Dynamical equivalence classes for Markov jump processes

Markov Equivalence Classes for Maximal Ancestral Graphs

Ancestral graphs provide a class of graphs that can encode conditional independence re­ lations that arise in directed acyclic graph (DAG) models with latent and selection vari­ ables, corresponding to marginalization and conditioning. However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent. We introduce a simple representation of a Markov equiv­ ale...

Markov Chains and Jump Processes

JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes

Markov jump processes (MJPs) are used to model a wide range of phenomena from disease progression to RNA path folding. However, maximum likelihood estimation of parametric models leads to degenerate trajectories and inferential performance is poor in nonparametric models. We take a small-variance asymptotics (SVA) approach to overcome these limitations. We derive the small-variance asymptotics ...

Transition Path Theory for Markov Jump Processes

The framework of transition path theory (TPT) is developed in the context of continuous-time Markov chains on discrete state-spaces. Under assumption of ergodicity, TPT singles out any two subsets in the state-space and analyzes the statistical properties of the associated reactive trajectories, i.e. these trajectories by which the random walker transits from one subset to another. TPT gives pr...

Variational inference for Markov jump processes

Markov jump processes play an important role in a large number of application domains. However, realistic systems are analytically intractable and they have traditionally been analysed using simulation based techniques, which do not provide a framework for statistical inference. We propose a mean field approximation to perform posterior inference and parameter estimation. The approximation allo...