Bayesian calibration of stochastic kinetic models using a Dirichlet process mixture of Gaussian processes

Abstract

Stochastic kinetic models (SKMs) are an effective way to model complex biochemical and cellular systems. They describe how a number of species in a system interact with one another through time. To infer the parameters of these models, a number of MCMC techniques exist but these can often be both computationally intensive and time consuming due to the constant need to simulate from the stochastic process at each iteration. When inferring parameters of quite large or complex models, these simulations can become unmanageable. To tackle this, emulators can be used to approximate SKM output, a popular choice being a Gaussian process, however these do not provide accurate descriptions of output with multiple modes. A SKM of particular interest which exhibits this behaviour is the Schl ogl system which describes an exchange of chemicals between two material baths. This system, under certain conditions, is bistable. This motivates the need to nd a exible emulator that can capture this bimodality. By using a Dirichlet process mixture of Gaussian processes we explain how this model has useful features such as the exibility to increase or decrease the number of components in the mixture throughout parameter space as necessary. We apply the model to training data for the Schl ogl system with the aim of inferring the rate constants that gave rise to some noisy data from the system. We also look at a further approximation using variational inference and nd that this gives signi cant gains in terms of e ciency.