Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers

by Thomas Leonard , John S. J. Hsu

• ISBN13: 9780521594172
• ISBN10: 0521594170
• Format: Hardcover
• Copyright: 1999-06-13
• Publisher: Cambridge University Press

Summary

This exposition of the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students is unique in presenting its subject with a practical flavor and an emphasis on mainstream statistics. It shows how to infer scientific, medical, and social conclusions from numerical data. The authors draw on many years of experience with practical and research programs and describe many new statistical methods, not available elsewhere. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.

Table of Contents

Preface	xi
Introductory Statistical Concepts	1	(74)
Preliminaries and Overview	1	(5)
Sampling Models and Likelihoods	6	(13)
Practical Examples	19	(14)
Large Sample Properties of Likelihood Procedures	33	(9)
Practical Examples	42	(3)
Some Further Properties of Likelihood	45	(18)
Practical Examples	63	(3)
The Midcontinental Rift	66	(2)
A Model for Genetic Traits in Dairy Science	68	(1)
Least Squares Regression with Serially Correlated Errors	68	(1)
Annual World Crude Oil Production (1880-1972)	69	(6)
The Discrete Version of Bayes' Theorem	75	(23)
Preliminaries and Overview	75	(1)
Bayes' Theorem	76	(5)
Estimating a Discrete-Valued Parameter	81	(1)
Applications to Model Selection	82	(4)
Practical Examples	86	(2)
Logistic Discrimination and the Construction of Neural Nets	88	(3)
Anderson's Prediction of Psychotic Patients	91	(1)
The Ontario Fetal Metabolic Acidosis Study	92	(4)
Practical Guidelines	96	(2)
Models with a Single Unknown Parameter	98	(67)
Preliminaries and Overview	98	(1)
The Bayesian Paradigm	99	(6)
Posterior and Predictive Inferences	105	(12)
Practical Examples	117	(3)
Inferences for a Normal Mean with Known Variance	120	(10)
Practical Examples	130	(4)
Vague Prior Information	134	(8)
Practical Examples	142	(1)
Bayes Estimators and Decision Rules and Their Frequency Properties	143	(12)
Practical Examples	155	(2)
Symmetric Loss Functions	157	(6)
Practical Example: Mixtures of Normal Distributions	163	(2)
The Expected Utility Hypothesis	165	(24)
Preliminaries and Overview	165	(1)
Classical Theory	166	(6)
The Savage Axioms	172	(4)
Modifications to the Expected Utility Hypothesis	176	(3)
The Experimental Measurement of E-Adjusted Utility	179	(3)
The Risk-Aversion Paradox	182	(3)
The Ellsberg Paradox	185	(2)
A Practical Case Study	187	(2)
Models with Several Unknown Parameters	189	(53)
Preliminaries and Overview	189	(1)
Bayesian Marginalization	190	(27)
Further Methods and Practical Examples	217	(16)
The Kalman Filter	233	(4)
An On-Line Analysis of Chemical Process Readings	237	(1)
An Industrial Control Chart	238	(1)
Forecasting Geographical Proportions for World Sales of Fibers	239	(1)
Bayesian Forecasting in Economics	240	(2)
Prior Structuras, Posterior Smoothing, and Bayes-Stein Estimation	242	(61)
Preliminaries and Overview	242	(1)
Multivariate Normal Priors for the Transformed Parameters	243	(10)
Posterior Mode Vectors and Laplacian Approximations	253	(6)
Prior Structures, and Modeling for Nonrandomized Data	259	(16)
Monte Carlo Methods and Importance Sampling	275	(6)
Further Special Cases and Practical Examples	281	(14)
Markov Chain Monte Carlo (MCMC) Methods: The Gibbs Sampler	295	(1)
Modeling Sampling Distributions, Using MCMC	295	(2)
Equally Weighted Mixtures and Survivor Functions	297	(3)
A Hierarchical Bayes Analysis	300	(3)
References	303	(18)
Author Index	321	(5)
Subject Index	326