Bayesian Statistics Seminar
North Carolina State University
presents
Dr. Stella Karuri
North Carolina State University
"Integration using Bayesian Quadrature"
ABSTRACT
Integration is a crucial aspect of Bayesian analysis and computer experiments. The general technique of Bayesian quadrature is to make the fullest possible use of function evaluations; hence it is an ideal method for the numerical integration of costly functions. We examine Bayesian quadrature using the Best Linear Unbiased Predictor approach. Application of Bayesian quadrature yields results with lower absolute errors, when compared to the mid-point rule. The spread of the design, as well as model specification is more crucial in functions which exhibit strong non-linear trends. We developed a sequential integration algorithm which works by dynamically dividing the region of integration into more homogenous sub-regions and applying Bayesian quadrature within the sub-regions. We present examples where the sequential algorithm yields good results with fewer evaluations as compared to Monte Carlo integration. The algorithm also enables high dimension integration with less computation cost.
Tuesday, October, 11, 2005
4:00 - 5:00 pm
208 Patterson Hall