Stochastic Efficiency of Bayesian Markov Chain Monte Carlo in Spatial Econometric Models: An Empirical Comparison of Exact Sampling Methods
Stochastic Efficiency of Bayesian Markov Chain Monte Carlo in Spatial Econometric Models: An Empirical Comparison of Exact Sampling Methods
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DOI：
10.1111/gean.12135
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发表时间：
2018
影响因子：
3.6
通讯作者：
L. Wolf;L. Anselin;Daniel Arribas-Bel
中科院分区：
文献类型：
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作者：
L. Wolf;L. Anselin;Daniel Arribas-Bel
空间计量经济学规范对贝叶斯分析提出了独特的计算挑战，使其难以有效地估计模型。在文献中，主要的重点一直是扩展贝叶斯分析越来越复杂的空间模型。比较而言，常用的马尔可夫链蒙特卡罗（MCMC）采样器的随机效率较少受到关注。具体而言，贝叶斯方法来分析有效样本量和采样器，提供大的有效尺寸尚未在文献中得到充分考虑。因此，我们比较三个MCMC技术：熟悉的大都市内吉布斯抽样，切片内吉布斯抽样，和汉密尔顿蒙特卡洛。后两种方法虽然在其他领域很常见，但在贝叶斯空间计量经济学中并不常见。我们评估这些方法在四个不同的情况下，我们估计的空间自回归参数的混合回归，空间自回归规范（或空间滞后模型）。我们发现，现成的实现较新的高产模拟技术需要显着的适应是可行的。我们进一步发现，有效尺寸往往显着小于标称尺寸。此外，我们发现，提前停止模拟可能低估后验可信区间宽度时，有效样本量是小的。更广泛地说，我们认为，样本信息和停止规则值得更多的关注，在应用和基础贝叶斯空间计量经济学研究。
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.