arXiv subjects

Alexander C Murph

Publications and source records attributed to Alexander C Murph.

3 recordsLinked to original sources

arXiv2026

Transfer Learning using 66 Diseases for Disease Forecasting Applications

Disease forecasting models typically rely on a single data stream, making models brittle when histories are short or noisy. Recent top-performing models have shown that synthesizing multiple reporting systems for the same disease improves performance. Other recent work takes this idea a step further, using transfer learning to train a forecasting model for one disease using data from a different disease. We expand upon each of these approaches greatly, training machine learning models on data that span 66 infectious diseases and several data streams. We investigate the value of incorporating different data streams for forecasting 20 different disease data streams. We find that incorporating other data streams improves forecasting in the vast majority (84.9%) of time series and model structures considered. However, our work highlights that the quality of the added data matters, where adding data extremely different from the target data stream can sometimes degrade forecast performance. A major contribution of this work is in compiling a publicly-available database of data for use by the infectious disease forecasting community.

cs.LG↗

arXiv2022

Generalized Fiducial Inference on Differentiable Manifolds

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. This new approach uses generalized fiducial inference to obtain a posterior-like distribution on the manifold, without needing to know a parameterization that maps the constrained space to an unconstrained Euclidean space. The proposed methodology, called the constrained generalized fiducial distribution (CGFD), is obtained by using mathematical tools from Riemannian geometry. A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To demonstrate the practical use of the CGFD, we provide three proof-of-concept examples: inference for data from a multivariate normal density with the mean parameters on a sphere, a linear logspline density estimation problem, and a reimagined approach to the AR(1) model, all of which exhibit desirable coverages via simulation. We discuss two Markov chain Monte Carlo algorithms for the exploration of these constrained parameter spaces and adapt them for the CGFD.

stat.ME↗

arXiv2022

A Geometric Perspective on Bayesian and Generalized Fiducial Inference

Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian posteriors. In the absence of prior information, we may still rely on objective Bayes or generalized fiducial inference (GFI). Inspired by approximate Bayesian computation, we propose a novel characterization of post-data inference with the aid of differential geometry. Under suitable smoothness conditions, we establish that Bayesian posteriors and generalized fiducial distributions (GFDs) can be respectively characterized by absolutely continuous distributions supported on the same differentiable manifold: The manifold is uniquely determined by the observed data and the data generating equation of the fitted model. Our geometric analysis not only sheds light on the connection and distinction between Bayesian inference and GFI, but also allows us to sample from posteriors and GFDs using manifold Markov chain Monte Carlo algorithms. A repeated-measures analysis of variance example is presented to illustrate the sampling procedure.

math.ST↗