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Variational Inference for Markov Jump Processes

Variational Inference for Markov Jump Processes

This video was recorded at Workshop on Practical Inference Methods for Mechanistic Modelling of Biological Systems (PIMMS), Glasgow 2007. Markov jump processes (MJPs) underpin our understanding of many important systems in science and technology. They provide a rigorous probabilistic framework to model the joint dynamics of groups (species) of interacting individuals, with applications ranging from information packets in a telecommunications network to epidemiology and population levels in the environment. These processes are usually non-linear and highly coupled, giving rise to non-trivial steady states (often referred to as emerging properties). Unfortunately, this also means that exact statistical inference is unfeasible and approximations must be made in the analysis of these systems. A traditional approach, which has been very successful throughout the past century, is to ignore the discrete nature of the processes and to approximate the stochastic process with a deterministic process whose behaviour is described by a system of non-linear, coupled ODEs. This approximation relies on the stochastic fluctuations being negligible compared to the average population counts. There are many important situations where this assumption is untenable: for example, stochastic fluctuations are reputed to be responsible for a number of important biological phenomena, from cell differentiation to pathogen virulence. Researchers are now able to obtain accurate estimates of the number of macromolecules of a certain species within a cell, prompting a need for practical statistical tools to handle discrete data.


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