An Integrated Treatment Of Monte Carlo Numerical Integration Procedures

蒙特卡罗数值积分程序的综合处理

• 批准号: 0516642
• 负责人: Jean-Francois Richard
• 金额: --
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0516642&HistoricalAwards=false
• 关键词: Integrated; Treatment; Monte; Carlo; Numerical

Monte Carlo simulation methods are widely used to analyze a wide range of econometric models involving integrals for which no analytical solutions exist. The objective of this project is integrating within a unified framework the two major Monte Carlo integration techniques currently available to econometricians: Efficient Importance Sampling (EIS) and Markov Chain Monte Carlo (MCMC). There are several important reasons for doing so. First, none of these two methods dominate the other for all purposes. Actually, they are highly complementary to one another. Loosely speaking EIS is very effective for the numerical integration of high-dimensional latent processes, which are increasingly key components of modern econometric models (examples are stochastic volatility in financial series and unobserved heterogeneity in panels) all situations for which there exist natural sequential factorizations which EIS fully exploits. On the other hand MCMC is at its best when such factorizations are not trivially available, e.g. when dealing with posterior densities of the parameters of highly non-linear models. Secondly, and even more fundamentally, both methods critically rely upon efficient samplers for their low-dimensional (typically univariate) components. EIS relies upon individual "efficient" importance samplers. MCMC, which requires exact draws from the individual component distributions relies upon Metropolis-Hastings (MH). The two methods are very closely related. The common criticism that the Monte Carlo variance of an EIS estimate might not exist also applies to MH.Broader Impacts: This proposal will develop and disseminate new tools for econometric analysis. More specifically, the investigator will provide detailed templates for the construction of efficient mixed EIS-MCMC procedures taking full advantage of the comparative advantages of both methods. The project will develop a fully integrated and flexible toolbox for the construction of efficient individual EIS and MH samplers. Specifically, the investigator will show that by the application of a simple EIS auxiliary technique he can fully automate the selection of optimized MH samplers.These auxiliary EIS techniques are currently fully operational for distributions from the exponential family, in which case they amount to trivial auxiliary OLS regressions. The investigator will extend the technique beyond that class by using techniques inspired from the pseudo Maximum Likelihood and non-parametric literatures. The project will provide operational diagnostic tests for the validation of these component samplers. All technical papers, source codes, documentation, applications, and datasets related to this proposal will be made available through a website dedicated to the proposal.

蒙特卡罗模拟方法被广泛地用于分析各种计量经济模型，这些模型涉及没有解析解的积分。该项目的目标是在一个统一的框架内整合目前可供计量经济学家使用的两种主要蒙特卡罗集成技术：有效重要性抽样（EIS）和马尔可夫链蒙特卡罗（MCMC）。这样做有几个重要的原因。首先，这两种方法中没有一种在所有目的下都优于另一种。实际上，它们是高度互补的。广义地说，EIS对于高维潜在过程的数值积分非常有效，这些过程越来越成为现代计量经济模型的关键组成部分（例如金融序列中的随机波动和面板中未观察到的异质性），所有存在EIS充分利用的自然顺序分解的情况。另一方面，当这种分解不容易获得时，例如处理高度非线性模型参数的后验密度时，MCMC是最佳的。其次，更根本的是，这两种方法都严重依赖于其低维（通常是单变量）成分的有效采样器。环境影响评估系统依赖于个体的“有效”重要性样本。MCMC依赖于Metropolis-Hastings (MH)，它需要从单个组件分布中获得精确的绘图。这两种方法密切相关。关于环境影响评估的蒙特卡罗方差可能不存在的普遍批评也适用于mh。更广泛的影响：本建议将开发和传播计量经济学分析的新工具。更具体地说，研究者将提供详细的模板，以构建有效的混合EIS-MCMC程序，充分利用两种方法的比较优势。该项目将开发一个完全集成和灵活的工具箱，用于构建高效的单个环境影响评估和MH采样器。具体来说，研究者将展示通过应用简单的EIS辅助技术，他可以完全自动化地选择优化的MH采样器。这些辅助的EIS技术目前完全适用于指数族的分布，在这种情况下，它们相当于微不足道的辅助OLS回归。研究者将通过使用从伪极大似然和非参数文献中获得灵感的技术，将技术扩展到该类之外。该项目将为这些组件取样器的验证提供操作诊断测试。与该提案相关的所有技术论文、源代码、文档、应用程序和数据集将通过一个专门针对该提案的网站提供。