An Integrated Treatment Of Monte Carlo Numerical Integration Procedures

蒙特卡罗模拟方法被广泛用于分析各种各样的计量经济学模型，这些模型涉及到没有解析解的积分。 该项目的目标是在一个统一的框架内集成两个主要的蒙特卡洛集成技术，目前可用于计量经济学家：有效的重要性抽样（EIS）和马尔可夫链蒙特卡洛（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上都优于另一种。实际上，它们是高度互补的。不严格地说，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学模型的关键组成部分（例如金融序列中的随机波动性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因子分解的情况。 另一方面，MCMC是在其最好的，当这种分解不是平凡的，例如，当处理高度非线性模型的参数的后验密度。 其次，甚至更根本的是，这两种方法都严重依赖于有效的采样器，用于其低维（通常是单变量）分量。EIS依赖于个人的“有效”的重要性抽样。MCMC需要从单个组分分布中精确提取，依赖于Metropolis-Hastings（MH）。 这两种方法密切相关。 普遍的批评是，环境影响报告书估计的蒙特卡罗方差可能不存在，这也适用于MH。更广泛的影响：这项建议将开发和传播新的计量经济学分析工具。 更具体地说，研究者将提供详细的模板，以充分利用两种方法的比较优势，构建高效的混合EIS-MCMC程序。 该项目将开发一个完全集成和灵活的工具箱，用于构建高效的个人EIS和MH采样器。 具体来说，调查人员将表明，通过应用一个简单的EIS辅助技术，他可以完全自动化的选择优化的MH samplers.These辅助EIS技术是目前完全运作的分布从指数家庭，在这种情况下，他们微不足道的辅助OLS回归。 研究者将通过使用从伪最大似然法和非参数文献中得到启发的技术来扩展该技术。 该项目将为验证这些组件采样器提供操作诊断测试。与本提案相关的所有技术论文、源代码、文档、应用程序和数据集都将通过专门针对该提案的网站提供。

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.