Abstract
Estimating the parameters that describe a thermal problem using Bayes statistics requires the specification of appropriate prior probabilities. That is p(P|D) = p(D|P)p(P)/p(D) where P = parameters, D = data and p(P) is the prior probability. For thermal problems this requires prior probabilities for density, specific heat, thermal conductivities, surface convective coefficients, radiative properties, and local heat release, Q. For many problems it is common to choose Gaussian probabilities to represent the errors. If the standard deviation is large, then the predictions can lead to negative values — a result that is not possible except for Q. Variational Bayes (VB) is an alternative to Markov Chain Monte Carlo (MCMC) and assumes that complex distributions p(a,b) can be replaced by factorization, p(a,b) = p(a)p(b), the mean field theory of physics. Overall Variational Bayes is particularly important for posterior probabilities, p(a|D), that have multiple maxima distributions.
