Chapters authored
Simulated Annealing of Constrained Statistical Functions
In 1987, Corana et al. published a simulated annealing (SA) algorithm. Soon thereafter in 1993, Goffe et al. coded the algorithm in FORTRAN and showed that SA could uncover global optima missed by traditional optimization software when applied to statistical modeling and estimation in economics (econometrics). This chapter shows how and why SA can be used successfully to perform likelihood-based statistical inference on models where likelihood is constrained by often very complicated functions defined on a compact parameter space. These constraints arise because likelihood-based inference involves comparing the maxima of constrained versus unconstrained statistical optimization models. The chapter begins with a review of the relevant literature on SA and constrained optimization using penalty techniques. Next, a constrained optimization problem based in maximum likelihood stress-strength modeling is introduced, and its statistical and numerical properties are summarized. SA is then used to solve a sequence of penalty-constrained optimization problems, and the results are used to construct a confidence interval for the parameter of interest in the statistical model. The chapter concludes with a brief summary of the results and some ways we were able to enhance the performance of SA in this setting.
Part of the book: Computational Optimization in Engineering