Jack C. Lee

Bio: Jack C. Lee is an academic researcher from National Chiao Tung University. The author has contributed to research in topics: Bayesian probability & Markov chain Monte Carlo. The author has an hindex of 19, co-authored 50 publications receiving 1356 citations.

Finite mixture modelling using the skew normal distribution

Abstract: Normal mixture models provide the most popular framework for mod- elling heterogeneity in a population with continuous outcomes arising in a variety of subclasses. In the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied prob- lems. In this article, we address the problem of analyzing a mixture of skew nor- mal distributions from the likelihood-based and Bayesian perspectives, respectively. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates. Also, a fully Bayesian approach using the Markov chain Monte Carlo method is developed to carry out posterior analyses. Numerical results are illustrated through two examples.

Robust mixture modeling using the skew t distribution

Abstract: A finite mixture model using the Student's t distribution has been recognized as a robust extension of normal mixtures. Recently, a mixture of skew normal distributions has been found to be effective in the treatment of heterogeneous data involving asymmetric behaviors across subclasses. In this article, we propose a robust mixture framework based on the skew t distribution to efficiently deal with heavy-tailedness, extra skewness and multimodality in a wide range of settings. Statistical mixture modeling based on normal, Student's t and skew normal distributions can be viewed as special cases of the skew t mixture model. We present analytically simple EM-type algorithms for iteratively computing maximum likelihood estimates. The proposed methodology is illustrated by analyzing a real data example.

Bayesian inference of threshold autoregressive models

Abstract: . The study of non-linear time series has attracted much attention in recent years. Among the models proposed, the threshold autoregressive (TAR) model and bilinear model are perhaps the most popular ones in the literature. However, the TAR model has not been widely used in practice due to the difficulty in identifying the threshold variable and in estimating the associated threshold value. The main focal point of this paper is a Bayesian analysis of the TAR model with two regimes. The desired marginal posterior densities of the threshold value and other parameters are obtained via the Gibbs sampler. This approach avoids sophisticated analytical and numerical multiple integration. It also provides an estimate of the threshold value directly without resorting to a subjective choice from various scatterplots. We illustrate the proposed methodology by using simulation experiments and analysis of a real data set.

Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data.

Abstract: This paper extends the classical linear mixed model by considering a multivariate skew-normal assumption for the distribution of random effects. We present an efficient hybrid ECME-NR algorithm for the computation of maximum-likelihood estimates of parameters. A score test statistic for testing the existence of skewness preference among random effects is developed. The technique for the prediction of future responses under this model is also investigated. The methodology is illustrated through an application to Framingham cholesterol data and a simulation study.

The Predictive Sample Reuse Method with Applications

Abstract: An account is given of a recently devised method of prediction based on sample reuse techniques. It is most useful in low structure data paradigms that involve minimal assumptions. A series of applications demonstrating the technique is presented.

Finite Mixture and Markov Switching Models

Abstract: WINNER OF THE 2007 DEGROOT PRIZE! The prominence of finite mixture modelling is greater than ever. Many important statistical topics like clustering data, outlier treatment, or dealing with unobserved heterogeneity involve finite mixture models in some way or other. The area of potential applications goes beyond simple data analysis and extends to regression analysis and to non-linear time series analysis using Markov switching models. For more than the hundred years since Karl Pearson showed in 1894 how to estimate the five parameters of a mixture of two normal distributions using the method of moments, statistical inference for finite mixture models has been a challenge to everybody who deals with them. In the past ten years, very powerful computational tools emerged for dealing with these models which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book reviews these techniques and covers the most recent advances in the field, among them bridge sampling techniques and reversible jump Markov chain Monte Carlo methods. It is the first time that the Bayesian perspective of finite mixture modelling is systematically presented in book form. It is argued that the Bayesian approach provides much insight in this context and is easily implemented in practice. Although the main focus is on Bayesian inference, the author reviews several frequentist techniques, especially selecting the number of components of a finite mixture model, and discusses some of their shortcomings compared to the Bayesian approach. The aim of this book is to impart the finite mixture and Markov switching approach to statistical modelling to a wide-ranging community. This includes not only statisticians, but also biologists, economists, engineers, financial agents, market researcher, medical researchers or any other frequent user of statistical models. This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated. Researchers familiar with the subject also will profit from reading this book. The presentation is rather informal without abandoning mathematical correctness. Previous notions of Bayesian inference and Monte Carlo simulation are useful but not needed.

DDSolver: An Add-In Program for Modeling and Comparison of Drug Dissolution Profiles

Abstract: In recent years, several mathematical models have been developed for analysis of drug dissolution data, and many different mathematical approaches have been proposed to assess the similarity between two drug dissolution profiles. However, until now, no computer program has been reported for simplifying the calculations involved in the modeling and comparison of dissolution profiles. The purposes of this article are: (1) to describe the development of a software program, called DDSolver, for facilitating the assessment of similarity between drug dissolution data; (2) to establish a model library for fitting dissolution data using a nonlinear optimization method; and (3) to provide a brief review of available approaches for comparing drug dissolution profiles. DDSolver is a freely available program which is capable of performing most existing techniques for comparing drug release data, including exploratory data analysis, univariate ANOVA, ratio test procedures, the difference factor f 1, the similarity factor f 2, the Rescigno indices, the 90% confidence interval (CI) of difference method, the multivariate statistical distance method, the model-dependent method, the bootstrap f 2 method, and Chow and Ki’s time series method. Sample runs of the program demonstrated that the results were satisfactory, and DDSolver could be served as a useful tool for dissolution data analysis.

A Predictive Approach to Model Selection

Abstract: This article offers a synthesis of Bayesian and sample-reuse approaches to the problem of high structure model selection geared to prediction. Similar methods are used for low structure models. Nested and nonnested paradigms are discussed and examples given.