Bayesian inference for a discretely observed stochastic kinetic model

Abstract

The ability to infer parameters of gene regulatory networks is emerging as a key problem in systems biology. The biochemical data are intrinsically stochastic and tend to be observed by means of discrete-time sampling systems, which are often limited in their completeness. In this paper we explore how to make Bayesian inference for the kinetic rate constants of regulatory networks, using the stochastic kinetic Lotka-Volterra system as a model. This simple model describes behaviour typical of many biochemical networks which exhibit auto-regulatory behaviour. Various MCMC algorithms are described and their performance evaluated in several data-poor scenarios. An algorithm based on an approximating process is shown to be particularly efficient.

Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

“…Rather, we can only observe the state of the system X(t i ) = x i at discrete time points t i ∈ [0, T]. The solution proposed by Boys et al [6] is to treat the trajectories, as well as the number, times and types of transitions, between observed time points to those latent variables. This leads to a data augmentation framework [24] in which a Markov chain is constructed to sample from the joint posterior of the parameters and the latent variables.…”

“…The resulting algorithm therefore is computationally demanding, thus limiting its applicability on small and relatively simple MJPs. A more efficient version of the algorithm is also suggested in Boys et al [6], where instead of simulating the trajectories between observations using the exact MJP an approximate proposal distribution is employed to sample trajectories which are accepted or rejected using the Metropolis-Hastings ratio. …”

“…Therefore, a data augmentation approach similar to the one in Boys et al [6] has to be followed. However, there is no longer the need to sample the number, times and types of state transitions as the MJP is approximated with a continuous process.…”

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

“…Application areas include (but are not limited to) systems biology (Golightly and Wilkinson 2005;Wilkinson 2012), predator-prey interaction (Ferm et al 2008;Boys et al 2008) and epidemiology (Lin and Ludkovski 2013;McKinley et al 2014). Here, we focus on the MJP representation of a stochastic kinetic model (SKM), whereby transitions of species in a reaction network are described probabilistically via an instantaneous reaction rate or hazard, which depends on the current system state and a set of rate constants, with the latter typically the object of inference.…”

“…Early attempts based on data augmentation were used by Gibson and Renshaw (1998) (see also O'Neill and Roberts (1999)) in the context of epidemiology, and by Boys et al (2008) for more general reaction networks. Unfortunately, such methods can suffer from poor mixing due to dependence between the parameters and latent states to be imputed.…”