Disease Surveillance using Bayesian Methods

Developing Markov Chain Monte Carlo (MCMC) algorithms has been an active area of research. Extensions of the original Metropolis-Hastings random walk (MHRW) algorithm, such as Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS), include gradient information about the posterior when proposing parameters in areas of higher probability within the target. Particle- Markov Chain Monte Carlo (p-MCMC) is a similar parameter estimation algorithm that utilises a particle filter to calculate an unbiased estimate of the log-likelihood which can be used in the MHRW algorithm. However, as noted in the literature, obtaining gradients of the log-likelihood w.r.t the parameters is difficult due to operations inherent to the particle filter being non-differentiable. This obstacle has hindered the use of gradient based proposals within p-MCMC. Therefore, in this thesis, a novel method for obtaining the gradient of the log-likelihood w.r.t the parameters by fixing the random number seed within the particle filter is considered. This allows the particle filter to be posed as a deterministic function, i.e. running the particle filter multiple times will result in the same resampling realisations, log-likelihood and associated gradient estimates. When a different resampling realisation occurs between two parameter values, a piecewise continuous estimate of the log-likelihood and gradient occurs. It is shown that these estimates are still compatible with gradient based proposals such as MALA, HMC and NUTS. A comparison of these samplers is made when estimating the parameters of two state-space models. Results indicate that although NUTS can make multiple gradient evaluations per MCMC iteration, it can produce more accurate estimates in shorter computation time. Frameworks for describing the differentiable particle filter and NUTS in PyTorch and PyMC3, respectively are also provided. This allows the derivatives and partial derivatives to be calculated via automatic differentiation. Particle filters have been used extensively to model and track infectious disease epidemics, with p-MCMC used to estimate the parameters of these models. Although gradient based proposals are used in non-particle methods when modelling epidemiology, the standard proposal when using p-MCMC is the MHRW. Applying the novel differentiable particle filter to two epidemiological models, NUTS can recover the correct parameters in shorter run time when compared to the MHRW proposal. In the context of epidemiological modelling it is essential for public health officials to understand how a disease spreads through a population. This has recently come to the forefront with the emergence of COVID-19. At the beginning of the pandemic it was vital to gather accurate open-source datasets from which to infer how quickly the virus was spreading. As well as parameter estimation, MCMC algorithms have the ability to make forecasts of quantities of interest. Evaluating these predictions with simple scoring rules gives an indication of how well the model represents reality. The scoring rule normalised estimation error squared (NEES) can detect shortcomings within a model such as incorrect parameters, resulting in forecasts that are over-confident or over-cautious. A detailed description of why being cautious rather than confident is more desirable is provided. NEES can also be used when evaluating the effectiveness of different open-source datasets when making future predictions. A novel machine learning framework for detecting COVID-19 symptomatic tweets in real-time in multiple languages is outlined. By collating the tweets from the previous 24 hours a time series of symptomatic tweets can be set up per geographic region. It is shown that, when compared with other traditional data sources, such as positive test results, ingesting tweet data can result in more consistent and accurate COVID-19 death predictions in the United States, United Kingdom and European and South American countries

An O(log⁡2N)\mathcal{O}(\log_2N) SMC2^2 Algorithm on Distributed Memory with an Approx. Optimal L-Kernel

Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC$^2$) are two methods that use an unbiased estimate of the log-likelihood obtained from a particle filter (PF) to evaluate the target distribution. P-MCMC constructs a single Markov chain which is sequential by nature so cannot be readily parallelized using Distributed Memory (DM) architectures. This is in contrast to SMC$^2$ which includes processes, such as importance sampling, that are described as \textit{embarrassingly parallel}. However, difficulties arise when attempting to parallelize resampling. None-the-less, the choice of backward kernel, recycling scheme and compatibility with DM architectures makes SMC$^2$ an attractive option when compared with p-MCMC. In this paper, we present an SMC$^2$ framework that includes the following features: an optimal (in terms of time complexity) $\mathcal{O}(\log_2N)$ parallelization for DM architectures, an approximately optimal (in terms of accuracy) backward kernel, and an efficient recycling scheme. On a cluster of $128$ DM processors, the results on a biomedical application show that SMC$^2$ achieves up to a $70\times$ speed-up vs its sequential implementation. It is also more accurate and roughly $54\times$ faster than p-MCMC. A GitHub link is given which provides access to the code.Comment: 8 pages, 6 figures, accepted to Combined SDF and MFI Conference 2023 conferenc

Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters

It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The {\itshape reparameterisation trick} was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the {\itshape reparameterisation trick} to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider two state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time.Comment: 35 pages, 10 figure

Bayesian Calibration to Address the Challenge of Antimicrobial Resistance: A Review

Antimicrobial resistance (AMR) emerges when disease-causing microorganisms develop the ability to withstand the effects of antimicrobial therapy. This phenomenon is often fueled by the human-to-human transmission of pathogens and the overuse of antibiotics. Over the past 50 years, increased computational power has facilitated the application of Bayesian inference algorithms. In this comprehensive review, the basic theory of Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods are explained. These inference algorithms are instrumental in calibrating complex statistical models to the vast amounts of AMR-related data. Popular statistical models include hierarchical and mixture models as well as discrete and stochastic epidemiological compartmental and agent based models. Studies encompassed multi-drug resistance, economic implications of vaccines, and modeling AMR in vitro as well as within specific populations. We describe how combining these topics in a coherent framework can result in an effective antimicrobial stewardship. We also outline recent advancements in the methodology of Bayesian inference algorithms and provide insights into their prospective applicability for modeling AMR in the future

Universal applicator for digitally-controlled pressing force and impact velocity insertion of microneedles into skin

Microneedle technologies have been developed for dermal drug and vaccine delivery, including hollow-, solid-, coated-, and dissolving microneedles. Microneedles have been made in many different geometries and of many different materials, all of which may influence their skin-penetrating ability. To ensure reproducible and effective drug and vaccine delivery via microneedles, the optimal insertion parameters should be known. Therefore, a digitally-controlled microneedle applicator was developed to insert microneedles into the skin via impact insertion (velocity) or via pressing force insertion. Six microneedle arrays with different geometries and/or materials were applied onto ex vivo human skin with varying velocities or pressing forces. Penetration efficiency and delivered antigen dose into the skin after application of microneedles were determined. In general, microneedles pierced the skin more efficiently when applied by impact application as compared to application via pressing force. However, the angle of application of the applicator on the skin can affect the velocity of the impact, influencing the penetration efficiency of microneedles. Regarding the antigen delivery into the skin, the delivered dose was increasing by increasing the velocity or pressure, and thus, increasing the penetration efficiency. These data demonstrate that an applicator is an important tool to determine optimal application conditions with ex vivo human skin

Refining Epidemiological Forecasts with Simple Scoring Rules

Estimates from infectious disease models have constituted a significant part of the scientific evidence used to inform the response to the COVID-19 pandemic in the UK. These estimates can vary strikingly in their bias and variability. Epidemiological forecasts should be consistent with the observations that eventually materialise. We use simple scoring rules to refine the forecasts of a novel statistical model for multisource COVID-19 surveillance data by tuning its smoothness hyperparameter.Comment: 14 pages, 2 figures, 3 table

Extracting Self-Reported COVID-19 Symptom Tweets and Twitter Movement Mobility Origin/Destination Matrices to Inform Disease Models

The emergence of the novel coronavirus (COVID-19) generated a need to quickly and accurately assemble up-to-date information related to its spread. In this research article, we propose two methods in which Twitter is useful when modelling the spread of COVID-19: (1) machine learning algorithms trained in English, Spanish, German, Portuguese and Italian are used to identify symptomatic individuals derived from Twitter. Using the geo-location attached to each tweet, we map users to a geographic location to produce a time-series of potential symptomatic individuals. We calibrate an extended SEIRD epidemiological model with combinations of low-latency data feeds, including the symptomatic tweets, with death data and infer the parameters of the model. We then evaluate the usefulness of the data feeds when making predictions of daily deaths in 50 US States, 16 Latin American countries, 2 European countries and 7 NHS (National Health Service) regions in the UK. We show that using symptomatic tweets can result in a 6% and 17% increase in mean squared error accuracy, on average, when predicting COVID-19 deaths in US States and the rest of the world, respectively, compared to using solely death data. (2) Origin/destination (O/D) matrices, for movements between seven NHS regions, are constructed by determining when a user has tweeted twice in a 24 h period in two different locations. We show that increasing and decreasing a social connectivity parameter within an SIR model affects the rate of spread of a disease.</jats:p