Considerations for Optimization and Estimation in the Real (Noisy) World
James Thompson · Wiley series in probability and statistics · 2011
As a matter of fact, the statistician is generally confronted with finding the maximum of an objective function which is contaminated by noise. In the case of simulation-based parameter estimation, the noise is introduced by the modeler himself. This chapter discusses two ways of dealing with this problem. Interestingly, both the Nelder-Mead algorithm and the Box-Hunter algorithm were built, not by numerical analysts, but by statisticians, working in the context of industrial product optimization. Any simulated annealing approach will be, effectively, a random search on a set much smaller than the entire feasible region of the parameter space. The power of the modern digital computer enables us realistically to carry out analysis for data of higher dimensionality. The multi-dimensional mode—finding algorithm dramatically improves with increasing dimensionality. Controlled Vocabulary Terms data analysis