Bayesian solution for nonlinear and non‐Gaussian inverse problems by Markov chain Monte Carlo method

Abstract

In this paper we apply the Bayesian approach for solving retrieval problems encountered in remote sensing measurements of the atmosphere. The approach gives as a solution the posterior probability distribution of the unknown parameters and allows a possibility to combine new measurements with prior knowledge. While the Bayesian solution can easily be computed in the case of linear, Gaussian inverse problems, the characterization of the solution in all other cases is difficult. Here we apply Markov chain Monte Carlo (MCMC) method for computing posterior distributions for inverse problems. The advantage of the MCMC technique is that it can easily be implemented in a great variety of inverse problems including nonlinear problems with various prior or noise structures. The MCMC algorithms are not yet effective enough for operational processing of large amounts of data, but they provide excellent tools for development and validation purposes. We have applied successfully the MCMC technique to the inverse problem arising from the Global Ozone Monitoring by Occultation of Stars instrument.