TY - JOUR
T1 - Stochastic Efficiency of Bayesian Markov Chain Monte Carlo in Spatial Econometric Models
T2 - An Empirical Comparison of Exact Sampling Methods
AU - Wolf, Levi John
AU - Anselin, Luc
AU - Arribas-Bel, Daniel
N1 - Funding Information:
This research was funded in part by NIH Award 7R01CA1266858–06, GeoSpatial Factors and Impacts II. An earlier version was presented at the 63rd Annual North American Meetings of the Regional Science Association International, November 9–12, 2016. Comments from the participants are greatly appreciated, as are suggestions on earlier drafts by Sergio Rey.
Publisher Copyright:
© 2017 The Ohio State University
PY - 2018/1
Y1 - 2018/1
N2 - Spatial econometric specifications pose unique computational challenges to Bayesian analysis, making it difficult to estimate models efficiently. In the literature, the main focus has been on extending Bayesian analysis to increasingly complex spatial models. The stochastic efficiency of commonly used Markov Chain Monte Carlo (MCMC) samplers has received less attention by comparison. Specifically, Bayesian methods to analyze effective sample size and samplers that provide large effective size have not been thoroughly considered in the literature. Thus, we compare three MCMC techniques: the familiar Metropolis-within-Gibbs sampling, Slice-within-Gibbs sampling, and Hamiltonian Monte Carlo. The latter two methods, while common in other domains, are not as widely encountered in Bayesian spatial econometrics. We assess these methods across four different scenarios in which we estimate the spatial autoregressive parameter in a mixed regressive, spatial autoregressive specification (or, spatial lag model). We find that off-the-shelf implementations of the newer high-yield simulation techniques require significant adaptation to be viable. We further find that the effective sizes are often significantly smaller than nominal sizes. In addition, we find that stopping simulation early may understate posterior credible interval widths when effective sample size is small. More broadly, we suggest that sample information and stopping rules deserve more attention in both applied and basic Bayesian spatial econometric research.
AB - Spatial econometric specifications pose unique computational challenges to Bayesian analysis, making it difficult to estimate models efficiently. In the literature, the main focus has been on extending Bayesian analysis to increasingly complex spatial models. The stochastic efficiency of commonly used Markov Chain Monte Carlo (MCMC) samplers has received less attention by comparison. Specifically, Bayesian methods to analyze effective sample size and samplers that provide large effective size have not been thoroughly considered in the literature. Thus, we compare three MCMC techniques: the familiar Metropolis-within-Gibbs sampling, Slice-within-Gibbs sampling, and Hamiltonian Monte Carlo. The latter two methods, while common in other domains, are not as widely encountered in Bayesian spatial econometrics. We assess these methods across four different scenarios in which we estimate the spatial autoregressive parameter in a mixed regressive, spatial autoregressive specification (or, spatial lag model). We find that off-the-shelf implementations of the newer high-yield simulation techniques require significant adaptation to be viable. We further find that the effective sizes are often significantly smaller than nominal sizes. In addition, we find that stopping simulation early may understate posterior credible interval widths when effective sample size is small. More broadly, we suggest that sample information and stopping rules deserve more attention in both applied and basic Bayesian spatial econometric research.
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U2 - 10.1111/gean.12135
DO - 10.1111/gean.12135
M3 - Article
AN - SCOPUS:85028765512
SN - 0016-7363
VL - 50
SP - 97
EP - 119
JO - Geographical Analysis
JF - Geographical Analysis
IS - 1
ER -