Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces

Understand

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space.

• Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time Markov processes.
• It may then be of interest to find a measure $\nu$, from within a simple class of measures, which approximates $\mu$.
• This problem is studied in the case where the Kullback-Leibler divergence is employed to measure the quality of the approximation.