Time series modelling methods to forecast the volume of self-assessment tax returns in the UK.

Her Majesty's Revenue and Customs (HMRC) has the ambitious target of making tax digital for all its customers and collecting tax in a more efficient, effective and accurate manner for both the government and UK taxpayers. Self-assessment tax returns, the biggest key business event for HMRC, is also one of the most popular digital services with over 90% of the approximately 12 million taxpayers in self assessment filing their return online each year. The majority of returns are filed in January immediately prior to the self-assessment deadline (31st January), putting significant pressure not only on the self-assessment digital service but also on all other HMRC digital services. Hence, understanding and predicting demand for the system is vital to provide a robust and responsive service. We therefore developed mathematical models with Bayesian inference techniques to forecast volumes of Self-assessment (SA) returns submitted online during January, providing accurate hourly predictions of traffic on the digital system in the run up to the SA deadline. Because none of the models being considered is believed to be the true model, we use an ensemble modelling technique that combines forecasts from different models to develop a less risky demand forecast.

Exact Bayesian inference of epidemiological parameters from mortality data: application to African swine fever virus.

Pathogens such as African swine fever virus (ASFV) are an increasing threat to global livestock production with implications for economic well-being and food security. Quantification of epidemiological parameters, such as transmission rates and latent and infectious periods, is critical to inform efficient disease control. Parameter estimation for livestock disease systems is often reliant upon transmission experiments, which provide valuable insights in the epidemiology of disease but which may also be unrepresentative of at-risk populations and incur economic and animal welfare costs. Routinely collected mortality data are a potential source of readily available and representative information regarding disease transmission early in outbreaks. We develop methodology to conduct exact Bayesian parameter inference from mortality data using reversible jump Markov chain Monte Carlo incorporating multiple routes of transmission (e.g. within-farm secondary and background transmission from external sources). We use this methodology to infer epidemiological parameters for ASFV using data from outbreaks on nine farms in the Russian Federation. This approach improves inference on transmission rates in comparison with previous methods based on approximate Bayesian computation, allows better estimation of time of introduction and could readily be applied to other outbreaks or pathogens.

Data-Driven Risk Assessment from Small Scale Epidemics: Estimation and Model Choice for Spatio-Temporal Data with Application to a Classical Swine Fever Outbreak.

Livestock epidemics have the potential to give rise to significant economic, welfare, and social costs. Incursions of emerging and re-emerging pathogens may lead to small and repeated outbreaks. Analysis of the resulting data is statistically challenging but can inform disease preparedness reducing potential future losses. We present a framework for spatial risk assessment of disease incursions based on data from small localized historic outbreaks. We focus on between-farm spread of livestock pathogens and illustrate our methods by application to data on the small outbreak of Classical Swine Fever (CSF) that occurred in 2000 in East Anglia, UK. We apply models based on continuous time semi-Markov processes, using data-augmentation Markov Chain Monte Carlo techniques within a Bayesian framework to infer disease dynamics and detection from incompletely observed outbreaks. The spatial transmission kernel describing pathogen spread between farms, and the distribution of times between infection and detection, is estimated alongside unobserved exposure times. Our results demonstrate inference is reliable even for relatively small outbreaks when the data-generating model is known. However, associated risk assessments depend strongly on the form of the fitted transmission kernel. Therefore, for real applications, methods are needed to select the most appropriate model in light of the data. We assess standard Deviance Information Criteria (DIC) model selection tools and recently introduced latent residual methods of model assessment, in selecting the functional form of the spatial transmission kernel. These methods are applied to the CSF data, and tested in simulated scenarios which represent field data, but assume the data generation mechanism is known. Analysis of simulated scenarios shows that latent residual methods enable reliable selection of the transmission kernel even for small outbreaks whereas the DIC is less reliable. Moreover, compared with DIC, model choice based on latent residual assessment correlated better with predicted risk.

Vulnerability of the British swine industry to classical swine fever.

Classical swine fever (CSF) is a notifiable, highly contagious viral disease of swine which results in severe welfare and economic consequences in affected countries. To improve preparedness, it is critical to have some understanding of how CSF would spread should it be introduced. Based on the data recorded during the 2000 epidemic of CSF in Great Britain (GB), a spatially explicit, premises-based model was developed to explore the risk of CSF spread in GB. We found that large outbreaks of CSF would be rare and generated from a limited number of areas in GB. Despite the consistently low vulnerability of the British swine industry to large CSF outbreaks, we identified concerns with respect to the role played by the non-commercial sector of the industry. The model further revealed how various epidemiological features may influence the spread of CSF in GB, highlighting the importance of between-farm biosecurity in preventing widespread dissemination of the virus. Knowledge of factors affecting the risk of spread are key components for surveillance planning and resource allocation, and this work provides a valuable stepping stone in guiding policy on CSF surveillance and control in GB.

Estimation of under-reporting in epidemics using approximations.

Under-reporting in epidemics, when it is ignored, leads to under-estimation of the infection rate and therefore of the reproduction number. In the case of stochastic models with temporal data, a usual approach for dealing with such issues is to apply data augmentation techniques through Bayesian methodology. Departing from earlier literature approaches implemented using reversible jump Markov chain Monte Carlo (RJMCMC) techniques, we make use of approximations to obtain faster estimation with simple MCMC. Comparisons among the methods developed here, and with the RJMCMC approach, are carried out and highlight that approximation-based methodology offers useful alternative inference tools for large epidemics, with a good trade-off between time cost and accuracy.

Modelling under-reporting in epidemics.

Under-reporting of infected cases is crucial for many diseases because of the bias it can introduce when making inference for the model parameters. The objective of this paper is to study the effect of under-reporting in epidemics by considering the stochastic Markovian SIR epidemic in which various reporting processes are incorporated. In particular, we first investigate the effect on the estimation process of ignoring under-reporting when it is present in an epidemic outbreak. We show that such an approach leads to under-estimation of the infection rate and the reproduction number. Secondly, by allowing for the fact that under-reporting is occurring, we develop suitable models for estimation of the epidemic parameters and explore how well the reporting rate and other model parameters can be estimated. We consider the case of a constant reporting probability and also more realistic assumptions which involve the reporting probability depending on time or the source of infection for each infected individual. Due to the incomplete nature of the data and reporting process, the Bayesian approach provides a natural modelling framework and we perform inference using data augmentation and reversible jump Markov chain Monte Carlo techniques.