Exploiting geometry to design MCMC methods for nonlinear dynamic systems



Abstract:



Nonlinear dynamic systems, in the form of massive sets of ordinary or delayed

differential equations (ODE), are becoming a key tool in systems biology,

enjoying soaring popularity in such problems as within-cell signalling pathways.

Most inference so far has used maximum-likelihood approaches: the indirect

and incomplete measurement of the hidden state, the high level of measurement noise, and the high

dimension of the parameter space make the full Bayesian inference rather

challenging. The intense computational cost of the ODE solver at each likelihood evaoluation

finishes the case for highly efficient Monte-Carlo methods: vanilla random walk

Metropolis Hastings is no option.

In this talk, we highlight those typical challenges on a few

concrete examples, and use recent Riemaniann Monte Carlo algorithms that exploit the geometry of the

parameter space endowed with the posterior Fisher information metric to sample more efficiently -- especially as

their slight overhead is more than compensated by reduction in the costly calls to ODE solvers.