Optimization & Numerical Methods in Statistics

This short course is part of our Master of Statistics & Data Science program for which non-students can exceptionally register.

Course outline

This is a web lecture with ONLINE Q&A sessions.
Numerical problems are frequently encountered by statisticians. Prominently, the estimation of the parameters of a statistical model requires the solution of an optimization problem. In a few simple cases, closed-form solutions exist but for many probability models the optimal parameter estimates have to be determined by means of an iterative algorithm. The goal of this course is threefold. First, we want to offer the readers an overview of some frequently used optimization algorithms in (applied) statistics. Second, we want to provide a framework for understanding the connections among several optimization algorithms as well as between optimization and aspects of statistical inference. Third, although very common, optimization is not the only numerical problem and therefore some important related topics such as numerical differentiation and integration will be covered.

Target audience

The intended target audience includes PhD students and researchers in a variety of fields, including biostatistics, psychometrics, educational measurement, public health, sociology. We aim at readers who apply and possibly develop statistical models and who wish to learn more about the basic concepts of numerical techniques, with an emphasis on optimization problems, and their use in statistics.

language

English

Prerequisites

Participants should have a basic knowledge of the principles of statistical inference. This includes some familiarity with the concept of a likelihood function and likelihood-based inference for linear, binomial, multinomial, and logistic regression models. Readers should also have a basic understanding of matrix algebra. A working knowledge of the basic elements of univariate calculus is also a prerequisite, including (the concepts of continuity of a function, derivative and integration).

Presenters

Francis Tuerlinckx is Professor of Psychology at the KU Leuven in Belgium. He received the Master degree in psychology (1996) and a Ph.D. in psychology (2000) from the KU Leuven. He was a postdoc at the Department of Statistics of Columbia University (New York). In general, Francis Tuerlinckx’ research deals with the mathematical modeling of various aspects of human behavior. More specifically, he works on item response theory, reaction time modeling, and dynamical systems data analysis for human emotions.

Geert Molenberghs is Professor of Biostatistics at the Universiteit Hasselt and KU Leuven in Belgium. He received the B.S. degree in mathematics (1988) and a Ph.D. in biostatistics (1993) from the Universiteit Antwerpen. Dr Molenberghs published methodological work on surrogate markers in clinical trials, categorical data, longitudinal data analysis, and on the analysis of non-response in clinical and epidemiological studies. He served as Joint Editor for Applied Statistics (2001-2004), Co-editor for Biometrics (2007–2009) and as President of the International Biometric Society (2004-2005). He currently is Co-editor for Biostatistics (2010–2012). He was elected Fellow of the American Statistical Association and received the Guy Medal in Bronze from the Royal Statistical Society. He has held visiting positions at the Harvard School of Public Health (Boston, MA). He is founding director of the Center for Statistics at Hasselt University and currently the director of the Interuniversity Institute for Biostatistics and statistical Bioinformatics, I-BioStat, a joint initiative of the
Hasselt and Leuven universities.

Katrijn van Deun obtained a Master in psychology, a Master’s degree in statistics and a PhD in psychology. Her main area of expertise is scaling, clustering and component analysis techniques, which she applies in the field of bioinformatics. She has various publications in both methodological and substantive journals in bioinformatics. Katrijn is secretary of the Dutch/Flemish Classification society.

Tom Wilderjans is a post-doctoral researcher at the Fund for Scientific Research (FWO-Flanders). He obtained a Masters degree (2005) and a PhD (2009) in Mathematical Psychology from the KU Leuven. Tom’s research deals with multivariate data analysis (component analysis, clustering, and combinations thereof) and model selection.

Course Materials

• The course material will be made available.
• Background reading:
  Everitt, B.S. (1987). Introduction to Optimization Methods and Their Application in Statistics. London: Chapman & Hall.
  Lange, K. (1999). Numerical Analysis for Statisticians. New York: Springer.
  Lange, K. (2004). Optimization. New York: Springer.