Sequential Monte Carlo and particle methods in inverse problems
Update: 2014-02-27
Description
Co-authors: Andrea Arnold (CWRU), Erkki Somersalo (CWRU)
In sequential Monte Carlo methods, the posterior distribution of an unknown of interest is explored in a sequential manner, by updating the Monte Carlo sample as new data arrive. In a similar fashion, particle filtering encompasses different sampling techniques to track the time course of a probability density that evolves in time based on partial observations of it. Methods that combine particle filters and sequential Monte Carlo have been developed for some time, mostly in connection with estimating unknown parameters in stochastic differential equations. In this talk, we present some new ideas suitable for treating large scale, non-stochastic, severely stiff systems of differential equations combining sequential Monte Carlo methods with classical numerical analysis concepts.
In sequential Monte Carlo methods, the posterior distribution of an unknown of interest is explored in a sequential manner, by updating the Monte Carlo sample as new data arrive. In a similar fashion, particle filtering encompasses different sampling techniques to track the time course of a probability density that evolves in time based on partial observations of it. Methods that combine particle filters and sequential Monte Carlo have been developed for some time, mostly in connection with estimating unknown parameters in stochastic differential equations. In this talk, we present some new ideas suitable for treating large scale, non-stochastic, severely stiff systems of differential equations combining sequential Monte Carlo methods with classical numerical analysis concepts.
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