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When fitting a multi-parameter model to a data set, computer algorithms may suggest that a range of parameters provide equally reasonable fits, making the parameter estimation difficult. Here, we prove this fact for an SIR model. We say a…

Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader…

Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…

For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…

Deep neural networks tend to make overconfident predictions and often require additional detectors for misclassifications, particularly for safety-critical applications. Existing detection methods usually only focus on adversarial attacks…

This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…

Difference-in-differences is undoubtedly one of the most widely used methods for evaluating the causal effect of an intervention in observational (i.e., nonrandomized) settings. The approach is typically used when pre- and post-exposure…

Sepsis is a major cause of mortality in the intensive care units (ICUs). Early intervention of sepsis can improve clinical outcomes for sepsis patients. Machine learning models have been developed for clinical recognition of sepsis. A…

Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…

Aims: To propose a general sample size framework for developing or updating a clinical prediction model using any statistical or machine learning method, based on drawing samples from anticipated posterior distributions and targeting…

Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…

The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field…

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence.…

Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

Epidemiologic screening programs often make use of tests with small, but non-zero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect…

Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…

Machine learning models of accelerator systems (`surrogate models') are able to provide fast, accurate predictions of accelerator physics phenomena. However, approaches to date typically do not include measured input diagnostics, such as…