TaChen Liang 梁大成教授

1972 B.S. in mathematics , National Tsing-Hua University
1976 M.S. in Applied Mathematicsistics , National Tsing-Hua University
1984 PhD in Statistics , Purdue University

        My research interests are in the areas of ranking and selection, Bayesian and empirical Bayes inferences. Recently, my research centers on the development of Bayesian and empirical Bayes methodologies dealing with empirical Bayes selection procedures, empirical Bayes estimation and testing, simultaneous selection and/or inspection, and Bayes sampling plans. Significant research results are obtained and summarized as follows.

1.Empirical Bayes selection procedures

Empirical Bayes selection procedure are constructed by borrowing information from historical data improve the decision for present component problem. According to the prior information about the parameters of interest, two approaches are adopted : parametric and nonparametric  empirical Bayes.

2.Bayesian and hierarchical Bayesian selection procedures

Bayesian and hierarchical Byesian selection procedures are derived using the decision-theoretic approach for several selection problems. The optimality of the Bayesian procedure is studied. The relative efficiency of the hierarchical Bayesian procedure compared with the pure Bayesian procedure is investigated.

3.Empirical Bayes testing and estimation 

Empirical Bayes testing and estimation problems are studied using nonparametric empirical Bayes approach. We investigate the relating asymptotic optimality and establish the rate of convergence of the proposed empirical Bayes estimators and/or tests. New estimators are proposed and new analysis approaches/techniques are developed. The research results are very fruitful.

4.Simultaneous selection / inspection

The empirical Bayes idea is applied for the simultaneous selection/testing/inspection problems. We incorporate information from each population involving in the n-component problem. Based on the combined information, we improve the decision for each component decision problem . The relative regret ( compared with the minimum Bayes risk) is used as a measure of performance of the concerned procedures. The asymptotic optimality of the procedures are investigated.

5.Bayesian sampling plans

Variable sampling plans for the exponential distribution based on type I censored data is investigated. Using a suitable loss function, a Bayesian variable sampling plan(n_0,t_0,δ₀^L) is derived. Technique for numerical computation are addressed. In terms of Bayes risks, we compare the performance of (n_0,t_0,δ₀^L) with "Bayesian" variable sampling plan (n_0,t_0,δ₀^L) of  Lam. The numerical results indicate that under the same conditions, the proposed sampling plan (n_0,t_0,δ₀^L) is superior to the sampling plan (n_0,t_0,δ₀^L) of Lam in the sense that the Bayes risk of (n_0,t_0,δ₀^L) is less than that of (n_0,t_0,δ₀^L)