| Description |
1 online resource (xxxiv, 564 pages) : illustrations |
| Series |
Wiley series in probability and statistics |
|
Wiley series in probability and statistics
|
| Contents |
Introducing Bayesian Analysis -- The foundations of Bayesian inference -- What is probability? -- Probability in classical statistics -- Subjective probability1 -- Subjective probability in Bayesian statistics -- Bayes theorem, discrete case -- Bayes theorem, continuous parameter -- Conjugate priors -- Bayesian updating with irregular priors -- Cromwell's Rule -- Bayesian updating as information accumulation -- Parameters as random variables, beliefs as distributions -- Communicating the results of a Bayesian analysis -- Bayesian point estimation -- Credible regions -- Asymptotic properties of posterior distributions -- Bayesian hypothesis testing -- Model choice -- Bayes factors -- From subjective beliefs to parameters and models -- Exchangeability -- Implications and extensions of de Finetti's Representation Theorem -- Finite exchangeability -- Exchangeability and prediction -- Conditional exchangeability and multiparameter models -- Exchangeability of parameters: hierarchical modeling -- Historical note -- Getting started: Bayesian analysis for simple models -- Learning about probabilities, rates and proportions -- Conjugate priors for probabilities, rates and proportions -- Bayes estimates as weighted averages of priors and data -- Parameterizations and priors -- The variance of the posterior density -- Associations between binary variables -- Learning from counts -- Predictive inference with count data -- Learning about a normal mean and variance -- Variance known -- Mean and variance unknown -- Conditionally conjugate prior -- An improper, reference prior -- Conflict between likelihood and prior -- Non-conjugate priors -- Regression models -- Bayesian regression analysis -- Likelihood function -- Conjugate prior -- Improper, reference prior -- Further reading -- Simulation Based Bayesian Analysis -- Monte Carlo methods -- Simulation consistency -- Inference for functions of parameters -- Marginalization via Monte Carlo integration -- Sampling algorithms -- Inverse-CDF method -- Importance sampling -- Accept-reject sampling -- Adaptive rejection sampling -- Further reading -- Markov chains -- Notation and definitions -- State space -- Transition kernel -- Properties of Markov chains -- Existence of a stationary distribution, discrete case -- Existence of a stationary distribution, continuous case -- Irreducibility -- Recurrence -- Invariant measure -- Reversibility -- Aperiodicity -- Convergence of Markov chains -- Speed of convergence -- Limit theorems for Markov chains -- Simulation inefficiency -- Central limit theorems for Markov chains -- Further reading -- Markov chain Monte Carlo -- Metropolis-Hastings algorithm -- Theory for the Metropolis-Hastings algorithm -- Choosing the proposal density -- Gibbs sampling -- Theory for the Gibbs sampler -- Connection to the Metropolis algorithm -- Deriving conditional densities for the Gibbs sampler: statistical models as conditional independence graphs -- Pathologies -- Data augmentation -- Missing data problems -- The slice sampler -- Implementing Markov chain Monte Carlo -- Software for Markov chain Monte Carlo -- Assessing convergence and run-length -- Working with BUGS/JAGS from R -- Tricks of the trade -- Thinning -- Blocking -- Reparameterization -- Other examples -- Further reading -- Advanced Applications in the Social Sciences -- Hierarchical Statistical Models -- Data and parameters that vary by groups: the case for hierarchical modeling -- Exchangeable parameters generate hierarchical models -- Borrowing strength via exchangeability -- Hierarchical modeling as a 'semi-pooling estimator -- Hierarchical modeling as a 'shrinkage estimator -- Computation via Markov chain Monte Carlo -- ANOVA as a hierarchical model -- One-way analysis of variance -- Two-way ANOVA -- Hierarchical models for longitudinal data -- Hierarchical models for non-normal data -- Multi-level models -- Bayesian analysis of choice making -- Regression models for binary responses -- Probit model via data augmentation -- Probit model via marginal data augmentation -- Logit model -- Binomial model for grouped binary data -- Ordered outcomes -- Identification -- Multinomial outcomes -- Multinomial logit (MNL) -- Independence of irrelevant alternatives -- Multinomial probit -- Bayesian analysis via MCMC -- Bayesian approaches to measurement -- Bayesian inference for latent states -- A formal role for prior information -- Inference for many parameters -- Factor analysis -- Likelihood and prior densities -- Identification -- Posterior density -- Inference over rank orderings of the latent variable -- Incorporating additional information via hierarchical modeling -- Item-response models -- Dynamic measurement models -- State-space models for [pooling the polls] -- Bayesian inference -- Appendices |
| Bibliography |
Includes bibliographical references and indexes |
| Notes |
Description based on print version record |
| Subject |
Social sciences -- Statistical methods
|
|
Bayesian statistical decision theory
|
| Form |
Electronic book
|
| Author |
Wiley InterScience (Online service)
|
| ISBN |
9780470686621 (electronic bk.) |
|
0470686626 (electronic bk.) |
|
