arXiv subjects

Jesse Wheeler

Publications and source records attributed to Jesse Wheeler.

8 recordsLinked to original sources

arXiv2025

Iterating marginalized Bayes maps for likelihood maximization with application to nonlinear panel models

Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become computationally unfeasible as the system dimension grows. The increasing prevalence of panel data, characterized by multiple related time series, therefore necessitates the development of inference algorithms that are effective for this class of high-dimensional mechanistic models. Nonlinear, non-Gaussian mechanistic models are routinely fitted to time series data but seldom to panel data, despite its widespread availability, suggesting that the practical difficulties for existing procedures are prohibitive. We investigate the use of iterated filtering algorithms for this purpose. We introduce a novel algorithm that contains a marginalization step that mitigates issues arising from particle filtering in high dimensions. Our approach enables likelihood-based inference for models that were previously considered intractable, thus broadening the scope of dynamic models available for panel data analysis.

stat.ME↗

arXiv2025

Mechanistic models for panel data: Analysis of ecological experiments with four interacting species

In an ecological context, panel data arise when time series measurements are made on a collection of ecological processes. Each process may correspond to a spatial location for field data, or to an experimental ecosystem in a designed experiment. Statistical models for ecological panel data should capture the high levels of nonlinearity, stochasticity, and measurement uncertainty inherent in ecological systems. Furthermore, the system dynamics may depend on unobservable variables. This study applies iterated particle filtering techniques to explore new possibilities for likelihood-based statistical analysis of these complex systems. We analyze data from a mesocosm experiment in which two species of the freshwater planktonic crustacean genus, Daphnia, coexist with an alga and a fungal parasite. Time series data were collected on replicated mesocosms under six treatment conditions. Iterated filtering enables maximization of the likelihood for scientifically motivated nonlinear partially observed Markov process models, providing access to standard likelihood-based methods for parameter estimation, confidence intervals, hypothesis testing, model selection and diagnostics. This toolbox allows scientists to propose and evaluate scientifically motivated stochastic dynamic models for panel data, constrained only by the requirement to write code to simulate from the model and to specify a measurement distribution describing how the system state is observed.

stat.AP↗

arXiv2024

panelPomp: Analysis of Panel Data via Partially Observed Markov Processes in R

Panel data arise when time series measurements are collected from multiple, dynamically independent but structurally related systems. Each system's time series can be modeled as a partially observed Markov process (POMP), and the ensemble of these models is called a PanelPOMP. If the time series are relatively short, statistical inference for each time series must draw information from across the entire panel. The component systems in the panel are called units; model parameters may be shared between units or may be unit-specific. Differences between units may be of direct inferential interest or may be a nuisance for studying the commonalities. The R package panelPomp supports analysis of panel data via a general class of PanelPOMP models. This includes a suite of tools for manipulation of models and data that take advantage of the panel structure. The panelPomp package currently highlights recent advances enabling likelihood based inference via simulation based algorithms. However, the general framework provided by panelPomp supports development of additional, new inference methodology for panel data.

stat.ME↗

arXiv2024

A tutorial on panel data analysis using partially observed Markov processes via the R package panelPomp

The R package panelPomp supports analysis of panel data via a general class of partially observed Markov process models (PanelPOMP). This package tutorial describes how the mathematical concept of a PanelPOMP is represented in the software and demonstrates typical use-cases of panelPomp. Monte Carlo methods used for POMP models require adaptation for PanelPOMP models due to the higher dimensionality of panel data. The package takes advantage of recent advances for PanelPOMP, including an iterated filtering algorithm, Monte Carlo adjusted profile methodology and block optimization methodology to assist with the large parameter spaces that can arise with panel models. In addition, tools for manipulation of models and data are provided that take advantage of the panel structure.

stat.CO↗

arXiv2023

Revisiting Inference for ARMA Models: Improved Fits and Superior Confidence Intervals

Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for ARMA likelihood maximization frequently lead to sub-optimal parameter estimates. Existing algorithms have theoretical support, but can result in parameter estimates that correspond to a local optimum. While this possibility has been previously identified, it remains unknown to most users, and no routinely applicable algorithm has been developed to resolve the issue. We introduce a novel random initialization algorithm, designed to take advantage of the structure of the ARMA likelihood function, which overcomes these optimization problems. Additionally, we show that profile likelihoods provide superior confidence intervals to those based on the Fisher information matrix. The efficacy of the proposed methodology is demonstrated through a data analysis example and a series of simulation studies. This work makes a significant contribution to statistical practice by identifying and resolving under-recognized shortcomings of existing procedures that frequently arise in scientific and industrial applications.

stat.ME↗

arXiv2023

Informing policy via dynamic models: Cholera in Haiti

Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.

stat.AP↗

arXiv2022

An iterated block particle filter for inference on coupled dynamic systems with shared and unit-specific parameters

We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation systems where a unit corresponds to a spatially distinct sub-population. Metapopulation systems are characterized by strong dependence through time within a single unit and relatively weak interactions between units, and these properties make block particle filters an effective tool for simulation-based likelihood evaluation. Iterated filtering algorithms can facilitate likelihood maximization for simulation-based filters. We introduce an iterated block particle filter applicable when parameters are unit-specific or shared between units. We demonstrate this algorithm by performing inference on a coupled epidemiological model describing spatiotemporal measles case report data for twenty towns.

stat.ME↗

arXiv2020

GPS-Denied Navigation Using SAR Images and Neural Networks

Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout the synthetic aperture. The proposed neural network approach is able to learn to predict the initial errors on both simulated and real SAR image data.

cs.CV↗