Achievements
Projects Utilizing Bayesian Methods	Bayesian methodolgy has been applied in the following NIST projects. Bayesian meta-analysis of the toxic potency of smoke data. Bayesian methods for Neutron Depth Profiling (NDP). Application of Bayesian methods in consensus mean problems (in particular, SRM's). Application of Bayesian methods to key comparisons problem. Computational Metrology of Manufactured Parts. Inference on a Common Mean in an Interlaboratory Study.
Publications and Presentations	In addition, Bayesian methodology is being promoted via presentations and publications. Presentations and workshops Courses Publications Bayesian metrology seminar series
Bayesian Meta-Analysis of the Toxic Potency of Smoke Data	Blaza Toman performed a Bayesian Meta-Analysis of the toxic potency data for the International Study of the Sublethal Effects of Fire Smoke on Survivability and Health (SEFS). One of the goals of this study was to assess the lethality and incapacitation properties of smoke produced by various materials under three different combustion conditions. As the available published data was of varying quality, the Bayesian hierarchical model used for the meta-analysis had to allow for some of the studies to provide means and standard deviations and for some to provide only means. The "borrowing strength" property of the Byesian hierarchical model made it possible to provide measures of precision that would not be possible in classical meta-anlysis.
Bayesian Methods for Neutron Depth Profiling	SED staff: Mark S. Levenson and Kevin J. Coakley NIST Collaborators: G.Lamaze and H. Chen-Mayer Analytical Chemistry Division, CSTL D.S. Simons Surface and Microanalysis Division, CSTL Industrial Customers: Semiconductor industry. For more information, visit: http://www.eeel.nist.gov/810.01/thin_film_boron_implant.html Neutron Depth Profiling (NDP) is a nondestructive method for analysis of the concentration profile of an element in material. When a neutron is absorbed by a element, a nuclear reaction creates a particle (e.g. an alpha particle). As the particle travels through a material, it loses energy. The energy loss process is stochastic. Inferences about the concentration depth profile are based on the observed NDP energy spectrum of charged particles emitted due to specific nuclear reactions. To estimate the concentration profile, we propose a flexible class of Bayesian models. These models allow for the existence of sharp boundaries between regions of different intensities in the signal, as well as the incorporation of prior information on the locations of the boundaries. The use of the prior boundary information is adaptive to the data. The models are applied to NDP data collected from a multilayer diamond-like carbon film. A more detailed description of this analysis is documented in the following publication. Coakley, K. J. and Levenson, M. S. (2000). "Adaptive Use of Prior Information in Inverse Problems: An Application to Neutron Depth Profiling", Measurement Science and Technology, 11:3(2000), pp. 278-284.
Application of Bayesian Methodology in Consensus Means (and SRMs)	Blaza Toman developed and implemented (in BUGS) a Bayesian version of the "Consensus mean procedure". This procedure can be used on data from multiple laboratories or multiple methods and computes an estimate of the consensus mean and the associated HPD region. As in the DATAPLOT version, the data can be in the form of individual data points or in the form of the sufficient statistics (means and standard deviations). The Bayesian procedure allows for more complex models than is the case in the DATAPLOT procedure. For example, it is possible to include model terms that account for additional variability in the data such as "country" in the case of key comparison data with multiple labs per country. Blaza Toman applied the above procedure to the data from the Lake Superior Fish Tissue SRM (1946). This resulted in Bayesian estimates of roughly 100 compounds. Stefan Leigh applied the bounds on bias (BOB) methodology to a large number of SRM's using the CONSENSUS MEAN command in Dataplot. In particular, the following SRM's were analzed using the BOB methodology in the years 1999 - 2001. SRM 2384: Baking Chocolate SRM 1887a: Portland Cement SRM 2731: Hydrogen Sulfide in Nitrogen SRM 2614a: CO/Air, 45 mol/mol SRM 1678c: CO/N2.50, mol/mol SRM 762: Nickel Disks Magnetic Moment SRM 1085b: Wear Materials in Lubricating Oil SRM 1848: Lubricating Oil Additive Package SRM 1941b: Organics in Marine Sediment SRM 1993: Yig Sphjere Magnetic Moment Std SRM 2783: Air Partiuclate Matter on Filter SRM 2784: Bromate and Chlorate Anion Concentration SRM 2850/2851: Zeolite SRM 3115: Fund Dysprosium Standard Solution (Spectrophotom) SRM 3117a: Fund Europium Standard Solution (Spectrophotom) SRM 3122: Hafnium Standard Solution (Spectrophotom) SRM 3129a: Lithium Standard Solution (Spectrophotom) SRM 3159: Thorium Standard Solution (Spectrophotom) SRM 3181/3186: Anion Sulfate/Phosphate SRM 8486-8488: Fund Portland Cement Reference Clinkers
Bayesian Analysis of a Key Comparison	Blaza Toman is in the final stages of analysis of the CIPM Key Comparison: CCPR-K2.a Spectral Responsivity (900nm to 1600nm). The Bayesian consensus mean procedure will be the core method of analysis of this data. The analysis will produce a reference value and a measure of posterior precision for 15 wavelengths. It will further produce a measure of agreement between each laboratory and this reference value. As the transfer artifacts were manufactured by four different companies, the model uses a term to account for variability due to manufacturer. The Accelerometer Key Comparison was analyzed using the bounds on bias (BOB) methodology.
Date created: 8/28/2001 Last updated: 9/21/2001 Please email comments on this WWW page to sedwww@nist.gov.

Achievements