Bayesian methods

Markov Chain Monte Carlo (MCMC)

Markov Chain Monte Carlo (MCMC) is a family of computational algorithms for sampling from complex probability distributions, most commonly the posterior distributions that arise in Bayesian inference. Rather than computing posteriors analytically — which is rarely possible for realistic models — MCMC constructs a Markov chain whose stationary distribution is the target posterior and draws dependent samples from it, enabling full probabilistic inference for virtually any model.

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Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955
Brooks, S., Gelman, A., Jones, G. & Meng, X.-L. (Eds.). (2011). Handbook of Markov Chain Monte Carlo. CRC Press. ISBN: 978-1420079418

Referenced by

Automatic Differentiation Variational Inference Bayes Factor Test Bayesian ANOVA Bayesian Factor Analysis Bayesian Hierarchical Model Bayesian Inference with Measurement Error Bayesian Linear Regression Bayesian Logistic Regression Bayesian Model Averaging Bayesian Model Averaging with Measurement Error Bayesian Network Bayesian Nonparametric Methods Bayesian Regression Bayesian SEM Bayesian Structural Time Series Conjugate Prior Analysis Dirichlet Process Mixture Model Empirical Bayes Expectation Propagation Gibbs Sampling Hamiltonian Monte Carlo Hierarchical Bayesian Inference Hierarchical Hamiltonian Monte Carlo Hierarchical Variational Inference Laplace Approximation MCMC for Model Comparison MCMC with Measurement Error Multilevel Bayesian Inference No-U-Turn Sampler Particle Filter Robust Bayesian Model Averaging Robust Markov chain Monte Carlo Sequential Monte Carlo Slice Sampling Variational Inference

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