To join this seminar virtually: Please request Zoom connection details from headsec [at] stat.ubc.ca.
Time: 11:00am – 11:30am
Speaker: William Laplante, UBC Statistics MSc student
Title: Improving Uncertainty Quantification of Epidemiological Models with Probabilistic Numerics
Abstract: Recent work in Probabilistic Numerics (PN) – a subfield of machine learning that aims to quantify uncertainty arising from intractable numerical computation – has developed a new class of numerical algorithms to solve ordinary differential equations (ODEs) with a latent force. These solvers pose the problem of numerically computing the solution of ODEs as one of statistical inference: each step of numerical integration is a task of prediction with uncertainty. By formulating a state-space model (SSM) with two likelihoods – one to fit the data, and one to ensure state alignment – and by using Kalman filters and smoothers to estimate the states of the SSM, the estimates (with uncertainty) of an ODE's solution and its latent force are obtained in a single, linear complexity pass. In this work, we demonstrate the practicality of these PN methods in epidemiology by fitting data from the COVID-19 pandemic with a compartmental model – a type of epidemiological model that divides a population in compartments and is expressed as ODEs. To facilitate the fitting process, we propose a "fix-all-vary-one" approach to calibrate the model's hyperparameters, and implement the EM algorithm to estimate the likelihood's covariance. From estimates of the compartmental model's states, we retrieve (1) the model's time-varying contact rate (the latent force), (2) an estimate of the time-varying instantaneous reproductive number, and (3) a prediction for daily and cumulative case counts. Overall, we show that the key feature of PN methods, "uncertainty-awareness", can greatly benefit quantitative epidemiologists that make extensive use of differential equations to describe epidemics.
Time: 11:30am – 12:00pm
Speaker: Elvis (Zhenglun) Cai, UBC Statistics MSc student
Title: Modeling and Estimating the Effective Reproduction Number
Abstract: The effective Reproduction Number (Rt) of an infectious disease is a latent variable that measures the total number of secondary infections generated by an individual on average. It informs policymakers on the virulence of infectious diseases so that they can decide on the type of non-medical intervention that should be implemented. In this project, we model Rt with penalized Poisson regression using the Renewal Equation and provide a framework that can handle various smoothness assumptions of Rt. The penalty terms that are determined by smoothness assumptions yield a convex, separable, but non-differentiable objective function that is solved with the linearized Alternating Direction Method of Multiplier (ADMM). The corresponding algorithm is implemented in our R package, “RtEstim”, with cross validation. We compare the RMSE/RMAE of the estimated Rt and its corresponding case counts between “RtEstim” and “EpiEstim” – one of the most widely used Rt estimation packages in R – using various synthetic datasets. We find that “RtEstim” has a smaller prediction error than “EpiEstim” on most synthetic datasets.