 2001 P values are the most commonly used tool to measure evidence against a hypothesis or hypothesized model. Unfortunately, they are often incorrectly viewed as an error probability for rejection of the hypothesis or, even worse, as the posterior probability t ... Full text Cite

Bayesian analysis: A look at today and thoughts of tomorrow

Chapter · January 1, 2001 The vignette series concludes with 22 contributions in Theory and Methods. It is, of course, impossible to cover all of theory and methods with so few articles, but we hope that a snapshot of what was, and what may be, is achieved. This is the essence of “ ... Cite

Bayesian testing of a parametric model versus nonparametric alternatives

Journal Article J. American Statistical Association · 2001 Cite

Semiparametric Bayesian analysis of selection models

Journal Article J. American Statistical Association · 2001 Cite

P Values for Composite Null Models

Journal Article Journal of the American Statistical Association · December 1, 2000 The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which la ... Full text Cite

Rejoinder

Journal Article Journal of the American Statistical Association · December 1, 2000 Full text Cite

Bayesian Analysis: A Look at Today and Thoughts of Tomorrow

Journal Article Journal of the American Statistical Association · December 1, 2000 Full text Cite

P Values for Composite Null Models

Journal Article Journal of the American Statistical Association · December 2000 Full text Cite

Robust Bayesian displays for standard inferences concerning a normal mean

Journal Article Computational Statistics and Data Analysis · June 28, 2000 Standard Bayesian inferences concerning a normal mean are considered when, for robustness reasons, Cauchy prior distributions are utilized. The inferences considered include testing a point null hypothesis, one-sided testing, estimation, and credible sets. ... Full text Cite

P-values for composite null models (with discussion)

Journal Article J. Amer. Statist. Assoc. · 2000 Cite

Default Bayes Factors for Nonnested Hypothesis Testing

Journal Article Journal of the American Statistical Association · June 1, 1999 Bayesian hypothesis testing for nonnested hypotheses is studied, using various “default” Bayes factors, such as the fractional Bayes factor, the median intrinsic Bayes factor, and the encompassing and expected intrinsic Bayes factors. The different default ... Full text Cite

Rejoinder

Journal Article Statistical Science · January 1, 1999 Cite

Integrated likelihood methods for eliminating nuisance parameters

Journal Article Statistical Science · January 1, 1999 Elimination of nuisance parameters is a central problem in statistical inference and has been formally studied in virtually all approaches to inference. Perhaps the least studied approach is elimination of nuisance parameters through integration, in the se ... Full text Cite

Estimation of quadratic functions: Noninformative priors for non-centrality parameters

Journal Article Statistica Sinica · April 1, 1998 The estimation of quadratic functions of a multivariate normal mean is an inferential problem which, while being simple to state and often encountered in practice, leads to surprising complications both from frequentist and Bayesian points of view. The dra ... Cite

Robust Bayesian analysis of selection models

Journal Article Annals of Statistics · January 1, 1998 Selection models arise when the data are selected to enter the sample only if they occur in a certain region of the sample space. When this selection occurs according to some probability distribution, the resulting model is often instead called a weighted ... Full text Cite

Reference priors with partial information

Journal Article Biometrika · January 1, 1998 In this paper, reference priors are derived for three cases where partial information is available. If a subjective conditional prior is given, two reasonable methods are proposed for finding the marginal reference prior. If, instead, a subjective marginal ... Full text Cite

Rejoinder

Journal Article Statistical Science · January 1, 1997 Cite

Unification of frequentist and Bayesian testing

Journal Article 51st Session of the International Statistical Institute · 1997 Cite

Unified frequentist and bayesian testing of a precise hypothesis

Journal Article Statistical Science · January 1, 1997 In this paper, we show that the conditional frequentist method of testing a precise hypothesis can be made virtually equivalent to Bayesian testing. The conditioning strategy proposed by Berger, Brown and Wolpert in 1994, for the simple versus simple case, ... Full text Cite

Some recent developments in Bayesian analysis, with astronomical illustrations

Conference STATISTICAL CHALLENGES IN MODERN ASTRONOMY II · January 1, 1997 Link to item Cite

Simple counterexamples against the conditionality principle - Comment

Journal Article AMERICAN STATISTICIAN · November 1, 1996 Link to item Cite

The Intrinsic Bayes Factor for Model Selection and Prediction

Journal Article Journal of the American Statistical Association · March 1996 Full text Cite

The intrinsic bayes factor for model selection and prediction

Journal Article Journal of the American Statistical Association · March 1, 1996 In the Bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions, it is typically not possible to utilize standard noninformative (or default) prior distributions. This has led Bayesians to use conventiona ... Full text Cite

Choice of hierarchical priors: Admissibility in estimation of normal means

Journal Article Annals of Statistics · January 1, 1996 In hierarchical Bayesian modeling of normal means, it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters (e.g., variances and highest-level means). This common practice often results in an inade ... Full text Cite

Approximations of Bayes decision problems: the epigraphical approach

Journal Article Annals of Operations Research · December 1, 1995 Solving Bayesian decision problems usually requires approximation procedures, all leading to study the convergence of the approximating infima. This aspect is analysed in the context of epigraphical convergence of integral functionals, as minimal context f ... Full text Cite

Discussion of David Freedman's "Some issues in the foundations of statistics"

Journal Article Foundations of Science · March 1, 1995 While results from statistical modelling too often receive blind acceptance, we question whether there is any real alternative to use of modelling. This does not diminish the main point of Professor Freedman, which is that healthy scepticism towards models ... Full text Cite

Recent developments and applications of Bayesian analysis

Journal Article 50th Session of the International Statistical Institute · 1995 Cite

Preface

Journal Article Seminars in Cutaneous Medicine and Surgery · January 1, 1995 Full text Cite

BAYESIAN ROBUSTNESS IN BIDIMENSIONAL MODELS - PRIOR INDEPENDENCE - REJOINDER

Journal Article JOURNAL OF STATISTICAL PLANNING AND INFERENCE · July 1, 1994 Link to item Cite

Bayesian sequential reliability for Weibull and related distributions

Journal Article Annals of the Institute of Statistical Mathematics · June 1, 1994 Assume that the probability density function for the lifetime of a newly designed product has the form: [H′(t)/Q(θ)] exp{-H(t)/Q(θ)}. The Exponential ε(θ), Rayleigh, Weibull W(θ, β) and Pareto pdf's are special cases. Q(θ) will be assumed to have an invers ... Full text Cite

An overview of robust Bayesian analysis

Journal Article Test · June 1, 1994 Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also re ... Full text Cite

A Bayesian testing procedure with valid conditional frequentist interpretation

Conference AMERICAN STATISTICAL ASSOCIATION 1994 PROCEEDINGS OF THE SECTION ON BAYESIAN STATISTICAL SCIENCE · January 1, 1994 Link to item Cite

Noninformative priors and Bayesian testing for the AR(1) model

Journal Article Econometric Theory · 1994 Cite

Robust Bayesian hypothesis testing in the presence of nuisance parameters

Journal Article Journal of Statistical Planning and Inference · January 1, 1994 Robust Bayesian testing of point null hypotheses is considered for problems involving the presence of nuisance parameters. The robust Bayesian approach seeks answers that hold for a range of prior distributions. Three techniques for handling the nuisance p ... Full text Cite

Bayesian robustness in bidimensional models: Prior independence

Journal Article Journal of Statistical Planning and Inference · January 1, 1994 When θ is a multidimensional parameter, the issue of prior dependence or independence of coordinates is a serious concern. This is especially true in robust Bayesian analysis; Lavine et al. (J. Amer. Statist. Assoc. 86, 964-971 (1991)) show that allowing a ... Full text Cite

Optimal robust credible sets for contaminated priors

Journal Article Statistics and Probability Letters · December 2, 1993 In robust Bayesian analysis, it is of interest to find the optimal robust credible set, viz: the smallest set with posterior probability at least, say γ, with respect to each prior in the class. Here, we derive the optimal robust credible set for the ε-con ... Full text Cite

Bayesian Analysis for the Poly-Weibull Distribution

Journal Article Journal of the American Statistical Association · December 1993 Full text Cite

Integration of Multimodal Functions by Monte Carlo Importance Sampling

Journal Article Journal of the American Statistical Association · June 1993 Full text Cite

THE PRESENT AND FUTURE OF BAYESIAN MULTIVARIATE-ANALYSIS

Conference MULTIVARIATE ANALYSIS: FUTURE DIRECTIONS · January 1, 1993 Link to item Cite

Robust Bayesian analysis of the binomial empirical Bayes problem

Journal Article Canadian J. Statist. · 1993 Cite

Integration of multimodal functions by Monte Carlo importance sampling

Journal Article J. Amer. Statist. Assoc. · 1993 Cite

Bayesian analysis for the poly-Weibull distribution

Journal Article J. Amer. Statist. Assoc. · 1993 Cite

Bayesian estimation of manufacturing effects in a fuel economy model

Journal Article J. of Applied Econometrics · 1993 Cite

Ordered group reference priors with application to the multinomial problem

Journal Article Biometrika · March 1, 1992 SUMMARY: Noninformative priors are developed, using the reference prior approach, for multipara-meter problems in which there may be parameters of interest and nuisance parameters. For a given grouping of parameters and ordering of the groups, intuitively, ... Full text Cite

The application of robust Bayesian analysis to hypothesis testing and Occam's Razor

Journal Article Journal of the Italian Statistical Society · February 1, 1992 Robust Bayesian analysis deals simultaneously with a class of possible prior distributions, instead of a single distribution. This paper concentrates on the surprising results that can be obtained when applying the theory to problems of testing precise hyp ... Full text Cite

Adaptive importance sampling in Monte Carlo integration

Journal Article J. Statist. Comput. Simul. · 1992 Cite

A comparison of minimal Bayesian tests of precise hypotheses

Journal Article Rassegna di Metodi Statistici ed Applicazioni · 1992 Cite

Ockham's razor and Bayesian analysis

Journal Article American Scientist · 1992 Cite

Noninformative priors for inferences in exponential regression models

Journal Article Biometrika · September 1, 1991 SUMMARY: In the exponential regression model, inference concerning the regression parameter is notoriously difficult, even when using the Bayesian noninformative prior approach. The reference prior approach (Bernardo, 1979; Berger & Bernardo, 1989) is cons ... Full text Cite

Comment

Journal Article Statistical Science · January 1, 1991 Full text Cite

Robust hierarchical Bayes estimation of exchangeable means

Journal Article Canadian J. of Statistics · 1991 Cite

Bayesian analysis with limited communication

Journal Article Journal of Statistical Planning and Inference · January 1, 1991 The i-th member of a group of m individuals (or stations) observes a random quantity Xi, where X=(X1,...,Xm) has a density g(x |π). Each individual can report only yi=hi(xi), because of a limitation on the amount of information that can be communicated. Ba ... Full text Cite

Interpreting the stars in precise hypothesis testing

Journal Article International Statistical Review · 1991 Cite

Introduction to Statistical Multiple Integration

Journal Article Contemporary Mathematics · 1991 Cite

Comment

Journal Article Statistical Science · January 1, 1990 Full text Cite

Comment

Journal Article Statistical Science · January 1, 1990 Full text Cite

Robust Bayesian analysis: sensitivity to the prior

Journal Article Journal of Statistical Planning and Inference · January 1, 1990 Full text Cite

On the inadmissibility of unbiased estimators

Journal Article Statistics and Probability Letters · January 1, 1990 It is observed that unbiased estimators are always inadmissible when the parameter (or function of the parameter) being estimated has either a maximum or a minimum at a parameter value for which the probability distribution is nondegenerate. Examples of pr ... Full text Cite

Letter: "Comment on Kempthorne (1989)"

Journal Article American Statistician · 1990 Cite

Estimating a Product of Means: Bayesian Analysis with Reference Priors

Journal Article Journal of the American Statistical Association · March 1989 Full text Cite

Estimating a product of means: Bayesian analysis with reference priors

Journal Article J. Amer. Statist. Assoc. · 1989 Cite

Estimated confidence procedures for multivariate normal means

Journal Article Journal of Statistical Planning and Inference · January 1, 1989 In estimation of a p-variate normal mean with identify covariance matrix, confidence sets recentered at Stein-type estimators have larger coverage probability then the usual confidence ellipsoids (see Hwang and Casella (1982)). However, the minimum coverag ... Full text Cite

Bayesian Variable Selection in Linear Regression: Comment

Journal Article Journal of the American Statistical Association · December 1988 Full text Cite

Ranges of Posterior Probabilities for Quasiunimodal Priors With Specified Quantiles

Journal Article Journal of the American Statistical Association · June 1988 Full text Cite

STATISTICAL-ANALYSIS AND THE ILLUSION OF OBJECTIVITY

Journal Article AMERICAN SCIENTIST · March 1, 1988 Link to item Cite

Comment

Journal Article Journal of the American Statistical Association · January 1, 1988 Full text Cite

Comment

Journal Article Statistical Science · January 1, 1988 Full text Cite

Analyzing data: Is objectivity possible?

Journal Article American Scientist · 1988 Cite

Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence

Journal Article Journal of the American Statistical Association · March 1987 Full text Cite

Testing precise hypotheses

Journal Article Statistical Science · January 1, 1987 Testing of precise (point or small interval) hypotheses is reviewed, with special emphasis placed on exploring the dramatic conflict between conditional measures (Bayes factors and posterior probabilities) and the classical P-value (or observed significanc ... Full text Cite

Rejoinder

Journal Article Journal of the American Statistical Association · January 1, 1987 Full text Cite

Testing a point null hypothesis: The irreconcilability of P values and evidence

Journal Article Journal of the American Statistical Association · January 1, 1987 The problem of testing a point null hypothesis (or a “small interval” null hypothesis) is considered. of interest is the relationship between the P value (or observed significance level) and conditional and Bayesian measures of evidence against the null hy ... Full text Cite

Rejoinder

Journal Article Statistical Science · January 1, 1987 Full text Cite

Testing precise hypothesis (with Discussion)

Journal Article Statist. Science · 1987 Cite

Discussion: On the Consistency of Bayes Estimates

Journal Article The Annals of Statistics · March 1, 1986 Full text Cite

Comment

Journal Article Statistical Science · January 1, 1986 Full text Cite

The Stein effect and Bayesian analysis: A reexamination

Journal Article Commun. in Statist. · 1986 Cite

Abraham Wald's Work on Aircraft Survivability: Comment

Journal Article Journal of the American Statistical Association · June 1984 Full text Cite

Comment

Journal Article Journal of the American Statistical Association · January 1, 1984 Full text Cite

Bayesian input in Stein estimation and a new minimax empirical Bayes estimator

Journal Article Journal of Econometrics · January 1, 1984 The relationship between Stein estimation of a multivariate normal mean and Bayesian analysis is considered. The necessity to involve prior information is discussed, and the various methods of so doing are reviewed. These include direct Bayesian analyses, ... Full text Cite

On Truncation of Shrinkage Estimators in Simultaneous Estimation of Normal Means

Journal Article Journal of the American Statistical Association · December 1983 Full text Cite

Empirical Bayes Estimation of Rates in Longitudinal Studies

Journal Article Journal of the American Statistical Association · December 1983 Full text Cite

Parametric Empirical Bayes Inference: Theory and Applications: Comment

Journal Article Journal of the American Statistical Association · March 1983 Full text Cite

Comment

Journal Article Journal of the American Statistical Association · January 1, 1983 Full text Cite

Combining coordinates in simultaneous estimation of normal means

Journal Article Journal of Statistical Planning and Inference · January 1, 1983 The problem of combining coordinates in Stein-type estimators, when simultaneously estimating normal means, is considered. The question of deciding whether to use all coordinates in one combined shrinkage estimator or to separate into groups and use separa ... Full text Cite

Empirical Bayes estimation of rates in longitudinal studies

Journal Article J. Amer. Statist. Assoc. · 1983 Cite

Estimating the mean function of a Gaussian process and the Stein effect

Journal Article Journal of Multivariate Analysis · January 1, 1983 The problem of global estimation of the mean function θ(·) of a quite arbitrary Gaussian process is considered. The loss function in estimating θ by a function a(·) is assumed to be of the form L(θ, a) = ∫ [θ(t) - a(t)]2μ(dt), and estimators are evaluated ... Full text Cite

Bayesian Robustness and the Stein Effect

Journal Article Journal of the American Statistical Association · June 1982 Full text Cite

Bayesian robustness and the Stein effect

Journal Article J. Amer. Statist. Assoc. · 1982 Cite

A modification of Brown's technique for proving inadmissibility

Journal Article Recent Developments in Statistical Inference and Data Analysis · 1980 Cite

Minimax estimation of a multivariate normal mean under polynomial loss

Journal Article Journal of Multivariate Analysis · January 1, 1978 Let X be an observation from a p-variate (p ≥ 3) normal random vector with unknown mean vector θ and known covariance matrix {A figure is presented}. The problem of improving upon the usual estimator of θ, δ0(X) = X, is considered. An approach is developed ... Full text Cite

Generalized Bayes esimators in multivariate problems

Journal Article Ann. Statist. · 1978 Cite

Eliminating singularities of Stein-type estimators of location vectors

Journal Article J. Roy. Statist. Soc., B · 1977 Cite

Minimax estimation of a multivariate normal mean under arbitrary quadratic loss

Journal Article Journal of Multivariate Analysis · January 1, 1976 Let X be a p-variate (p ≥ 3) vector normally distributed with mean θ and known covariance matrix {A figure is presented}. It is desired to estimate θ under the quadratic loss (δ - θ)t Q(δ - θ), where Q is a known positive definite matrix. A broad class of ... Full text Cite