Speaker：Guoliang Tian（South University of Science Technology of China）

Time：2021-07-23 09:30

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

In statistics teaching and research, Reverse Thinking and Divergent Thinking are two very important ways of thinking. Linear Inverse Problems with Positivity Restrictions has a very important application in signal processing and image reconstruction. It is called the first Fredholm integral equation in mathematics, and it is called the mixed density formula in statistics ( Formula for a Mixture of Densities). For the continuous case, Vardi and Lee (1993, JRSSB, Discussion Paper) used the EM algorithm to obtain an iterative solution to the integral equation. This report will show that by applying the inverse Bayesian formula twice, an iterative solution to this integral equation can be obtained immediately. For discrete cases, we will first explore how to transform the mathematical problem of the solution of a system of linear equations (A System of Linear Equations) into optimization problems with different objective functions; secondly, we will use reverse thinking and divergent thinking methods to further These optimization problems are transformed into different statistical estimation problems, so that the EM/MM algorithm can be effectively applied.