Adaptive Markov chain Monte Carlo sampling and estimation in Mata
Matthew J. Baker
Hunter College and the Graduate Center, CUNY
New York, NY
matthew.baker@hunter.cuny.edu
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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.
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Matthew J. Baker
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amcmc(), amcmc_*(), bayesmixedlogit, mcmccqreg, Mata, Markov chain Monte Carlo, drawing from distributions, Bayesian estimation, mixed logit
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