Epidemic mitigation by statistical inference from contact tracing data

Contact tracing is an essential tool to mitigate the impact of a pandemic, such as the COVID-19 pandemic. In order to achieve efficient and scalable contact tracing in real time, digital devices can play an important role. While a lot of attention has been paid to analyzing the privacy and ethical risks of the associated mobile applications, so far much less research has been devoted to optimizing their performance and assessing their impact on the mitigation of the epidemic. We develop Bayesian inference methods to estimate the risk that an individual is infected. This inference is based on the list of his recent contacts and their own risk levels, as well as personal information such as results of tests or presence of syndromes. We propose to use probabilistic risk estimation to optimize testing and quarantining strategies for the control of an epidemic. Our results show that in some range of epidemic spreading (typically when the manual tracing of all contacts of infected people becomes practically impossible but before the fraction of infected people reaches the scale where a lockdown becomes unavoidable), this inference of individuals at risk could be an efficient way to mitigate the epidemic. Our approaches translate into fully distributed algorithms that only require communication between individuals who have recently been in contact. Such communication may be encrypted and anonymized, and thus, it is compatible with privacy-preserving standards. We conclude that probabilistic risk estimation is capable of enhancing the performance of digital contact tracing and should be considered in the mobile applications.

Semiparametric Bayesian Risk Estimation for Complex Extremes

Thomas Lugrin

Extreme events are responsible for huge material damage and are costly in terms of their human and economic impacts. They strike all facets of modern society, such as physical infrastructure and insurance companies through environmental hazards, banking and finance through stock market crises, and the internet and communication systems through network and server overloads. It is thus of increasing importance to accurately assess the risk of extreme events in order to mitigate them. Extreme value theory is a statistical approach to extrapolation of probabilities beyond the range of the data, which provides a robust framework to learn from an often small number of recorded extreme events. In this thesis, we consider a conditional approach to modelling extreme values that is more flexible than standard models for simultaneously extreme events. We explore the subasymptotic properties of this conditional approach and prove that in specific situations its finite-sample behaviour can differ significantly from its limit characterisation. For modelling extremes in time series with short-range dependence, the standard peaks-over-threshold method relies on a pre-processing step that retains only a subset of observations exceeding a high threshold and can result in badly-biased estimates. This method focuses on the marginal distribution of the extremes and does not estimate temporal extremal dependence. We propose a new methodology to model time series extremes using Bayesian semiparametrics and allowing estimation of functionals of clusters of extremes. We apply our methodology to model river flow data in England and improve flood risk assessment by explicitly describing extremal dependence in time, using information from all exceedances of a high threshold. We develop two new bivariate models which are based on the conditional tail approach, and use all observations having at least one extreme component in our inference procedure, thus extracting more information from the data than existing approaches. We compare the efficiency of these models in a simulation study and discuss generalisations to higher-dimensional setups. Existing models for extremes of Markov chains generally rely on a strong assumption of asymptotic dependence at all lags and separately consider marginal and joint features. We introduce a more flexible model and show how Bayesian semiparametrics can provide a suitable framework allowing simultaneous inference for the margins and the extremal dependence structure, yielding efficient risk estimates and a reliable assessment of uncertainty.

EPFL2018

Variational Gaussian Inference for Bilinear Models of Count Data

Mohammad Emtiyaz Khan, Young Jun Ko

Bilinear models of count data with Poisson distribution are popular in applications such as matrix factorization for recommendation systems, modeling of receptive fields of sensory neurons, and modeling of neural-spike trains. Bayesian inference in such models remains challenging due to the product term of two Gaussian random vectors. In this paper, we propose new algorithms for such models based on variational Gaussian (VG) inference. We make two contributions. First, we show that the VG lower bound for these models, previously known to be intractable, is available in closed form under certain non-trivial constraints on the form of the posterior. Second, we show that the lower bound is biconcave and can be efficiently optimized for mean-field approximations. We also show that bi-concavity generalizes to the larger family of log-concave likelihoods, that subsume the Poisson distribution. We present new inference algorithms based on these results and demonstrate better performance on real-world problems at the cost of a modest increase in computation. Our contributions in this paper, therefore, provide more choices for Bayesian inference in terms of a speed-vs-accuracy tradeoff.

2014

Semiparametric Bayesian Risk Estimation for Complex Extremes

Thomas Lugrin

EPFL2018