Title:
Stochastic Monte Carlo methods for non-linear statistical inverse problems

Abstract:
Non-linear inverse problems using sparse measurement sets suffer from
difficulties of non Gaussian uncetainty distributions and multiple
maximum a posteriori solutions.  As an example, lidar instrumentation
can estimate aerosol extinction and backscatter coefficients at a
limited number of wavelengths, typically lower than the number of
degrees of freedom of aerosol models.  
Acurate uncertainty assesment is crucial to situations such as this
one.  Uncertainty is represented in the form of a posterior
probability density function (PDF).  This can include a prior PDF
which can be incorporated as a more robust alternative to parameter
constraints.  
The posterior PDF can theoretically be used to assess uncertainty of
specific aerosol properties in the form of a derived marginal PDF,
however it is not computationally practical with PDFs having more
than a few dimensions.  In the approach that I present for performing
uncertainty assesments the Metropolis-Hastings Markov chain Monte
Carlo algorithm is used to generate samples of aerosol model
parameters congruent with their posterior PDF.  The method is
effectivly a blending of Metropolis-Hastings, genetic algorithm, and
Gauss-Newton inverse method, and can deal with the difficulties put
forth.