Inverse prediction of PuO 2 processing conditions using Bayesian seemingly unrelated regression with functional data Provisionally Accepted

Audrey L. McCombs^1* Madeline A. Stricklin² Katherine Goode¹ Jose G. Huerta¹ Kurtis W. Shuler¹ James D. Tucker¹ Adah Zhang¹ Daniel Ries¹

• ¹Sandia National Laboratories (DOE), United States
• ²Los Alamos National Laboratory (DOE), United States

Over the past decade, a variety of innovative methodologies have been developed to better characterize the relationships between processing conditions and the physical, morphological, and chemical features of special nuclear material (SNM). Different processing conditions generate SNM products with different features, known as "signatures" because they are indicative of the processing conditions used to produce the material. These signatures can potentially allow a forensic analyst to determine which processes were used to produce the SNM, and make inferences about where the material originated. This paper investigates a statistical technique for relating processing conditions to the morphological features of PuO 2 particles. We develop a Bayesian implementation of seemingly unrelated regression (SUR) to inverse-predict unknown PuO 2 processing conditions from known PuO 2 features. Model results from simulated data demonstrate the usefulness of the technique. Applied to empirical data from a benchscale experiment specifically designed with inverse prediction in mind, our model successfully predicts nitric acid concentration, while results for Pu concentration and precipitation temperature were equivalent to a simple mean model. Our technique compliments other recent methodologies developed for forensic analysis of nuclear material, and can be generalized across the field of chemometrics for application to other materials.