Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem

We consider the statistical non-linear inverse problem of recovering the absorption term f > 0 in the heat equation {∂tu-12Δu+fu=0onO×(0,T)u=gon∂ O×(0,T)u(·,0)=u0onO, where O ϵ ℝd is a bounded domain, T < ∞ is a fixed time, and g, u 0 are given sufficiently smooth functions describing boundary and initial values respectively. The data...