Bayesian theory / / Jose M. Bernardo, Adrian F.M. Smith

• Record Nr.: UNINA9910877315203321
• Autore: Bernardo J. M
• Pubbl/distr/stampa: Chichester ; ; New York, : Wiley, c2000
• ISBN: 1-282-30786-X; 9786612307867; 0-470-31687-X; 0-470-31771-X
• Descrizione fisica: 1 online resource (611 p.)
• Collana: Wiley series in probability and statistics
• Altri autori (Persone): SmithAdrian F. M
• Disciplina: 519.5; 519.542
• Soggetti: Bayesian statistical decision theory; Statistical decision
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Originally published: 1994.
• Nota di bibliografia: Includes bibliographical references (p. [489]-554) and indexes.
• Nota di contenuto: BAYESIAN THEORY; Contents; 1. INTRODUCTION; 1.1. Thomas Bayes; 1.2. The subjectivist view of probability; 1.3. Bayesian Statistics in perspective; 1.4. An overview of Bayesian Theory; 1.4.1. Scope; 1.4.2. Foundations; 1.4.3. Generalisations; 1.4.4. Modelling; 1.4.5. Inference; 1.4.6. Remodelling; 1.4.7. Basic formulae; 1.4.8. Non-Bayesian theories; 1.5. A Bayesian reading list; 2. FOUNDATIONS; 2.1. Beliefs and actions; 2.2. Decision problems; 2.2.1. Basic elements; 2.2.2. Formal representation; 2.3. Coherence and quantification; 2.3.1. Events, options and preferences; 2.3.2. Coherent preferences2.3.3. Quantification; 2.4. Beliefs and probabilities; 2.4.1. Representation of beliefs; 2.4.2. Revision of beliefs and Bayes' theorem; 2.4.3. Conditional independence; 2.4.4. Sequential revision of beliefs; 2.5. Actions and utilities; 2.5.1. Bounded sets of consequences; 2.5.2. Bounded decision problems; 2.5.3. General decision problems; 2.6. Sequential decision problems; 2.6.1. Complex decision problems; 2.6.2. Backward induction; 2.6.3. Design of experiments; 2.7. Inference and information; 2.7.1. Reporting beliefs as a decision problem; 2.7.2. The utility of a probability distribution2.7.3. Approximation and ; discrepancy; 2.7.4. Information; 2.8. Discussion and further references; 2.8.1. Operational definitions; 2.8.2. Quantitative coherence theories; 2.8.3. Related theories; 2.8.4. Critical issues; 3. GENERALISATIONS; 3.1. Generalised representation of beliefs; 3.1.1. Motivation; 3.1.2. Countable additivity; 3.2. Review of probability theory; 3.2.1. Random quantities and distributions; 3.2.2. Some particular univariate distributions; 3.2.3. Convergence and limit theorems; 3.2.4. Random vectors, Bayes' theorem; 3.2.5. Some particular multivariate distributions3.3. Generalised options and utilities; 3.3.1. Motivation and preliminaries; 3.3.2. Generalised preferences; 3.3.3. The value of information; 3.4. Generalised information measures; 3.4.1. The general problem of reporting beliefs; 3.4.2. The utility of a general probability distribution; 3.4.3. Generalised approximation and discrepancy; 3.4.4. Generalised information; 3.5. Discussion and further references; 3.5.1. The role of mathematics; 3.5.2. Critical issues; 4. MODELLING; 4.1 Statistical models; 4.1.1. Beliefs and models; 4.2. Exchangeability and related concepts4.2.1. Dependence and independence; 4.2.2. Exchangeability and partial exchangeability; 4.3. Models via exchangeability; 4.3.1. The Bernoulli and binomial models; 4.3.2. The multinomial model; 4.3.3. The general model; 4.4. Models via invariance; 4.4.1. The normal model; 4.4.2. The multivariate normal model; 4.4.3. The exponential model; 4.4.4. The geometric model; 4.5. Models via sufficient statistics; 4.5.1. Summary statistics; 4.5.2. Predictive sufficiency and parametric sufficiency; 4.5.3. Sufficiency and the exponential family; 4.5.4. Information measures and the exponential family
• Sommario/riassunto: This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critica