Bayesian Data Analysis

  title={Bayesian Data Analysis},
  author={Andrew Gelman and John B. Carlin and Hal S. Stern and David B. Dunson and Aki Vehtari and Donald B. Rubin},
FUNDAMENTALS OF BAYESIAN INFERENCE Probability and Inference Single-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian Approaches Hierarchical Models FUNDAMENTALS OF BAYESIAN DATA ANALYSIS Model Checking Evaluating, Comparing, and Expanding Models Modeling Accounting for Data Collection Decision Analysis ADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation… Expand
Non-linear regression models for Approximate Bayesian Computation
A machine-learning approach to the estimation of the posterior density by introducing two innovations that fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. Expand
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additiveExpand
Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models
A general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models to cover: nonlinear evolution and observation functions, unknown parameters and (precision) hyperparameters and model comparison and prediction under uncertainty is described. Expand
Bayesian posterior mean estimates for Poisson hidden Markov models
  • J. Murakami
  • Mathematics, Computer Science
  • Comput. Stat. Data Anal.
  • 2009
An algorithm for calculating the exact posterior mean estimates of the parameter set of Poisson hidden Markov models in which the observation sequence is generated by a Poisson distribution whose parameter depends on the underlining discrete-time time-homogeneous Markov chain is exhibited. Expand
Hierarchical estimation of parameters in Bayesian networks
The main idea is to introduce a hyper-prior in the Multinomial–Dirichletmodel, traditionally used for conditional distribution estimation in Bayesian networks, and the resulting hierarchical model jointly estimates different conditional distributions belonging to the same conditional probability table, thus borrowing statistical strength from each other. Expand
Bayesian sensitivity analysis in elliptical linear regression models
Bayesian influence measures for linear regression models have been developed mostly for normal regression models with noninformative prior distributions for the unknown parameters. In this work weExpand
Accounting for parameter uncertainty in simulation input modeling
  • F. Zouaoui, James R. Wilson
  • Computer Science, Mathematics
  • Proceeding of the 2001 Winter Simulation Conference (Cat. No.01CH37304)
  • 2001
A Bayesian approach to probabilistic input modeling takes into account the parameter and stochastic uncertainties inherent in most simulations, and yields valid predictive inferences about the output quantities of interest. Expand
Computational Bayesian Statistics
This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes, along with a brief but complete and mathematically rigorous introduction to Bayesian inference. Expand
Nonparametric Bayesian modeling of complex networks: an introduction
This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks by deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. Expand
Semiparametric Bayesian inference in multiple equation models
This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equationsExpand