arXiv subjects

Alun L. Lloyd

Publications and source records attributed to Alun L. Lloyd.

3 recordsLinked to original sources

arXiv2020

The Estimation of the Effective Reproductive Number from Disease Outbreak Data

We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.

q-bio.PE↗

arXiv2020

A Sensitivity Matrix Based Methodology for Inverse Problem Formulation

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1\% of the estimate.

stat.ME↗

arXiv2018

An approach to periodic, time-varying parameter estimation using nonlinear filtering

Many systems arising in biological applications are subject to periodic forcing. In these systems the forcing parameter is not only time-varying but also known to have a periodic structure. We present an approach to estimating periodic, time-varying parameters that imposes periodic structure by treating the time-varying parameter as a piecewise function with unknown coefficients. This method allows the resulting parameter estimate more flexibility in shape than prescribing a specific functional form (e.g., sinusoidal) to model its behavior, while still maintaining periodicity. We employ nonlinear filtering, more specifically, a version of the augmented ensemble Kalman filter (EnKF), to estimate the unknown coefficients comprising the piecewise approximation of the periodic, time-varying parameter. This allows for straightforward comparison of the proposed method with an EnKF-based parameter tracking algorithm, where periodicity is not guaranteed. We demonstrate the effectiveness of the proposed approach on two biological examples: a synthetic example with data generated from the nonlinear FitzHugh-Nagumo system, modeling the excitability of a nerve cell, to estimate the external voltage parameter, and a case study using reported measles incidence data from three locations during the pre-vaccine era to estimate the seasonal transmission parameter. The formulation of the proposed approach also allows for simultaneous estimation of initial conditions and other static system parameters, such as the reporting probability of measles cases, which is vital for predicting under-reported incidence data.

q-bio.QM↗