# 5.6 Bayesian Metrology

Keith Eberhardt, Charles Hagwood, Raghu Kacker, Mark Levenson, Hung-kung Liu, Mark Vangel, James Yen, Nien Fan Zhang
Statistical Engineering Division, ITL

Christoph Witzgall
Mathematical and Computational Sciences Division, ITL

During the past decade with increased computing power and new research developments, Bayesian statistical methods have proven to be valuable tools in diverse areas of statistical applications. Bayesian methods provide a unified framework for optimally combining information from multiple sources, resulting in simpler and improved statistical analyses. Despite the widespread growth in Bayesian methods, for the most part the field of metrology has not taken advantage of these methods. Both NIST researchers and their customers have much to gain from these methods.

Recognizing this potential, NIST statisticians have begun exploring the use of Bayesian methods in several metrological applications. After some initial research, a five year competence initiative on Bayesian metrology was started in FY99. Four specific areas are targeted: traceability, interlaboratory comparisons, calibration, and part inspection. These areas were chosen because of their importance to NIST and their potential benefit from Bayesian methods.

So far, members of the group have completed work on a Bayesian model for interlaboratory comparisons; explored the relationship between the ISO uncertainty procedure and Bayesian statistics; presented a review of Bayesian statistics to NIST staff; examined the use of Bayesian statistics in the certification of reference materials; and applied a Bayesian decision rule to the part inspection problem. For example, the accompanying figure displays the reduced cost of using a Bayesian decision rule in the part inspection problem, and the sensitivity of the result to various misspecifications. The left figure shows the resulting cost of the decision rule that does not use prior information. The three points correspond to three estimates of the measurement uncertainty, in which the value of 100% is correct. The right figure contains the same information for the decision rule that does use prior information. The three lines correspond to three estimates of the prior uncertainty, again where the value of 100% is correct. It is seen that even when incorrect values of the prior or measurement uncertainty are used, the Bayesian rule results in lower cost.

In the future, we will continue to research Bayesian statistical methods for metrological applications and demonstrate their value to NIST problems.

Figure 22: Reduced costs using a Bayesian decision rule.

Date created: 7/20/2001
Last updated: 7/20/2001