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PurposeThis paper aims to present several Bayesian specification tests for both in- and out-of-sample situations.Design/methodology/approachThe authors focus on the Bayesian equivalents of the frequentist approach for testing heteroskedasticity, autocorrelation and functional form specification. For out-of-sample diagnostics, the authors consider several tests to evaluate the predictive ability of the model.FindingsThe authors demonstrate the performance of these tests using an application on the relationship between price and occupancy rate from the hotel industry. For purposes of comparison, the authors also provide evidence from traditional frequentist tests.Research limitations/implicationsThere certainly exist other issues and diagnostic tests that are not covered in this paper. The issues that are addressed, however, are critically important and can be applied to most modeling situations.Originality/valueWith the increased use of the Bayesian approach in various modeling contexts, this paper serves as an important guide for diagnostic testing in Bayesian analysis. Diagnostic analysis is essential and should always accompany the estimation of regression models.

Bayesian data analysis relies on Bayes's Theorem, using data to update prior beliefs about parameters. In this review, I introduce & contrast Bayesian analysis with conventional frequentist inference & then distinguish two types of Bayesian analysis in political science. First, Bayesian analysis is used to merge historical information with current data in an analysis of likely election outcomes in FL in 2000; particular attention is paid to the sensitivity of the results to the choice of prior (ie, how much confidence one places in the historical information). Second, a more "modern" style of Bayesian analysis is reviewed, relying on Markov chain Monte Carlo algorithms to generate computationally intensive "random tours" of the high dimensional posterior distributions that are the focus of many contemporary Bayesian analyses; the example used is a central problem in political science, the analysis of legislators' preferences using roll call data. 1 Table, 6 Figures, 44 References. Adapted from the source document.

In many branches of science relevant observations are taken sequentially over time. Bayesian Analysis of Time Series discusses how to use models that explain the probabilistic characteristics of these time series and then utilizes the Bayesian approach to make inferences about their parameters. This is done by taking the prior information and via Bayes theorem implementing Bayesian inferences of estimation, testing hypotheses, and prediction. The methods are demonstrated using both R and WinBUGS. The R package is primarily used to generate observations from a given time series model, while the WinBUGS packages allows one to perform a posterior analysis that provides a way to determine the characteristic of the posterior distribution of the unknown parameters. Features Presents a comprehensive introduction to the Bayesian analysis of time series. Gives many examples over a wide variety of fields including biology, agriculture, business, economics, sociology, and astronomy. Contains numerous exercises at the end of each chapter many of which use R and WinBUGS. Can be used in graduate courses in statistics and biostatistics, but is also appropriate for researchers, practitioners and consulting statisticians. About the author Lyle D. Broemeling, Ph.D., is Director of Broemeling and Associates Inc., and is a consulting biostatistician. He has been involved with academic health science centers for about 20 years and has taught and been a consultant at the University of Texas Medical Branch in Galveston, The University of Texas MD Anderson Cancer Center and the University of Texas School of Public Health. His main interest is in developing Bayesian methods for use in medical and biological problems and in authoring textbooks in statistics. His previous books for Chapman & Hall/CRC include Bayesian Biostatistics and Diagnostic Medicine, and Bayesian Methods for Agreement.

Novel Statistical Tools for Conserving and Managing Populations By gathering information on key demographic parameters, scientists can often predict how populations will develop in the future and relate these parameters to external influences, such as global warming. Because of their ability to easily incorporate random effects, fit state-space models, evaluate posterior model probabilities, and deal with missing data, modern Bayesian methods have become important in this area of statistical inference and forecasting. Emphasising model choice and model averaging, Bayesian Analysis for Population Ecology presents up-to-date methods for analysing complex ecological data. Leaders in the statistical ecology field, the authors apply the theory to a wide range of actual case studies and illustrate the methods using WinBUGS and R. The computer programs and full details of the data sets are available on the book's website. The first part of the book focuses on models and their corresponding likelihood functions. The authors examine classical methods of inference for estimating model parameters, including maximum-likelihood estimates of parameters using numerical optimisation algorithms. After building this foundation, the authors develop the Bayesian approach for fitting models to data. They also compare Bayesian and traditional approaches to model fitting and inference. Exploring challenging problems in population ecology, this book shows how to use the latest Bayesian methods to analyse data. It enables readers to apply the methods to their own problems with confidence.

This article provides an applied introduction to Bayesian statistics for sociologists. Unlike frequentist statistics, which attaches repeated-sampling frequencies to test statistics, Bayesian statistics directly describes uncertainty about unknown statistical parameters with a probability distribution. With this foundation, much of Bayesian statistics follows from basic rules of probability theory. Three areas of Bayesian statistics are especially relevant for sociologists. First, hierarchical regression models allow several levels of uncertainty into an analysis. Second, Bayes factors provide a useful approach to the problems of model selection, model averaging, and posterior inference about model indexes. Third, recent breakthroughs in estimation methods offer valuable new tools for analysis of Bayesian models that were previously intractable.

1 Introduction -- 2 Bayesian Decision Theory -- 3 Behavioral and Control Theory of the Firm -- 4 Bayesian Analysis and Duopoly Theory -- 5 Multiperiod Decision Models with Alternating Choice as a Solution to the Duopoly Problem -- 6 Cooperation and Learning in a Duopoly Context -- 7 Interfirm Learning and the Kinked Demand Curve -- 8 Sequential Strategies in Dual Control Problems -- 9 Adaptive Utility -- 10 Some Examples of Adaptive Utility -- 11 Sequential Investment Decisions -- 12 Capital Allocation within Firms -- 13 Rational Expectations -- 14 Epilogue -- References -- Author Index.