Inference for epidemic models with time-varying infection rates: Tracking the dynamics of oak processionary moth in the UK.

Invasive pests pose a great threat to forest, woodland, and urban tree ecosystems. The oak processionary moth (OPM) is a destructive pest of oak trees, first reported in the UK in 2006. Despite great efforts to contain the outbreak within the original infested area of South-East England, OPM continues to spread.Here, we analyze data consisting of the numbers of OPM nests removed each year from two parks in London between 2013 and 2020. Using a state-of-the-art Bayesian inference scheme, we estimate the parameters for a stochastic compartmental SIR (susceptible, infested, and removed) model with a time-varying infestation rate to describe the spread of OPM.We find that the infestation rate and subsequent basic reproduction number have remained constant since 2013 (with R 0 between one and two). This shows further controls must be taken to reduce R 0 below one and stop the advance of OPM into other areas of England. Synthesis. Our findings demonstrate the applicability of the SIR model to describing OPM spread and show that further controls are needed to reduce the infestation rate. The proposed statistical methodology is a powerful tool to explore the nature of a time-varying infestation rate, applicable to other partially observed time series epidemic data.

Guided proposals for efficient weighted stochastic simulation.

Rare event probabilities play an important role in the understanding of the behavior of biochemical systems. Due to the intractability of the most natural Markov jump process representation of a system of interest, rare event probabilities are typically estimated using importance sampling. While the resulting algorithm is reasonably well developed, the problem of choosing a suitable importance density is far from straightforward. We therefore leverage recent developments on simulation of conditioned jump processes to propose an importance density that is simple to implement and requires no tuning. Our results demonstrate superior performance over some existing approaches.

Paediatric Rehabilitation Ingredients Measure: a new tool for identifying paediatric neurorehabilitation content.

AIM: To develop an instrument (Paediatric Rehabilitation Ingredients Measure [PRISM]) for quantitative estimation of contents of interdisciplinary neurorehabilitation for use in studies of relationships between rehabilitation treatment delivered and severity-adjusted outcomes after acquired brain injury (ABI). METHOD: The measure was developed using an ingredients-mediators-outcomes model consistent with the International Classification of Functioning, Disability and Health, a literature review, and other current initiatives in the development of rehabilitation treatment taxonomies, with item codevelopment in workshops with rehabilitation professionals. Interrater reliability was assessed in inpatient and residential paediatric rehabilitation settings. RESULTS: Although sometimes an initially unfamiliar perspective on rehabilitation practice, PRISM's acceptability amongst professionals was excellent. Internal consistency of scores was sometimes an issue for users unfamiliar with the tool; however, this improved with practice and interrater reliability (assessed by Kendall's W) was good. The tool was felt to have particular value in facilitating interdisciplinary communication and working. Modifications to the design of the tool have improved internal consistency. INTERPRETATION: PRISM supports identification of the 'active ingredients' of an interdisciplinary rehabilitation package and facilitates interdisciplinary communication. It also has potential as a research tool examining relationships between rehabilitation delivered and severity-adjusted outcomes observed after paediatric ABI. WHAT THIS PAPER ADDS: Identifying contribution of rehabilitation to outcomes after acquired brain injury requires quantification of rehabilitation 'dose' and 'content'. Previous approaches to 'parsing' of rehabilitation dose and content may have overemphasized one-to-one sessions with therapists. We present a novel, holistic tool for identification of ingredients of an interdisciplinary rehabilitation package. It supports interdisciplinary communication and has potential as a research tool.

Diagnostics for assessing the linear noise and moment closure approximations.

Solving the chemical master equation exactly is typically not possible, so instead we must rely on simulation based methods. Unfortunately, drawing exact realisations, results in simulating every reaction that occurs. This will preclude the use of exact simulators for models of any realistic size and so approximate algorithms become important. In this paper we describe a general framework for assessing the accuracy of the linear noise and two moment approximations. By constructing an efficient space filling design over the parameter region of interest, we present a number of useful diagnostic tools that aids modellers in assessing whether the approximation is suitable. In particular, we leverage the normality assumption of the linear noise and moment closure approximations.

Bayesian inference for Markov jump processes with informative observations.

In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.

Simulation of stochastic kinetic models.

A growing realization of the importance of stochasticity in cell and molecular processes has stimulated the need for statistical models that incorporate intrinsic (and extrinsic) variability. In this chapter we consider stochastic kinetic models of reaction networks leading to a Markov jump process representation of a system of interest. Traditionally, the stochastic model is characterized by a chemical master equation. While the intractability of such models can preclude a direct analysis, simulation can be straightforward and may present the only practical approach to gaining insight into a system's dynamics. We review exact simulation procedures before considering some efficient approximate alternatives.

Bayesian inference for a wave-front model of the neolithization of Europe.

We consider a wave-front model for the spread of neolithic culture across Europe, and use Bayesian inference techniques to provide estimates for the parameters within this model, as constrained by radiocarbon data from southern and western Europe. Our wave-front model allows for both an isotropic background spread (incorporating the effects of local geography) and a localized anisotropic spread associated with major waterways. We introduce an innovative numerical scheme to track the wave front, and use Gaussian process emulators to further increase the efficiency of our model, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and discuss the inferred distribution of the parameter specifying this uncertainty, along with the distributions of the parameters of our wave-front model. We subsequently use predictive distributions, taking account of parameter uncertainty, to identify radiocarbon sites which do not agree well with our model. These sites may warrant further archaeological study or motivate refinements to the model.

Gross energy metabolism in mice under late onset, short term caloric restriction.

Late onset, short-term moderate caloric restriction (CR) may have beneficial health effects. A 26% CR regime induced at 14 months of age for 70 days in male C57Bl/6 (ICRFa) mice resulted in a reduction in body mass of 17%. A decrease in daily energy expenditure was associated with decreased body mass in CR mice. There was no difference in total levels of physical activity between the CR and ad libitum (AL) groups; however, activity patterns were different. We developed a Bayesian model to dissect the impact of food anticipation activity (FAA) and feeding on physical activity. FAA was stronger in CR mice and remaining basal activity was higher in AL mice, but CR mice displayed larger diurnal variations as well as a phase shift in their diurnal activity. CR mice displayed lower body temperature, especially late during the dark phase. This was due to lower basal (activity-independent) temperature at all times of the day, coupled to a phase shift in the diurnal rhythm. The correlation between body temperature and physical activity was independent of feeding regimen and light/dark cycles. Reduction of body mass and basal temperature were major compensatory mechanisms to reduced food availability during late-onset, short-term CR.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo.

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka-Volterra system and a prokaryotic auto-regulatory network.

Bayesian sequential inference for stochastic kinetic biochemical network models.

As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discrete-time (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters on-line in several data-poor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic auto-regulatory gene network.