Bayesian approach is developed for estimating the thermal conductivity of a homogeneous material from the temperature evolution acquired in few internal points. Temperature evolution is described by the classical one-dimensional heat equation, in which the thermal conductivity is one of the coefficients. Noisy measurements lead to a partial differential equation with stochastic coefficients and, after discretization in time and space, to a stochastic differential equation. Euler approximation at sampled points leads to a likelihood function, used in the Bayesian estimation of the thermal conductivity under different prior densities. An approach for generating latent observations over time in points where the temperature is not acquired is also included. Finally, the methodology is experimentally validated, considering a heated piece of polymethyl methacrylate (PMMA) with temperature measurements available in few points of the material and acquired at high frequency.
Fabrizio Ruggeri (B.Sc. Math Milano, M.Sc. Stats Carnegie Mellon, Ph.D. Stats Duke) is Research Director at the Italian National Research Council in Milano. His interests are mostly in Bayesian and industrial statistics, especially in robustness, decision analysis, reliability, stochastic processes; recently, he got involved in biostatistics and biology as well. Dr. Ruggeri is Adjunct Faculty at Polytechnic Institute (New York University), Faculty in the Ph.D. program in Mathematics and Statistics at University of Pavia, Foreign Faculty in the Ph.D. program in Statistics at the University of Valparaiso, Member of the Advisory Board of the Ph.D. program in Mathematical Engineering at Polytechnic of Milano. ASA Fellow and ISI Elected Member, Dr. Ruggeri is the current ISBA (International Society for Bayesian Analysis) President and former ENBIS (European Network for Business and Industrial Statistics) President. Author of more than 100 papers, one book and editor of three books, he is also the Editor-in-Chief of Applied Stochastic Models in Business and Industry (the official ISBIS journal) and Encyclopedia of Statistics in Quality and Reliability, besides being the Chair of the Bayesian Inference in Stochastic Processes workshops and Co-Director of the Applied Bayesian Statistics summer schools.