Elicitation of Information for Physical Science Problems

• Activity Number: 464
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 PM
• Sponsor: Government Statistics Section
• Author(s): Dipak K. Dey*+ and Nell Sedransk and Gyuhyeong Goh and Blaza Toman
• Companies: University of Connecticut and National Institute of Statistical Sciences and University of Connecticut and National Institute of Standars and Technology
• Keywords: Bayesian elicitation ; subjective probability ; higher moment elicitation ; calibration ; variance modeling ; key comparisons (metrology)

Abstract

In the physical sciences and engineering, variances and variance components are often of direct interest in addition to the primary quantity of interest. The functional models are often complex; and these often fail outside a region of measurement capability either because of departure from the functional form or because the signal to noise ratio increases rapidly at extremes of the range of measurement. Thus modeling non-homogeneous noise across the range of measurement is of intrinsic interest. Bayesian construction of models for the quantity of interest and also for the variance require elicitation of expert opinion, especially when these models are themselves complicated functions. In calibration, limits of measurement capability may be set either by excessive variance at each extreme or by failure of monotonicity of measurements. In metrological multi-laboratory studies several laboratories perform parallel calibrations of the same functional relationship. In both these cases implementing the Bayesian paradigm requires expert opinion to be elicited for variances or for higher moments. The theoretical basis for this process is presented and illustrated with data from examples.