Tailored randomized block MCMC methods with application to DSGE models
适配随机分块 MCMC 方法及其在 DSGE 模型中的应用AI 解读 ↓
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适配随机分块 MCMC 方法及其在 DSGE 模型中的应用
- 研究问题
- 如何改善贝叶斯模型后验抽样的混合效率，并处理高维或多峰分布中随机游走 Metropolis–Hastings 探索不足的问题？
- 方法与思路
- 作者提出 TaRB-MH，每轮随机分块并适配提议密度，以混合提议实现跨峰跳转，同时讨论边际似然估计。
- 材料陈述的贡献
- 摘要称在所列 DSGE 例子中，该方法降低抽样自相关；扩展算法能跨越多个后验峰，并给出边际似然估计的适配方式。
- 阅读关注点
- 应核对提议构造、随机分块与跨峰接受机制的有效性，以及比较算法的调参、计算成本和后验探索诊断是否充分。
- 阅读边界
- 仅据所给出版社摘要，效率优势来自特定示例，不能推广到所有后验分布；一般收敛条件与等成本比较未说明。
原文摘要
In this paper we develop new Markov chain Monte Carlo schemes for the estimation of Bayesian models. One key feature of our method, which we call the tailored randomized block Metropolis-Hastings (TaRB-MH) method, is the random clustering of the parameters at every iteration into an arbitrary number of blocks. Then each block is sequentially updated through an M-H step. Another feature is that the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing, following [7] and [8] and Chib and Ergashev (in press). We also provide an extended version of our method for sampling multi-modal distributions in which at a pre-specified mode jumping iteration, a single-block proposal is generated from one of the modal regions using a mixture proposal density, and this proposal is then accepted according to an M-H probability of move. At the non-mode jumping iterations, the draws are obtained by applying the TaRB-MH algorithm. We also discuss how the approaches of Chib (1995) and Chib and Jeliazkov (2001) can be adapted to these sampling schemes for estimating the model marginal likelihood. The methods are illustrated in several problems. In the DSGE model of Smets and Wouters (2007), for example, which involves a 36-dimensional posterior distribution, we show that the autocorrelations of the sampled draws from the TaRB-MH algorithm decay to zero within 30-40 lags for most parameters. In contrast, the sampled draws from the random-walk M-H method, the algorithm that has been used to date in the context of DSGE models, exhibit significant autocorrelations even at lags 2500 and beyond. Additionally, the RW-MH does not explore the same high density regions of the posterior distribution as the TaRB-MH algorithm. Another example concerns the model of An and Schorfheide (2007) where the posterior distribution is multi-modal. While the RW-MH algorithm is unable to jump from the low modal region to the high modal region, and vice-versa, we show that the extended TaRB-MH method explores the posterior distribution globally in an efficient manner.