Capistrán, Marcos A.Infante Del Río, Juan Antonio2023-06-172023-06-172019-06-261741-597710.1080/17415977.2019.1632841https://hdl.handle.net/20.500.14352/12429“This is an Accepted Manuscript of an article published by Taylor & Francis in Inverse Problems in Science and Engineering on 26-jun-2019, available online: https://www.tandfonline.com/doi/full/10.1080/17415977.2019.1632841.”In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. The strong smoothing effect of the corresponding direct problem renders the inverse problem under consideration severely ill-posed. Thus specially tailored methods are necessary in order to obtain a stable solution. Consequently, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. [1]. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm (SVEMH) to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 10 cubed suffices to reliably retrieve the thermal conductivity coefficient.engjournal articlehttps://doi.org/10.1080/17415977.2019.1632841https://www.tandfonline.comopen accessMetropolis-HastingsFood technologyThermal conductivity coefficientGaussian Markov Random FieldHierarchical modelFísica-Modelos matemáticosInvestigación operativa (Matemáticas)Probabilidades (Matemáticas)Procesos estocásticosTecnología de los alimentos1207 Investigación Operativa1208.08 Procesos Estocásticos3309 Tecnología de Los Alimentos