Bayesian Multiple-Use Calibration

• Activity Number: 246
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): Mark Vangel*+
• Affiliation(s): Dana-Farber Cancer Institute
• Keywords: Gibbs Sampler ; metrology ; Bayesian classification

Abstract

Consider a linear regression model in which some (or all) of the independent variables are functions of a single unknown parameter of interest (e.g., a polynomial model). The data consist of a training dataset followed by observations of the dependent variable alone. One would like to express uncertainty in the parameter of interest. This problem is usually referred to as linear calibration. Measurement systems almost always involve calibration, so statistical techniques for calibration are of central importance to metrology.

Most of the literature on this topic concerns inference on the value of the independent variable corresponding to a single future dependent value. In practice, however, one usually uses a calibration curve many times before recalibrating. A Bayesian approach to this problem is, in principle, less complex than the standard frequentist metholdogy, and the resulting intervals are much easier to interpret. Recent work on this Bayesian calibration problem will be discussed and illustrated with examples.