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Adaptive Markov chain Monte Carlo sampling and estimation in Mata

Matthew Baker ()

Stata Journal, 2014, vol. 14, issue 3, 623-661

Abstract: I describe algorithms for drawing from distributions using adaptive Markov chain Monte Carlo (MCMC) methods; I introduce a Mata function for performing adaptive MCMC, amcmc(); and I present a suite of functions, amcmc_*(), that allows an alternative implementation of adaptive MCMC. amcmc() and amcmc_*() can be used with models set up to work with Mata’s moptimize( ) (see [M-5] moptimize( )) or optimize( ) (see [M-5] optimize( )) or with standalone functions. To show how the routines can be used in estimation problems, I give two examples of what Chernozhukov and Hong (2003, Journal of Econometrics 115: 293–346) refer to as quasi-Bayesian or Laplace-type estimators—simulationbased estimators using MCMC sampling. In the first example, I illustrate basic ideas and show how a simple linear model can be fit by simulation. In the next example, I describe simulation-based estimation of a censored quantile regression model following Powell (1986, Journal of Econometrics 32: 143–155); the discussion describes the workings of the command mcmccqreg. I also present an example of how the routines can be used to draw from distributions without a normalizing constant and used in Bayesian estimation of a mixed logit model. This discussion introduces the command bayesmixedlogit. Copyright 2014 by StataCorp LP.

Keywords: amcmc(); amcmc_*(); bayesmixedlogit; mcmccqreg; Mata; Markov chain Monte Carlo; drawing from distributions; Bayesian estimation; mixed logit (search for similar items in EconPapers)
Date: 2014
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Working Paper: Adaptive Markov chain Monte Carlo sampling and estimation in Mata (2014) Downloads
Working Paper: Adaptive Markov chain Monte Carlo sampling and estimation in Mata (2013) Downloads
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Handle: RePEc:tsj:stataj:v:14:y:2014:i:3:p:623-661