Data processing of the GOMOS instrument by using an adaptive MCMC method

Abstract

European Space Agency's GOMOS (Global Ozone Monitoring by Occultation of Stars) instrument is a part of the ENVISAT-1 satellite, which will be launched in 1999. The GOMOS instrument will measure ozone and other trace gas densities in the stratosphere with stellar occultation technique. The data inversion of the GOMOS instrument is a non-linear problem, which can be solved with iterative least squares routines. In the statistical inversion theory the Bayesian approach to the problem involves the computation of the whole posteriori distribution instead of iteratively locating the maximum of it. We have studied different MCMC (Markov chain Monte Carlo) methods for this purpose. The choice of a suitable MCMC method is crucial for the convergence of the Markov chain. We have found the basic Metropolis algorithm with an adaptive proposal distribution most promising for the GOMOS data processing. This MCMC method allows us easily to study the sensitivity of the solution. Moreover, our examples show that sometimes a better estimate for the interesting quantity is achieved by computing the expectation value instead of the maximum likelihood solution.