  We consider the nonlinear inverse problem of reconstructing the heat
conductivity of a cooling fin, modeled by a 2-dimensional steady-state equation
with Robin boundary conditions. The Metropolis Hastings Markov Chain Monte
Carlo algorithm is studied and implemented, as well as the notion of priors. By
analyzing the results using certain trial conductivities, we formulate several
distinct priors to aid in obtaining the solution. These priors are associated
with different identifiable parts of the reconstruction, such as areas with
vanishing, constant, or varying slopes. Although more research is required for
some non-constant conductivities, we believe that using several priors
simultaneously could help in solving the problem.
