Efficient $$\hbox {SMC}^2$$ SMC 2 schemes for stochastic kinetic models

Abstract

Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed-data likelihood. There has therefore been considerable attention given to the design of pseudo-marginal Markov chain Monte Carlo algorithms for such models. However, these methods are typically computationally intensive, often require careful tuning and must be restarted from scratch upon receipt of new observations. Sequential Monte Carlo (SMC) methods on the other hand aim to efficiently reuse posterior samples at each time point. Despite their appeal, applying SMC schemes in scenarios with both dynamic states and static parameters is made difficult by the problem of particle degeneracy. A principled approach for overcoming this problem is to move each parameter particle through a Metropolis-Hastings kernel that leaves the target invariant. This rejuvenation step is key to a recently proposed SMC 2 algorithm, which can be seen as the pseudo-marginal analogue of an idealised scheme known as iterated batch importance sampling. Computing the parameter weights in SMC 2 requires running a particle filter over dynamic states to unbiasedly estimate the intractable observed-data likelihood up to the current time point. In this paper, we propose to use an auxiliary particle filter inside the SMC 2 scheme. Our method uses two recently proposed constructs for sampling conditioned jump processes, and we find that the resulting inference schemes typically require fewer state particles than when using a simple bootstrap filter. Using two applications, we compare the performance B Andrew Golightly

A framework for variational inference and data assimilation of soil biogeochemical models using state space approximations and normalizing flows

“…Going forward, we recommend that inference approaches involving state space model approximation of stochastic SBMs be used in future biogeochemical data assimilation, fitting, and model comparison research in pursuit of superior computational stability, flexibility, and efficiency. SDE systems are far more robust than ODE systems at accommodating prior density, initial condition, and model structure proposals that are inconsistent with the true data generating process (Whitaker, 2016;Wiqvist et al, 2021) (Golightly & Kypraios, 2018), stochastic gradient Hamiltonian Monte Carlo (Chen et al, 2014), stochastic gradient langevin dynamics (Brosse et al, 2018), and stochastic gradient Markov chain Monte Carlo (Aicher et al, 2019;Nemeth & Fearnhead, 2021).…”

A framework for variational inference and data assimilation of soil biogeochemical models using state space approximations and normalizing flows

“…Going forward, we recommend that inference approaches involving state space model approximation of stochastic SBMs be used in future biogeochemical data assimilation, fitting, and model comparison research in pursuit of superior computational stability, flexibility, and efficiency. SDE systems are far more robust than ODE systems at accommodating prior density, initial condition, and model structure proposals that are inconsistent with the true data generating process (Whitaker, 2016;Wiqvist et al, 2021) (Golightly & Kypraios, 2018), stochastic gradient Hamiltonian Monte Carlo (Chen et al, 2014), stochastic gradient langevin dynamics (Brosse et al, 2018), and stochastic gradient Markov chain Monte Carlo (Aicher et al, 2019;Nemeth & Fearnhead, 2021).…”

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

“…Interpolation of observed data with MCMC sampling is used in (Golightly and Wilkinson, 2005) to jointly estimate unobserved states and reaction rates. MCMC sampling can be combined with importance sampling to reduce computational complexity and simulation times (Golightly et al, 2015). Conditional density importance sampling (CDIS) is introduced in (Gupta and Rawlings, 2014) as an alternative to MCMC parameter estimation.…”

“…Sequential MC (SMC) method represents posterior distribution in Bayesian inference by a set of samples referred to as particles (Gordon et al, 1993;Doucet et al, 2001;Tanevski et al, 2010;Yang et al, 2014), so it is also known as particle filter (Gordon et al, 1993;Doucet et al, 2001;Lillacci and Khammash, 2012;Golightly et al, 2015). SMC methods for joint state and parameter estimation are proposed in (Nemeth et al, 2014).…”

“…A proposal distribution for Bayesian analysis is obtained by pMCMC sampling in . Proposal samples to calculate marginal likelihoods are obtained for CLE and LNA approximations in (Golightly et al, 2015). Particle filter is validated and shown to be more robust than LS data fitting by exploiting noise statistics of data in (Lillacci and Khammash, 2012).…”