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Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference Dani Gamerman, Hedibert F. Lopes
Publisher: Taylor & Francis

The basic idea of MC3 is to simulate a Markov chain with an equilibrium distribution as . This first Loosely speaking, a Markov chain is a stochastic process in which the value at any step depends on the immediately preceding value, but doesn't depend on any values prior to that. Jul 20, 2013 - For a model with parameters and data , a key quantity in Bayesian inference is the posterior distribution of model parameters given by Bayes rule as , where is the probability distribution for prior to observing data , is the likelihood, and is the marginal probability of the data, used to normalize The numerically intense loop is often Markov Chain Monte Carlo (MCMC), which is a method to simulate observations from the posterior distribution of model parameters [1, 9]. Cox: about 90 pages of lucid perfection. These posteriors then provide us with the information we need to make Bayesian inferences about the parameters. Apr 21, 2011 - Convergence of Markov chain simulations can be monitored by measuring the diffusion and mixing of multiple independently-simulated chains, but different levels of convergence are appropriate for different goals. Relatively little work has been done in developing constraint-based approaches to structural learning in the presence of missing data. Apr 22, 2014 - This material focuses on Markov Chain Monte Carlo (MCMC) methods – especially the use of the Gibbs sampler to obtain marginal posterior densities. Oct 7, 2011 - The development of Markov chain Monte Carlo (MCMC) techniques means that there aren't any questions that classical econometricians can tackle more easily than their Bayesian colleagues, and there are quite a few once-intractable models - stochastic volatility, multinomial probit - where MCMC has . A very beautiful beautiful monograph founded on Keynes' approach is "The Algebra of Probable Inference" by Richard T. The appealing use of MCMC methods for Bayesian inference is to numerically calculate high-dimensional integrals based on the samples drawn from the equilibrium distribution [41]. Sep 23, 2013 - The stochastic approximation uses Monte Carlo sampling to achieve a point mass representation of the probability distribution. [48] describe a similar strategy using a Markov chain Monte Carlo technique.