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

Documento depositado en el repositorio arxiv.org. Versión: arXiv:1512.03976v1 [stat.CO]We investigate a stochastic version of the synthetic multicellular cloc k 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 mult icellular system and pave the way for the design of probabilistic methods for the estimation of any unknow ns 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 the oretical 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 et al., 2010, applied to the same model and an approximate Bayesian comp utation sequential Monte Carlo method introduced by Mariño et al., 2013.This research has been partially supported by the Spanish Ministry of Economy and Competitiveness (projects TEC2012-38883-C02-01 COMPREHENSION and FIS2013-40653-P), the Spanish Ministry of Education, Culture and Sport (mobility award PRX15/00378), the Office of Naval Research (ONR) Global (Grant Award no. N62909-15-1-2011), the regional Government of Madrid (program CASI-CAM-CM S2013/ICE-2845) and the Cancer Research UK and the Eve Appeal Gynaecological Cancer Research Fund (grant ref. A12677) supported by the National Institute for Health Research (NIHR) University College London Hospitals (UCLH) Biomedical Research Centre