Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

Abstract

We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

A general framework for quantifying uncertainty at scale and its application to fusion research

“…In our experiments, we have used tol = 10 −4 × 1 63 , which were sufficiently small for our purposes. We note that when d is large, 2 d −1 will be prohibitively large making the computation of all 2 d −1 sensitivities in (8). Nevertheless, as noted above, in most practical applications it is unlikely that pairings beyond few, e.g., two, three parameters are important and therefore (8) can be truncated to comprise only these interactions.…”

“…, tol 2 d −1 ) which are a heuristic for the accuracy with which we want the algorithm to explore the d individual directions and all their 2 d − d − 1 interactions. We compare the mth term in (8) with tol m and if this tolerance is exceed, s is increased by one. In other words, if an individual parameter or an interaction are important in a candidate subspace for refinement -as compared to the prescribed tolerance -the sensitivity index will reflect this information.…”

“…Obviously, UQ and SA are highly relevant for a large number of high-impact and practically relevant tasks in science and technology. This includes fields like (computational) fluid dynamics [29] -which is one of the first fields in which UQ and SA became prominent-, combustion in rocket engines [18], climate modeling [28], materials science [20], tsunami and earthquake simulations [37,32], computational medicine [39,2], or, highly relevant at the time of the writing of this article, the mathematical modeling of epidemics, in particular the Coronavirus Disease (COVID-19) [36,1,8], to name just a few. Any of these examples, and many more, could be used to make the case, but here, we will focus on one of the key physics problems in fusion research, namely how to quantify and predict turbulent transport in magnetic confinement experiments [6,14].…”

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

“…where Φ(m), Φ(m) are the potentials defined with F, F w as in (9). Using Jensen's, Hölder's, and Minkowski inequalities, we have…”

“…These scenarios arise, for example, when the parameters are possibly spatially varying with uncertain spatial structures. Bayesian inverse problems are fundamental to constructing predictive models [1][2][3][4], and the need for inferring parameters as functions can be found in many areas of engineering, sciences, and medicine [5][6][7][8][9][10].…”