Alamo Symposium in Statistics

Narayanaswamy Balakrishnan
Department of Mathematics and Statistics
McMaster University, Canada

Title: Linear Prediction
Abstract: In this talk, I will briefly introduce the problem of optimal linear prediction and then point out various interesting connections of it to different notions in statistical inference. I will then discuss the idea of joint prediction and the associated optimality properties. I will also present some examples to illustrate the importance and usefulness of the developed results.

Professor N. Balakrishnan's Homepage (mcmaster.ca)

Biography
Professor Balakrishnan is a Distinguished University Professor at McMaster University, Hamilton, Ontario, Canada. He completed his Ph.D. in 1981 from the Indian Institute of Technology, Kanpur, India. Balakrishnan is a Fellow of the American Statistical Association, Fellow of the Institute of Mathematical Statistics, Elected Member of the International Statistical Institute, Honorary Member of the Greek Statistical Institute, and many more, including the Professor C. R. Rao Lifetime Achievement Award in 2020, by the Indian Society for Probability and Statistics. Balakrishnan's research interests include ordered data analysis, univariate and multivariate distribution theory, reliability theory, survival analysis, applied probability, stochastic orderings, nonparametric statistics, censoring methodology and statistical inference. “Bala”, as he prefers to be called, has well over 75 thousand citations of his work and an H-Index of 87! He holds editorial positions in more than 20 scholarly and professional journals, as well as over 60 distinguished visiting professorship positions in many universities around the world. He has been awarded an Honorary Doctorate Degree from the National and Kapodistrian University of Athens, Greece.

David W. Scott
Department of Statistics
Rice University

Title: Synergy of Nonparametric and Parametric Methods
Abstract: Parametric methodology by Fisher's maximum likelihood is 102 years old, largely supplanting Pearson's method of moments. Data science relies more and more on nonparametric methodology for function estimation and exploration. In this talk, we examine useful ways parametric and nonparametric approaches can complement each other, with examples in clustering.

Professor David Scott's Homepage (rice.edu)

Biography
Professor Scott's research interests focus on the analysis and understanding of data with many variables and cases. The research program encompasses basic theoretical studies of multivariate probability density estimation, computationally intensive algorithms in statistical computing, clustering, robust estimation, and data exploration using advanced techniques in computer visualization. Scott is a Fellow of the ASA, IMS, RSS, AAAS and ISI. He received the ASA Don Owen Award in 1993. He is the author of "Multivariate Density Estimation: Theory, Practice, and Visualization (John Wiley & Sons, 1992, 2nd edition 2015, and "STATISTICS: A Concise Mathematical Introduction for Students, Scientists, and Engineers (John Wiley & Sons, 2020). Scott is on the editorial board of the Probability and Statistics series of John Wiley & Sons. He served on the Committee on Applied and Theoretical Statistics, as editor of JCGS, co-editor (with W. Haerdle) of computational Statistics, and on the editorial board of Statistical Sciences. He has served as Associate Editor of JCGS, JASA, and the Annals of Statistics. Scott is currently co-editor-in-chief of Wiley's WIRES Review Journal, Computational Statistics. He has held several offices in the Statistical Graphics Section of the American Statistical Association, and elected to the Council of the IMS and IASC.

Brani Vidakovic
Department of Statistics
Texas A&M University

Title: Gamma-Minimax Wavelet Denoising of Signals with Low SNR
Abstract: One of the premises of robust Bayesian approach is that prior distributions can seldom be quantified or elicited exactly. It is assumed instead that a family of priors, Gamma, reflecting prior beliefs is elicited. The Gamma-minimax decision-theoretic approach to statistical inference favors an action/rule which utilizes information specified via Gamma, but guards against the least favorable prior in Gamma. This paradigm falls between Bayesian and minimax approaches. Under mild conditions on the model structure, the problem of finding the Gamma-minimax rule can be solved by a Bayesian machinery; the optimal rule is Bayes' with respect to the least favorable prior in Gamma.

We overview some early results in Gamma-minimax approach focusing on the results of Purdue's decision theory school in the context of robust Bayesian estimation. Some recent applications of Gamma-minimax in the context of wavelet shrinkage will be discussed. We demonstrate that wavelet shrinkage achieved with simple three-point priors can be competitive in the cases when signal-to-noise ratio is low. Some related Bayesian wavelet shrinkage methods will be discussed as well.

Finally, we argue that Gamma-minimax may see a renaissance in years to come with the increasing interest in Artificial Intelligence research. Some thinkers argue that particular aspects of human decision making can be well modeled by a Gamma-minimax paradigm.

Professor Brani Vidakovic's Homepage (tamu.edu)

Biography
Branislav Vidakovic, is a professor and head of the Department of Statistics at Texas A&M University, H.O. Hartley Chair in Statistics. Vidakovic holds a Ph.D. in statistics from Purdue University. His research interests include wavelets, Bayesian statistics, biostatistics, statistics in medicine, environmental statistics, and statistical signal and image processing. He is a fellow of the American Statistical Association and an elected member of the International Statistical Institute. Vidakovic has authored or co-authored several books and numerous journal articles.