Continuous football player tracking from discrete broadcast data

Player tracking data remains out of reach for many professional football teams as their video feeds are not sufficiently high quality for computer vision technologies to be used. To help bridge this gap, we present a method that can estimate continuous full-pitch tracking data from discrete data made from broadcast footage. Such data could be collected by clubs or players at a similar cost to event data, which is widely available down to semi-professional level. We test our method using open-source tracking data, and include a version that can be applied to a large set of over 200 games with such discrete data.

Leaping through tree space: continuous phylogenetic inference for rooted and unrooted trees

Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains challenging. To address this problem, for the first time, we perform both tree exploration and inference in a continuous space where the computation of gradients is possible. This continuous relaxation allows for major leaps across tree space in both rooted and unrooted trees, and is less susceptible to convergence to local minima. Our approach outperforms the current best methods for inference on unrooted trees and, in simulation, accurately infers the tree and root in ultrametric cases. The approach is effective in cases of empirical data with negligible amounts of data, which we demonstrate on the phylogeny of jawed vertebrates. Indeed, only a few genes with an ultrametric signal were generally sufficient for resolving the major lineages of vertebrate. With cubic-time complexity and efficient optimisation via automatic differentiation, our method presents an effective way forwards for exploring the most difficult, data-deficient phylogenetic questions.

Deep learning and MCMC with aggVAE for shifting administrative boundaries: mapping malaria prevalence in Kenya

Model-based disease mapping remains a fundamental policy-informing tool in public health and disease surveillance with hierarchical Bayesian models being the current state-of-the-art approach. When working with areal data, e.g. aggregates at the administrative unit level such as district or province, routinely used models rely on the adjacency structure of areal units to account for spatial correlations. The goal of disease surveillance systems is to track disease outcomes over time, but this provides challenging in situations of crises, such as political changes, leading to changes of administrative boundaries. Kenya is an example of such country. Moreover, adjacency-based approach ignores the continuous nature of spatial processes and cannot solve the change-of-support problem, i.e. when administrative boundaries change. We present a novel, practical, and easy to implement solution relying on a methodology combining deep generative modelling and fully Bayesian inference. We build on the recent work of PriorVAE able to encode spatial priors over small areas with variational autoencoders, to map malaria prevalence in Kenya. We solve the change-of-support problem arising from Kenya changing its district boundaries in 2010. We draw realisations of the Gaussian Process (GP) prior over a fine artificial spatial grid representing continuous space and then aggregate these realisations to the level of administrative boundaries. The aggregated values are then encoded using the PriorVAE technique. The trained priors (aggVAE) are then used at the inference stage instead of the GP priors within a Markov chain Monte Carlo (MCMC) scheme. We demonstrate that it is possible to use the flexible and appropriate model for areal data based on aggregation of continuous priors, and that inference is orders of magnitude faster when using aggVAE than combining the original GP priors and the aggregation step.

A comparison of short-term probabilistic forecasts for the incidence of COVID-19 using mechanistic and statistical time series models

Short-term forecasts of infectious disease spread are a critical component in risk evaluation and public health decision making. While different models for short-term forecasting have been developed, open questions about their relative performance remain. Here, we compare short-term probabilistic forecasts of popular mechanistic models based on the renewal equation with forecasts of statistical time series models. Our empirical comparison is based on data of the daily incidence of COVID-19 across six large US states over the first pandemic year. We find that, on average, probabilistic forecasts from statistical time series models are overall at least as accurate as forecasts from mechanistic models. Moreover, statistical time series models better capture volatility. Our findings suggest that domain knowledge, which is integrated into mechanistic models by making assumptions about disease dynamics, does not improve short-term forecasts of disease incidence. We note, however, that forecasting is often only one of many objectives and thus mechanistic models remain important, for example, to model the impact of vaccines or the emergence of new variants.

Phylo2Vec: a vector representation for binary trees

Binary phylogenetic trees inferred from biological data are central to understanding the shared evolutionary history of organisms. Inferring the placement of latent nodes in a tree by any optimality criterion (e.g., maximum likelihood) is an NP-hard problem, propelling the development of myriad heuristic approaches. Yet, these heuristics often lack a systematic means of uniformly sampling random trees or effectively exploring a tree space that grows factorially, which are crucial to optimisation problems such as machine learning. Accordingly, we present Phylo2Vec, a new parsimonious representation of a phylogenetic tree. Phylo2Vec maps any binary tree with $n$ leaves to an integer vector of length $n$. We prove that Phylo2Vec is both well-defined and bijective to the space of phylogenetic trees. The advantages of Phylo2Vec are twofold: i) easy uniform sampling of binary trees and ii) systematic ability to traverse tree space in very large or small jumps. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets and show that a simple hill climbing-based optimisation efficiently traverses the vastness of tree space from a random to an optimal tree.

The interaction of transmission intensity, mortality, and the economy: a retrospective analysis of the COVID-19 pandemic

The COVID-19 pandemic has caused over 6.4 million registered deaths to date, and has had a profound impact on economic activity. Here, we study the interaction of transmission, mortality, and the economy during the SARS-CoV-2 pandemic from January 2020 to December 2022 across 25 European countries. We adopt a Bayesian vector autoregressive model with both fixed and random effects. We find that increases in disease transmission intensity decreases Gross domestic product (GDP) and increases daily excess deaths, with a longer lasting impact on excess deaths in comparison to GDP, which recovers more rapidly. Broadly, our results reinforce the intuitive phenomenon that significant economic activity arises from diverse person-to-person interactions. We report on the effectiveness of non-pharmaceutical interventions (NPIs) on transmission intensity, excess deaths and changes in GDP, and resulting implications for policy makers. Our results highlight a complex cost-benefit trade off from individual NPIs. For example, banning international travel increases GDP however reduces excess deaths. We consider country random effects and their associations with excess changes in GDP and excess deaths. For example, more developed countries in Europe typically had more cautious approaches to the COVID-19 pandemic, prioritising healthcare and excess deaths over economic performance. Long term economic impairments are not fully captured by our model, as well as long term disease effects (Long Covid). Our results highlight that the impact of disease on a country is complex and multifaceted, and simple heuristic conclusions to extract the best outcome from the economy and disease burden are challenging.

Seq2Seq Surrogates of Epidemic Models to Facilitate Bayesian Inference

Epidemic models are powerful tools in understanding infectious disease. However, as they increase in size and complexity, they can quickly become computationally intractable. Recent progress in modelling methodology has shown that surrogate models can be used to emulate complex epidemic models with a high-dimensional parameter space. We show that deep sequence-to-sequence (seq2seq) models can serve as accurate surrogates for complex epidemic models with sequence based model parameters, effectively replicating seasonal and long-term transmission dynamics. Once trained, our surrogate can predict scenarios a several thousand times faster than the original model, making them ideal for policy exploration. We demonstrate that replacing a traditional epidemic model with a learned simulator facilitates robust Bayesian inference.

Encoding spatiotemporal priors with VAEs for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatiotemporal statistical modelling. In this context they are used to encode correlation structures over space and time and can generalise well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge: for a particular spatiotemporal setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatiotemporal inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatiotemporal priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two stage approach on Bayesian, small-area estimation tasks.

Gaussian Process Nowcasting: Application to COVID-19 Mortality Reporting

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the changing auto-correlation structure present in the reporting time-delay surface. This approach also yields robust estimates of uncertainty for the estimated nowcasted numbers of deaths. We test assumptions in model specification such as the choice of kernel or hyper priors, and evaluate model performance on a challenging real dataset from Brazil. Our experiments show that Gaussian process nowcasting performs favourably against both comparable methods, and a small sample of expert human predictions. Our approach has substantial practical utility in disease modelling -- by applying our approach to COVID-19 mortality data from Brazil, where reporting delays are large, we can make informative predictions on important epidemiological quantities such as the current effective reproduction number.