arXiv subjects

Alexander C. Murph

Publications and source records attributed to Alexander C. Murph.

6 recordsLinked to original sources

arXiv2026

Leveraging Synthetic and Genetic Data to Improve Epidemic Forecasting

Forecasting infectious disease outbreaks is hard. Forecasting emerging infectious diseases with limited historical data is even harder. In this paper, we investigate ways to improve emerging infectious disease forecasting under operational constraints. Specifically, we explore two options likely to be available near the start of an emerging disease outbreak: synthetic data and genetic information. For this investigation, we conducted an experiment where we trained deep learning models on different combinations of real and synthetic data, both with and without genetic information, to explore how these models compare when forecasting COVID-19 cases for US states. All models are developed with an eye towards forecasting the next pandemic. We find that models trained with synthetic data have better forecast accuracy than models trained on real data alone, and models that use genetic variants have better forecast accuracy compared to those that do not. All models outperformed a baseline persistence model (a feat only accomplished by 7 out of 22 real-time COVID-19 cases forecasting models as reported in [38]) and multiple models outperformed the COVIDHub-4_week_ensemble. This paper demonstrates the value of these underutilized sources of information and provides a blueprint for forecasting future pandemics.

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arXiv2024

A New Method for Multinomial Inference using Dempster-Shafer Theory

A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on the unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior is then strengthened to improve symmetry and learning properties with the final posterior model being characterized by a Dirichlet distribution. In addition to computational simplicity, the new model has desirable invariance properties related to category permutations, refinements, and coarsenings. Furthermore, posterior inference on relative probabilities amongst certain cells depends only on data for the cells in question. Finally, the model is quite flexible with regard to parameterization and the range of testable assertions. Comparisons are made to existing methods and illustrated with two examples.

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arXiv2024

Mapping Incidence and Prevalence Peak Data for SIR Forecasting Applications

Infectious disease modeling and forecasting have played a key role in helping assess and respond to epidemics and pandemics. Recent work has leveraged data on disease peak infection and peak hospital incidence to fit compartmental models for the purpose of forecasting and describing the dynamics of a disease outbreak. Incorporating these data can greatly stabilize a compartmental model fit on early observations, where slight perturbations in the data may lead to model fits that project wildly unrealistic peak infection. We introduce a new method for incorporating historic data on the value and time of peak incidence of hospitalization into the fit for a Susceptible-Infectious-Recovered (SIR) model by formulating the relationship between an SIR model's starting parameters and peak incidence as a system of two equations that can be solved computationally. This approach is assessed for practicality in terms of accuracy and speed of computation via simulation. To exhibit the modeling potential, we update the Dirichlet-Beta State Space modeling framework to use hospital incidence data, as this framework was previously formulated to incorporate only data on total infections.

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arXiv2024

Sensitivity Analysis in the Presence of Intrinsic Stochasticity for Discrete Fracture Network Simulations

Large-scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub-surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have seen numerous successes over several engineering applications, estimations on quantities of interest (QoI) - such as breakthrough time of particles reaching the edge of the system - suffer from a two distinct types of uncertainty. A run of a DFN simulator requires several parameter values to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameter choices will lead to some amount of uncertainty in the QoI, called epistemic uncertainty. Furthermore, since DFN simulators rely on stochastic processes to place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e. different seeds) of the same random process leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. We make several design choices to handle an observed heteroskedasticity in DFN simulators, where the aleatoric uncertainty changes for different inputs, since the quality makes several standard statistical methods inadmissible. Beyond the specific takeaways on which input variables affect uncertainty the most for DFN simulators, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity.

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arXiv2023

Bayes Watch: Bayesian Change-point Detection for Process Monitoring with Fault Detection

When a predictive model is in production, it must be monitored in real-time to ensure that its performance does not suffer due to drift or abrupt changes to data. Ideally, this is done long before learning that the performance of the model itself has dropped by monitoring outcome data. In this paper we consider the problem of monitoring a predictive model that identifies the need for palliative care currently in production at the Mayo Clinic in Rochester, MN. We introduce a framework, called \textit{Bayes Watch}, for detecting change-points in high-dimensional longitudinal data with mixed variable types and missing values and for determining in which variables the change-point occurred. Bayes Watch fits an array of Gaussian Graphical Mixture Models to groupings of homogeneous data in time, called regimes, which are modeled as the observed states of a Markov process with unknown transition probabilities. In doing so, Bayes Watch defines a posterior distribution on a vector of regime assignments, which gives meaningful expressions on the probability of every possible change-point. Bayes Watch also allows for an effective and efficient fault detection system that assesses what features in the data where the most responsible for a given change-point.

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arXiv2023

Introduction to Generalized Fiducial Inference

Fiducial inference was introduced in the first half of the 20th century by Fisher (1935) as a means to get a posterior-like distribution for a parameter without having to arbitrarily define a prior. While the method originally fell out of favor due to non-exactness issues in multivariate cases, the method has garnered renewed interest in the last decade. This is partly due to the development of generalized fiducial inference, which is a fiducial perspective on generalized confidence intervals: a method used to find approximate confidence distributions. In this chapter, we illuminate the usefulness of the fiducial philosophy, introduce the definition of a generalized fiducial distribution, and apply it to interesting, non-trivial inferential examples.

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