An iterative importance sampler for Bayesian parameter estimation in stochastic models of multicellular clocks

TL;DR

This paper introduces an iterative importance sampling method for Bayesian parameter estimation in stochastic multicellular clock models, accounting for experimental noise and providing convergence guarantees.

Contribution

It develops a novel nonlinear population Monte Carlo algorithm with proven convergence for estimating parameters in noisy stochastic biological models.

Findings

The NPMC algorithm accurately estimates model parameters from noisy data.

Theoretical proof shows almost sure convergence of the importance sampling scheme.

Numerical comparisons demonstrate NPMC's effectiveness over existing methods.

Abstract

We investigate a stochastic version of the synthetic multicellular clock model proposed by Garcia-Ojalvo, Elowitz and Strogatz. By introducing dynamical noise in the model and assuming that the partial observations of the system can be contaminated by additive noise, we enable a principled mechanism to represent experimental uncertainties in the synthesis of the multicellular system and pave the way for the design of probabilistic methods for the estimation of any unknowns in the model. Within this setup, we investigate the use of an iterative importance sampling scheme, termed nonlinear population Monte Carlo (NPMC), for the Bayesian estimation of the model parameters. The algorithm yields a stochastic approximation of the posterior probability distribution of the unknown parameters given the available data (partial and possibly noisy observations). We prove a new theoretical result for this algorithm, which indicates that the approximations converge almost surely to the actual distributions, even when the weights in the importance sampling scheme cannot be computed exactly. We also provide a detailed numerical assessment of the stochastic multicellular model and the accuracy of the proposed NPMC algorithm, including a comparison with the popular particle Metropolis-Hastings algorithm of Andrieu {\em et al.}, 2010, applied to the same model and an approximate Bayesian computation sequential Monte Carlo method introduced by Mari\~no {\em et al.}, 2013.