Importance reweighting reduces dependence on temperature in Gibbs samplers: an application to the coseismic geodetic inverse problem

S U M M A R Y We employ importance reweighting to extend Gibbs sampling (GS) to a larger class of unnormalized, multidimensional probability functions and to reduce the dependence of the results on critical temperature T ∗ , which is sometimes poorly known. Instead of sampling at T ∗ , we sample at several sampling temperatures, T S, in an interval centred on an estimate of T ∗ , correcting the results for each temperature to T = 1. Convergence is verified in part by agreement of marginal posterior distributions obtained at different T s. For the coseismic geodetic problem, experiments with synthetic data suggest that optimal sampling temperature varies inversely with the signal-to-noise ratio (SNR): as signal strength increases, optimal sampling temperature decreases. Inversion of surface displacement data from the 1994 Northridge earthquake confirms coseismic source parameters from other methods, while providing extra information in the form of properly scaled marginal posterior probability density functions.