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.

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.

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.

Simulating normalising constants with referenced thermodynamic integration: application to COVID-19 model selection

Model selection is a fundamental part of Bayesian statistical inference; a widely used tool in the field of epidemiology. Simple methods such as Akaike Information Criterion are commonly used but they do not incorporate the uncertainty of the model's parameters, which can give misleading choices when comparing models with similar fit to the data. One approach to model selection in a more rigorous way that uses the full posterior distributions of the models is to compute the ratio of the normalising constants (or model evidence), known as Bayes factors. These normalising constants integrate the posterior distribution over all parameters and balance over and under fitting. However, normalising constants often come in the form of intractable, high-dimensional integrals, therefore special probabilistic techniques need to be applied to correctly estimate the Bayes factors. One such method is thermodynamic integration (TI), which can be used to estimate the ratio of two models' evidence by integrating over a continuous path between the two un-normalised densities. In this paper we introduce a variation of the TI method, here referred to as referenced TI, which computes a single model's evidence in an efficient way by using a reference density such as a multivariate normal - where the normalising constant is known. We show that referenced TI, an asymptotically exact Monte Carlo method of calculating the normalising constant of a single model, in practice converges to the correct result much faster than other competing approaches such as the method of power posteriors. We illustrate the implementation of the algorithm on informative 1- and 2-dimensional examples, and apply it to a popular linear regression problem, and use it to select parameters for a model of the COVID-19 epidemic in South Korea.

A unified machine learning approach to time series forecasting applied to demand at emergency departments

There were 25.6 million attendances at Emergency Departments (EDs) in England in 2019 corresponding to an increase of 12 million attendances over the past ten years. The steadily rising demand at EDs creates a constant challenge to provide adequate quality of care while maintaining standards and productivity. Managing hospital demand effectively requires an adequate knowledge of the future rate of admission. Using 8 years of electronic admissions data from two major acute care hospitals in London, we develop a novel ensemble methodology that combines the outcomes of the best performing time series and machine learning approaches in order to make highly accurate forecasts of demand, 1, 3 and 7 days in the future. Both hospitals face an average daily demand of 208 and 106 attendances respectively and experience considerable volatility around this mean. However, our approach is able to predict attendances at these emergency departments one day in advance up to a mean absolute error of +/- 14 and +/- 10 patients corresponding to a mean absolute percentage error of 6.8% and 8.6% respectively. Our analysis compares machine learning algorithms to more traditional linear models. We find that linear models often outperform machine learning methods and that the quality of our predictions for any of the forecasting horizons of 1, 3 or 7 days are comparable as measured in MAE. In addition to comparing and combining state-of-the-art forecasting methods to predict hospital demand, we consider two different hyperparameter tuning methods, enabling a faster deployment of our models without compromising performance. We believe our framework can readily be used to forecast a wide range of policy relevant indicators.

$π$VAE: Encoding stochastic process priors with variational autoencoders

Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($\pi$VAE). The $\pi$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $\pi$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $\pi$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.

Modeling Popularity in Asynchronous Social Media Streams with Recurrent Neural Networks

Understanding and predicting the popularity of online items is an important open problem in social media analysis. Considerable progress has been made recently in data-driven predictions, and in linking popularity to external promotions. However, the existing methods typically focus on a single source of external influence, whereas for many types of online content such as YouTube videos or news articles, attention is driven by multiple heterogeneous sources simultaneously - e.g. microblogs or traditional media coverage. Here, we propose RNN-MAS, a recurrent neural network for modeling asynchronous streams. It is a sequence generator that connects multiple streams of different granularity via joint inference. We show RNN-MAS not only to outperform the current state-of-the-art Youtube popularity prediction system by 17%, but also to capture complex dynamics, such as seasonal trends of unseen influence. We define two new metrics: promotion score quantifies the gain in popularity from one unit of promotion for a Youtube video; the loudness level captures the effects of a particular user tweeting about the video. We use the loudness level to compare the effects of a video being promoted by a single highly-followed user (in the top 1% most followed users) against being promoted by a group of mid-followed users. We find that results depend on the type of content being promoted: superusers are more successful in promoting Howto and Gaming videos, whereas the cohort of regular users are more influential for Activism videos. This work provides more accurate and explainable popularity predictions, as well as computational tools for content producers and marketers to allocate resources for promotion campaigns.

A Tutorial on Hawkes Processes for Events in Social Media

This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point processes. We then introduce the Hawkes process, its event intensity function, as well as schemes for event simulation and parameter estimation. We also describe a practical example drawn from social media data - we show how to model retweet cascades using a Hawkes self-exciting process. We presents a design of the memory kernel, and results on estimating parameters and predicting popularity. The code and sample event data are available as an online appendix