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Bayesian Metrology Project


During the past decade with increased computing power and new research developments, Bayesian statistical methods have become practical 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 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 the potential, NIST statisticians began 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.


Research, develop, and apply Bayesian methods to the metrological problems of NIST; promulgate results to other metrology laboratories and to NIST customers.

Four specific areas are targeted:

  1. traceability,  
  2. interlaboratory comparisons,  
  3. calibration, and  
  4. part inspection.
These areas were chosen because of their importance to NIST and their potential benefit from Bayesian methods.

Additional Technical Details:

ITL has performed the following work for this project.

  • Multiple publications on interlaboratory and key comparisons.
  • Organization of a session on Bayesian Methods in Physical Sciences at ASA 1999.
  • Portion of NIST uncertainty course devoted to Bayesian statistics.
  • Within-project seminars on ISO uncertainty and Bayesian statistics, BUGS (a software program for Bayesian computation), Bayesian calibration and tolerance intervals, Bayesian approach to SRM certification, and empirical Bayes methods.
  • Initial work on a monograph on Bayesian metrology.


Major Accomplishments:

The timelines and milestones for this project are:
  • FY99: Complete publication on a Bayesian model for interlaboratory comparisons; explore the relationship between the ISO uncertainty procedure and Bayesian statistics; present review of Bayesian statistics to NIST staff.  
  • FY00: Learn applicable theory and methodology for Bayesian hierchial model (Gaussian) models, acquire BUGS (Bayesian computational software), and apply it to an example of NIST data.  
  • FY 01: Apply hierarchical Bayes model to NIST examples--Interlaboratory Proficiency Study. Formulate Bayesian models for (Gaussian and non-Gaussian) SRM data, for calibration data, part inspection plans; construct optimal Bayesian designs for calibrations and for prototypical interlaboratory comparison experiments.  
  • FY 02: Implement Bayesian hierarchical (Gaussian) analytic methodology as web-product. Develop Bayesian model for Type "B" uncertainty, and develop elicitation methodology and software for modeling expert opinion. Define analyses for canonical applications and continue to implement Bayesian methodology as web-product in parallel to SEMATECH HANDBOOK (for frequentist approach).  
  • FY 03: Develop or implement graphical representations of Bayesian hierarchical models; Implement Bayesian methodology and incorporate into standard NIST statistical practices.

Lead Organizational Unit:



  • Charles Hagwood (Division 898, ITL),  
  • Raghu Kacker (Division 898, ITL),   
  • Mark Vangel (Division 898, ITL),  
  • Christoph Witzgall (Division 891, ITL),  
  • Hung-kung Liu (Division 898, ITL),  
  • James Yen (Division 898, ITL),  
  • Nien-Fan Zhang (Division 898, ITL),  
  • Andrew Rukhin (Division 898, ITL and UMBC).  
  • Barry Taylor (Division 840, PL),  
  • Tyler Estler (Division 821, MEL),

Charles Hagwood
100 Bureau Drive, M/S 8980
Gaithersburg, MD 20899-8980