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Title: Inverse prediction using functional data in a Bayesian framework Authors:  Audrey McCombs - Sandia National Laboratories (United States) [presenting]
Katherine Goode - Sandia National Laboratories (United States)
Kurtis Shuler - Sandia National Laboratories (United States)
Derek Tucker - Sandia National Laboratories (United States)
Adah Zhang - Sandia National Laboratories (United States)
Daniel Ries - Sandia National Laboratories (United States)
Abstract: Inverse prediction models have commonly been developed to handle scalar data from physical experiments. However, it is not uncommon for data to be collected in functional form, after which it must be aggregated to fit the structure of traditional methods. The resulting loss of information can be costly in expensive experiments. The functional inverse prediction (FIP) framework is a general approach which uses the full information in functional response data to provide inverse predictions. We build upon the FIP framework by applying Bayesian methods, creating more seamless uncertainty quantification, and adding flexibility through seemingly unrelated regression (SUR). Basis functions represent the functional response data in a matrix of response variables, which are regressed against a matrix of predictor variables for which inverse prediction is desired. Each variable in the response matrix defines a valid regression with its own set of predictor variables and mean function form, with error terms across the regression equations assumed to be correlated. The Bayesian implementation of the FIP is demonstrated with an application to nuclear forensics. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly-owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.