China
Africa
Explore chapters and articles related to this topic
Markov Chain Monte Carlo
Published in Richard McElreath, Statistical Rethinking, 2020
In practice, Gibbs sampling can be very efficient, and it’s the basis of popular Bayesian model fitting software like BUGS (Bayesian inference Using Gibbs Sampling) and JAGS (Just Another Gibbs Sampler). In these programs, you compose your statistical model using definitions very similar to what you’ve been doing so far in this book. The software automates the rest, to the best of its ability.
Postauditing and Cost Estimation Applications: An Illustration of MCMC Simulation for Bayesian Regression Analysis
Published in The Engineering Economist, 2019
There are numerous kinds of software, both open source and proprietary, that can be used to implement Bayesian analysis using MCMC simulation. Popular open source MCMC software include WinBUGS, OpenBUGS, JAGS, BRugs, R2WinBUGS, R-based MCMC, Python-based MCMC (PyMC), Stan, and RStan among others. Proprietary software include Stata (14) Bayesian Analysis and SAS/STAT(R) 9.2. The popular WinBUGS software is an interactive Windows program for Bayesian analysis of complex statistical models. It uses BUGS (Bayesian inference Using Gibbs Sampling), and samples are drawn from their conditional (posterior) distribution instead of the marginal posterior distributions (Stata Bayesian Analysis Reference Manual 2015). Standard MCMC software such as WinBUGS uses the Gibbs sampling algorithm, the MH algorithm, or a hybrid of both. In addition, the reversible-jump MCMC algorithm is gaining acceptance. In order to overcome the inefficiencies in Gibbs sampling and MH algorithms, ideas from physics have been used develop the newer and more robust HMC algorithm, which can be used independently (continuous parameters) or combined with Gibbs sampling and the MH algorithm for discrete parameters (Gelman et al. 2014). The HMC algorithm is implemented in the open source project Stan (Sampling through adoptive neighborhoods).