报告题目：Discretization approximation: An alternative to Monte Carlo in Bayesian computation

报告人：熊世峰

时间：10月17日 9：30-10：30

地点：国产自拍 106会议室

报告摘要：In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating posterior density values as probability masses at pre-specified support points. The resulting discrete distribution can be a good approximation to the target posterior distribution. All posterior quantities, including means, standard deviations, and quantiles, can be approximated by those of this completely known discrete distribution. We establish the convergence rate of discretization approximation as the number of support points goes to infinity. If the support points are generated from quasi-Monte Carlo sequences, then the rate is actually the same as that in integration approximation, generally faster than the optimal statistical rate. In this sense, discretization approximation is superior to the popular Markov chain Monte Carlo method. We also provide random sampling and representation point construction methods based on discretization approximation. Numerical examples including some benchmarks demonstrate that the proposed method performs quite well for both low-dimensional and high-dimensional cases.

报告人简介：熊世峰，中国科学院数学与系统科学研究院研究员，实验设计与不确定性量化研究中心主任，中国现场统计研究会数字孪生与不确定性量化分会理事长。研究方向包括计算机实验与不确定性量化、高维数据分析、统计推断、机器学习等。统计应用方面的研究主要是计算机辅助工艺设计与产品设计、数字孪生、交通大数据分析等。曾获国防科技进步二等奖、国科大校级研究生优秀课程教师奖等。