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Title: Backward filtering forward guiding for Markov processes Authors:  Frank van der Meulen - Delft University of Technology (Netherlands) [presenting]
Moritz Schauer - Chalmers University of Technology - University of Gothenburg (Sweden)
Abstract: Consider a Markovian process $X$ that evolves on a tree where transitions over edges correspond to running a continuous-time Markov process for a fixed time interval. At each vertex, leaves can be attached that represent observations. A key example consists of a diffusion process on a tree, appearing for example in phylogenetics. Assume the forward dynamics are parametrised by the parameter theta. We will discuss the Backward Filtering Forward Guiding algorithm for sampling $X$ conditional on its values at the leaf vertices. This in turn can be exploited for designing Bayesian computational methods such as MCMC and SMC for inferring theta.