A0508
Title: Accurate Likelihood Evaluation via Geometrically Weighted Power Posterior and Efficient Importance Sampling
Authors: Nianling Wang - Capital University of Economics and Business (China) [presenting]
Abstract: Likelihood evaluation for latent variable models poses a formidable challenge in economics and finance, as the high dimensional integration with respect to the latent variables is required. The power posterior proposed by Friel and Pettitt(2008)is popular and convenient tool for high dimensional integral. And the efficient importance sampling (EIS, Richard and Zhang, 2007) algorithm is a useful tool. However, EIS algorithm does not guarantee a good proposal distribution for importance sampling and often suffers from numerical instability. In this paper, we firstly propose a reliable and robust method to likelihood estimation by defining a weighted power posterior (WPP) based on the proposal distribution from EIS algorithm, called as WPP-EIS approach. The new approach combines the advantages of EIS and power posteriors while avoiding their respective drawbacks. Then, we specify a set of regularity conditions, under which the consistency property of proposed likelihood estimators are provided. Finally, we use extensive simulation and empirical examples to compare the performance of traditional EIS estimators and proposed estimators for likelihood function. The results show that the performance of EIS estimator heavily relies on the quality of optimized proposal distribution while our WPP-EIS estimator is more reliable and robust to this problem.
