MCMC, SMC and IS in High and Infinite Dimensional Spaces
Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations August 24, 2015 - August 28, 2015
Location: MSRI: Simons Auditorium
Bayesian inverse problem
elliptic inverse problems
absolutely continuous measure
measure preserving dynamics
Stochastic differential equation
28C20 - Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
60J10 - Markov chains (discrete-time Markov processes on discrete state spaces)
60H15 - Stochastic partial differential equations [See also 35R60]
The objective of these lectures is to demonstrate a unifying role played by the property of absolute continuity in understanding the behaviour of, and construction of effective algorithms to explore, probability measures in high and infinite dimensional spaces. Furthermore links to continuo time processes, and SPDEs in particular, will be made. These attached notes outline the structure of the lectures, and give various references to the literature that I will not, for reasons of brevity, give in full during the lectures themselves. These also include references to related material that I will not have time to cover in the lectures at all.
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