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Register a new userA Bayesian Nonparametric Analysis of the 2003 Outbreak of Highly Pathogenic Avian Influenza in the Netherlands
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Added by
Rowland Seymour
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Infectious diseases on farms pose both public and animal health risks, so understanding how they spread between farms is crucial for developing disease control strategies to prevent future outbreaks. We develop novel Bayesian nonparametric methodology to fit spatial stochastic transmission models in which the infection rate between any two farms is a function that depends on the distance between them, but without assuming a specified parametric form. Making nonparametric inference in this context is challenging since the likelihood function of the observed data is intractable because the underlying transmission process is unobserved. We adopt a fully Bayesian approach by assigning a transformed Gaussian Process prior distribution to the infection rate function, and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to perform Bayesian inference. We use the posterior predictive distribution to simulate the effect of different disease control methods and their economic impact. We analyse a large outbreak of Avian Influenza in the Netherlands and infer the between-farm infection rate, as well as the unknown infection status of farms which were pre-emptively culled. We use our results to analyse ring-culling strategies, and conclude that although effective, ring-culling has limited impact in high density areas.
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We propose a Bayesian nonparametric approach to modelling and predicting a class of functional time series with application to energy markets, based on fully observed, noise-free functional data. Traders in such contexts conceive profitable strategies if they can anticipate the impact of their bidding actions on the aggregate demand and supply curves, which in turn need to be predicted reliably. Here we propose a simple Bayesian nonparametric method for predicting such curves, which take the form of monotonic bounded step functions. We borrow ideas from population genetics by defining a class of interacting particle systems to model the functional trajectory, and develop an implementation strategy which uses ideas from Markov chain Monte Carlo and approximate Bayesian computation techniques and allows to circumvent the intractability of the likelihood. Our approach shows great adaptation to the degree of smoothness of the curves and the volatility of the functional series, proves to be robust to an increase of the forecast horizon and yields an uncertainty quantification for the functional forecasts. We illustrate the model and discuss its performance with simulated datasets and on real data relative to the Italian natural gas market.
Identifying the most deprived regions of any country or city is key if policy makers are to design successful interventions. However, locating areas with the greatest need is often surprisingly challenging in developing countries. Due to the logistical challenges of traditional household surveying, official statistics can be slow to be updated; estimates that exist can be coarse, a consequence of prohibitive costs and poor infrastructures; and mass urbanisation can render manually surveyed figures rapidly out-of-date. Comparative judgement models, such as the Bradley--Terry model, offer a promising solution. Leveraging local knowledge, elicited via comparisons of different areas affluence, such models can both simplify logistics and circumvent biases inherent to house-hold surveys. Yet widespread adoption remains limited, due to the large amount of data existing approaches still require. We address this via development of a novel Bayesian Spatial Bradley--Terry model, which substantially decreases the amount of data comparisons required for effective inference. This model integrates a network representation of the city or country, along with assumptions of spatial smoothness that allow deprivation in one area to be informed by neighbouring areas. We demonstrate the practical effectiveness of this method, through a novel comparative judgement data set collected in Dar es Salaam, Tanzania.
We consider Bayesian inference for stochastic differential equation mixed effects models (SDEMEMs) exemplifying tumor response to treatment and regrowth in mice. We produce an extensive study on how a SDEMEM can be fitted using both exact inference based on pseudo-marginal MCMC and approximate inference via Bayesian synthetic likelihoods (BSL). We investigate a two-compartments SDEMEM, these corresponding to the fractions of tumor cells killed by and survived to a treatment, respectively. Case study data considers a tumor xenography study with two treatment groups and one control, each containing 5-8 mice. Results from the case study and from simulations indicate that the SDEMEM is able to reproduce the observed growth patterns and that BSL is a robust tool for inference in SDEMEMs. Finally, we compare the fit of the SDEMEM to a similar ordinary differential equation model. Due to small sample sizes, strong prior information is needed to identify all model parameters in the SDEMEM and it cannot be determined which of the two models is the better in terms of predicting tumor growth curves. In a simulation study we find that with a sample of 17 mice per group BSL is able to identify all model parameters and distinguish treatment groups.
The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. There is one previous analysis of the full data set, but this relies on approximation methods to derive a likelihood. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations. Results include estimates of basic model parameters as well as reproduction numbers and the likely path of infection. Model assessment is carried out using simulation-based methods.
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical paradigms can be considered and Bayesian probabilistic numerical methods (PNMs) are obtained when Bayesian statistical principles are deployed. Bayesian PNM have the appealing property of being closed under composition, such that uncertainty due to different sources of discretisation in a numerical method can be jointly modelled and rigorously propagated. Despite recent attention, no exact Bayesian PNM for the numerical solution of ordinary differential equations (ODEs) has been proposed. This raises the fundamental question of whether exact Bayesian methods for (in general nonlinear) ODEs even exist. The purpose of this paper is to provide a positive answer for a limited class of ODE. To this end, we work at a foundational level, where a novel Bayesian PNM is proposed as a proof-of-concept. Our proposal is a synthesis of classical Lie group methods, to exploit underlying symmetries in the gradient field, and non-parametric regression in a transformed solution space for the ODE. The procedure is presented in detail for first and second order ODEs and relies on a certain strong technical condition -- existence of a solvable Lie algebra -- being satisfied. Numerical illustrations are provided.
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