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MCMCpack is a software package designed to allow users to perform Bayesian inference via Markov chain Monte Carlo (MCMC). More specifically, MCMCpack is a formal R package. R is an extremely powerful language and environment for statistical computation and graphics. The lead developers of the MCMCpack project are Andrew D.Martin (University of Michigan), Kevin M. Quinn (UC Berkeley), and Jong Hee Park (Seoul National University). We assume that users of this package will be familiar with R.

Currently MCMCpack allows the user to perform Bayesian inference via simulation from the posterior distributions of the following models: linear regression (with Gaussian errors), Quinn's dynamic ecological inference model, Wakefield's hierarchial ecological inference model, a probit model, a logistic regression model, a one-dimensional item response theory model, a K-dimensional item response theory model, a robust k-dimensional item response theory model, a Normal theory factor analysis model, a mixed response factor analysis model, an ordinal item response theory model, a Poisson regression, a Poisson changepoint model, a tobit regression, a multinomial logit model, an SVD regression model, and an ordered probit model. The package also contains densities and random number generators for commonly used distributions that are not part of the standard R distribution, a general purpose Metropolis sampling algorithm, functions to compute Bayes factors for some models, a handful of teaching models, and some data visualization tools for ecological inference.

To maximize computational efficiency, the actual sampling for each model is done in compiled C++ using the Scythe Statistical Library. The posterior samples returned by each function are returned as mcmc objects, which can easily be summarized and manipulated by the coda package. Please consult the coda documentation for a comprehensive list of functions that can be used to analyze the posterior sample.