【数学学院】A novel MM algorithm and the mode-sharing method in Bayesian computation for the analysis of general incomplete categorical data

报告题目： A novel MM algorithm and the mode-sharing method in Bayesian computation for the analysis of general incomplete categorical data

报告人：Guo-Liang TIAN

报告人单位：Dept of Mathematics, Southern University of Science and Technology

报告时间：7月16日（周一）下午16:00-17:00

报告地点：数学学院北110

邀请人：潘建新

Abstract:

Incomplete categorical data often occur in the fields such as biomedicine, 

epidemiology, psychology and sports. In this paper, we first develop a novel 

minorization-maximization (MM) algorithm for calculating the MLE of parameters for 

general incomplete categorical data. How to develop the corresponding stochastic 

counterparts to existing MM algorithms is an important research topic. Up to now, we 

have not seen any papers that proposed a stochastic version of an MM algorithm. This 

is the first paper to propose a mode-sharing method in Bayesian computation for 

general incomplete categorical data by developing a new acceptance-rejection (AR) 

algorithm aided with the proposed MM algorithm. The key idea is to construct a class of

envelope densities indexed by a working parameter and to identify a specific 

envelope density which can overcome the four drawbacks associated with the traditional

AR algorithm. The proposed mode-sharing method has three significant characteristics:

(1) it can automatically establish a family of envelope densities  {g_\lambda(.):  

\lambda \in S_\lambda} indexed by a working parameter \lambda, where each member in the

family shares mode with the posterior density; (2) With the one-dimensional grid method

searching over the finite interval S_\lambda, it can identify an optimal working 

parameter \lambda_opt by maximizing the theoretical acceptance probability, yielding a

best easy-sampling envelope density g_{\lambda_opt}(.), which is more dispersive than 

the posterior density; (3) it can obtain the most optimal envelope constant c_opt by 

using the mode-sharing theorem (indicating that the high-dimensional optimization can 

be completely avoided) or by using the proposed MM algorithm again. Finally, four real

data sets are used to illustrate the proposed methodologies.

(This is a joint work with Dr. Yin LIU and Professor Man-Lai TANG)

来源链接：http://math.scu.edu.cn/info/1062/3352.htm