Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction A multiscale, non-parametric, Bayesian framework for identification of model parameters

A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation T (0) = T 0 q(1) = q 0 l = 1 c(x) =?    d dx −c(x) dT dx = 0 T (0) = T 0 q(1) = −c(x) dT dx x=1 = q 0 (1) 2 / 56 A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation T (0) = T 0 q(1) = q 0 c(x) =? T (x 1) = T 1 T (x 2) = T 2 T (x i) = T i T (x i+1) = T i+1 A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation T (0) = T 0 q(1) = q 0 c(x) =? T (x 1) = T 1 T (x 2) = T 2 T (x i) = T i T (x i+1) = T i+1 Motivation ∆x i = x i+1 − x i c(x) =? T (x i) = T i T (x i+1) = T i+1 d dx −c(x) dT dx = 0 → T i+1 − T i = −q 0 x i+1 x i 1 c(x) dx (2) c eff = x i+1 x i 1 c(x) dx −1 = − q 0 T i+1 − T i (3) 5 / 56 A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation ∆x i = x i+1 − x i c(x) =? T (x i) = T i T (x i+1) = T i+1 d dx −c(x) dT dx = 0 → T i+1 − T i = −q 0 x i+1 x i 1 c(x) dx (2) c eff = x i+1 x i 1 c(x) dx −1 = − q 0 T i+1 − T i (3) 5 / 56 A multiscale, non-parametric, Bayesian framework for identification of model parameters Motivation Bayesian Paradigm Nonparametric prior Inference Numerical Results Prediction Motivation c eff = x i+1 x i 1 c(x) dx −1 = − q 0 T i+1 − T i (4) Even in the absence of noise in the measurements, we can at best estimate the effective conductivity over the interval between two measurements. The actual conductivity …