Kai-Tang Fang

Bio: Kai-Tang Fang is an academic researcher from University of Oxford. The author has contributed to research in topics: Statistical inference & Multivariate statistics. The author has an hindex of 6, co-authored 6 publications receiving 2451 citations.

Design and Modeling for Computer Experiments

Abstract: PART I AN OVERVIEW INTRODUCTION Experiments and Their Statistical Designs Some Concepts in Experimental Design Computer Experiments Examples of Computer Experiments Space-Filling Designs Modeling Techniques Sensitivity Analysis Strategies for Computer Experiments and An Illustration Case Study Remarks on Computer Experiments Guidance of Reading This Book PART II DESIGNS FOR COMPUTER EXPERIMENTS Latin Hypercube Sampling and its Modifications Uniform Experimental Design Optimization in Construction of Designs for Computer Experiments PART III MODELING FOR COMPUTER EXPERIMENTS METAMODELING Model Interpretation Functional Response APPENDIX Abbreviation References Index Author Index

Number-theoretic methods in statistics

Abstract: Introduction and number-theoretic method. Numerical evaluation of multiple integral in statistics. Optimization and its applications in statistics. Representative points of a multivariate distribution. Experimental design and design of computer experiments. Statistical inference. Appendices: Tables of glp set. Integrations and uniform distributions on D.

Generalized Multivariate Analysis

Abstract: The theory of generalized multivariate analysis, based on elliptically contoured distributions, represents a great achievement in the field of multivariate analysis. The text discusses estimation of parameters, testing of hypotheses, and linear models employing the method of stochastic representation, rather than following the classical treatments. It is designed as a textbook for a one-semester course at postgraduate level and as a reference source for lecturers and researchers.

Growth Curve Models And Statistical Diagnostics

Abstract: Growth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the longitudinal study. It is not uncommon, however, to find outliers and influential observations in growth data that heavily affect statistical inference in growth curve models. This book provides a comprehensive introduction to the theory of growth curve models with an emphasis on statistical diagnostics. A variety of issues on model fittings and model diagnostics are addressed, and many criteria for outlier detection and influential observation identification are created within likelihood and Bayesian frameworks. This book is intended for postgraduates and statisticians whose research involves longitudinal study, multivariate analysis and statistical diagnostics, and also for scientists who analyze longitudinal data and repeated measures. The authors provide theoretical details on the model fittings and also emphasize the application of growth curve models to practical data analysis, which are reflected in the analysis of practical examples given in each chapter. The book assumes a basic knowledge of matrix algebra and linear regression. Jian-Xin Pan is a lecturer in Medical Statistics of Keele University in the U.K. He has published more than twenty papers on growth curve models, statistical diagnostics and linear/non-linear mixed models. He has a long-standing research interest in longitudinal data analysis and repeated measures in medicine and agriculture. Kai-Tai Fang is a chair professor in Statistics of Hong Kong Baptist University and a fellow of the Institute of Mathematical Statistics. He has published several books with Springer-Verlag, Chapman & Hall, and Science Press and is an author or co-author of over one hundred papers. His research interest includes generalized multivariate analysis, elliptically contoured distributions and uniform design.

The design and analysis of computer experiments

Abstract: Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example

Design and analysis of computer experiments

Abstract: The design and analysis of computer experiments as a relatively young research field is not only of high importance for many industrial areas but also presents new challenges and open questions for statisticians. This editorial introduces a special issue devoted to the topic. The included papers present an interesting mixture of recent developments in the field as they cover fundamental research on the design of experiments, models and analysis methods as well as more applied research connected to real-life applications.

Experimental design

Abstract: Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model

Abstract: This paper proposes the use of a quasi-random sequence for the estimation of the mixed multinomial logit model. The mixed multinomial structure is a flexible discrete choice formulation which accommodates general patterns of competitiveness as well as heterogeneity across individuals in sensitivity to exogenous variables. The estimation of this model has been achieved in the past using the pseudo-random maximum simulated likelihood method that evaluates the multi-dimensional integrals in the log-likelihood function by computing the integrand at a sequence of pseudo-random points and taking the average of the resulting integrand values. We suggest and implement an alternative quasi-random maximum simulated likelihood method which uses cleverly crafted non-random but more uniformly distributed sequences in place of the pseudo-random points in the estimation of the mixed logit model. Numerical experiments, in the context of intercity travel mode choice, indicate that the quasi-random method provides considerably better accuracy with much fewer draws and computational time than does the pseudo-random method. This result has the potential to dramatically influence the use of the mixed logit model in practice; specifically, given the flexibility of the mixed logit model, the use of the quasi-random estimation method should facilitate the application of behaviorally rich structures in discrete choice modeling.

Handbook of Monte Carlo Methods

Abstract: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: - Random variable and stochastic process generation - Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run - Discrete-event simulation - Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation - Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo - Estimation of derivatives and sensitivity analysis - Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB, a related Web site houses the MATLAB code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.