Dynamic Bayesian Approaches to the Statistical Calibration Problem

Abstract

DYNAMIC BAYESIAN APPROACHES TO THE STATISTICAL CALIBRATION PROBLEM By Derick L. Rivers, Ph.D. A Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University. Virginia Commonwealth University, 2014. Director: Dr. Edward L. Boone, Associate Professor, Department of Statistical Sciences and Operations Research The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the “classical” approach and the “inverse” regression approach. Both of these models are static models and are used to estimate “exact” measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM framework is used to capture the time-varying parameters that may be changing or drifting over time. Dynamic based approaches to the linear, nonlinear, and multivariate calibration problem are presented in this dissertation. Simulation studies are conducted where the dynamic models are compared to some well known “static” calibration approaches in the literature from both the frequentist and Bayesian perspectives. Applications to microwave radiometry are given. Chapter