Speaker
Description
Modern experimental and imaging technologies provide high-resolution time-series measurements of biological systems, revealing dynamic behaviours that are difficult to analyze statistically. The underlying biological processes are typically noisy, partially observed, and high-dimensional, making Bayesian state-space models a natural framework for their analysis. However, exact Bayesian inference is intractable for nonlinear and non-Gaussian systems, and particle filters – widely used approximation schemes – suffer from high Monte Carlo variance in such settings. This limits their applicability to complex biological networks, where inference must remain stable to obtain reliable results. We developped a variance-reduced Bayesian inference method tailored to partially observed stochastic processes. Building on the Rao-Blackwell theorem, our approach decomposes the full system into two nonlinear subsystems: components that are kept explicit in the particle filter and components that are analytically marginalized. While classical Rao–Blackwellized particle filters rely on conditional linear-Gaussian assumptions, our method generalises the concept to fully nonlinear reaction-network dynamics by deriving conditional moment equations for the marginalized components. This yields a marginal particle filter that maintains the flexibility of simulation-based inference while reducing Monte Carlo variance. We demonstrate the approach using case studies of varying complexity.
