Bayesian Statistics An Introduction.

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Detalles Bibliográficos
Autor principal: Lee, Peter M.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2012.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Bayesian Statistics
  • Contents
  • Preface
  • Preface to the First Edition
  • 1 Preliminaries
  • 1.1 Probability and Bayes' Theorem
  • 1.1.1 Notation
  • 1.1.2 Axioms for probability
  • 1.1.3 'Unconditional' probability
  • 1.1.4 Odds
  • 1.1.5 Independence
  • 1.1.6 Some simple consequences of the axioms
  • Bayes' Theorem
  • 1.2 Examples on Bayes' Theorem
  • 1.2.1 The Biology of Twins
  • 1.2.2 A political example
  • 1.2.3 A warning
  • 1.3 Random variables
  • 1.3.1 Discrete random variables
  • 1.3.2 The binomial distribution
  • 1.3.3 Continuous random variables
  • 1.3.4 The normal distribution
  • 1.3.5 Mixed random variables
  • 1.4 Several random variables
  • 1.4.1 Two discrete random variables
  • 1.4.2 Two continuous random variables
  • 1.4.3 Bayes' Theorem for random variables
  • 1.4.4 Example
  • 1.4.5 One discrete variable and one continuous variable
  • 1.4.6 Independent random variables
  • 1.5 Means and variances
  • 1.5.1 Expectations
  • 1.5.2 The expectation of a sum and of a product
  • 1.5.3 Variance, precision and standard deviation
  • 1.5.4 Examples
  • 1.5.5 Variance of a sum
  • covariance and correlation
  • 1.5.6 Approximations to the mean and variance of a function of a random variable
  • 1.5.7 Conditional expectations and variances
  • 1.5.8 Medians and modes
  • 1.6 Exercises on Chapter 1
  • 2 Bayesian inference for the normal distribution
  • 2.1 Nature of Bayesian inference
  • 2.1.1 Preliminary remarks
  • 2.1.2 Post is prior times likelihood
  • 2.1.3 Likelihood can be multiplied by any constant
  • 2.1.4 Sequential use of Bayes' Theorem
  • 2.1.5 The predictive distribution
  • 2.1.6 A warning
  • 2.2 Normal prior and likelihood
  • 2.2.1 Posterior from a normal prior and likelihood
  • 2.2.2 Example
  • 2.2.3 Predictive distribution
  • 2.2.4 The nature of the assumptions made
  • 2.3 Several normal observations with a normal prior
  • 2.3.1 Posterior distribution
  • 2.3.2 Example
  • 2.3.3 Predictive distribution
  • 2.3.4 Robustness
  • 2.4 Dominant likelihoods
  • 2.4.1 Improper priors
  • 2.4.2 Approximation of proper priors by improper priors
  • 2.5 Locally uniform priors
  • 2.5.1 Bayes' postulate
  • 2.5.2 Data translated likelihoods
  • 2.5.3 Transformation of unknown parameters
  • 2.6 Highest density regions
  • 2.6.1 Need for summaries of posterior information
  • 2.6.2 Relation to classical statistics
  • 2.7 Normal variance
  • 2.7.1 A suitable prior for the normal variance
  • 2.7.2 Reference prior for the normal variance
  • 2.8 HDRs for the normal variance
  • 2.8.1 What distribution should we be considering?
  • 2.8.2 Example
  • 2.9 The role of sufficiency
  • 2.9.1 Definition of sufficiency
  • 2.9.2 Neyman's factorization theorem
  • 2.9.3 Sufficiency principle
  • 2.9.4 Examples
  • 2.9.5 Order statistics and minimal sufficient statistics
  • 2.9.6 Examples on minimal sufficiency
  • 2.10 Conjugate prior distributions
  • 2.10.1 Definition and difficulties

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