BAYESIAN INFERENCE BASED ONLY ON SIMULATED LIKELIHOOD: PARTICLE FILTER ANALYSIS OF DYNAMIC ECONOMIC MODELS
证明在Metropolis-Hastings算法中使用无偏模拟似然估计量可实现贝叶斯推断，并通过粒子滤波生成似然估计，适用于微观、宏观和金融计量经济学，为可模拟的经济模型提供基于似然的推断方法。
We note that likelihood inference can be based on an unbiased simulation-based estimator of the likelihood when it is used inside a Metropolis–Hastings algorithm. This result has recently been introduced in statistics literature by Andrieu, Doucet, and Holenstein (2010, Journal of the Royal Statistical Society, Series B , 72, 269–342) and is perhaps surprising given the results on maximum simulated likelihood estimation. Bayesian inference based on simulated likelihood can be widely applied in microeconomics, macroeconomics, and financial econometrics. One way of generating unbiased estimates of the likelihood is through a particle filter. We illustrate these methods on four problems, producing rather generic methods. Taken together, these methods imply that if we can simulate from an economic model, we can carry out likelihood–based inference using its simulations.