Statistics Seminar on

Threshold Accepting in Statistics

by

Prof. Peter Winker, Justus-Liebig-Universität Gießen

Abstract. Applied statistical research depends to a large extent on optimization techniques. Classical examples comprise parameter estimation and model selection. There is no guarantee that standard optimization tools, e.g. generalized gradient methods, are able to solve these problems efficiently. In the presence of multiple local optima or flat regions of the objective function, suboptimal results might challenge the quality of the statistical analysis based on such methods. Some examples will be discussed.

During the last few years, the use of optimization heuristics is increasingly considered as a potential alternative to overcome the shortcomings of classical procedures in highly complex problem settings. After providing an attempt to classify the growing number of such methods, a specific local search heuristic, threshold accepting, is introduced and discussed in some more detail with references to several applications in statistics. Threshold accepting is particularly well suited for problems on discrete search spaces.
Threshold accepting as most other optimization heuristics contains stochastic components. Thus, not only an application of such methods to statistics is of interest, but also the application of statistics to the analysis of the stochastic properties of the results produced with such tools. Some approaches are presented.

This seminar is organised within the School on High Dimensional Design an Data Modelling organised at ECLT by Prof. Phil Brown and Prof. Irene Poli.