arXiv subjects

Aaron A. King

Publications and source records attributed to Aaron A. King.

17 recordsLinked to original sources

arXiv2026

Exact phylodynamic likelihood via structured Markov genealogy processes

We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed genealogy in terms of a filter equation, the structure of which is completely determined by the population model. We show that existing phylodynamic methods based on the coalescent and linear birth-death processes are special cases. We derive some properties of filter equations and describe a class of algorithms that can be used to numerically solve them. Importantly, because these algorithms rely only on simulation of the population model, they retain the plug-and-play property upon which simulation-based inference depends. Our results open the door to statistically efficient likelihood-based phylodynamic inference for a much wider class of models than has been possible.

q-bio.QM↗

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↗

arXiv2025

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↗

arXiv2024

A tutorial on spatiotemporal partially observed Markov process models via the R package spatPomp

We describe a computational framework for modeling and statistical inference on high-dimensional stochastic dynamic systems. Our primary motivation is the investigation of metapopulation dynamics arising from a collection of spatially distributed, interacting biological populations. To make progress on this goal, we embed it in a more general problem: inference for a collection of interacting partially observed nonlinear non-Gaussian stochastic processes. Each process in the collection is called a unit; in the case of spatiotemporal models, the units correspond to distinct spatial locations. The dynamic state for each unit may be discrete or continuous, scalar or vector valued. In metapopulation applications, the state can represent a structured population or the abundances of a collection of species at a single location. We consider models where the collection of states has a Markov property. A sequence of noisy measurements is made on each unit, resulting in a collection of time series. A model of this form is called a spatiotemporal partially observed Markov process (SpatPOMP). The R package spatPomp provides an environment for implementing SpatPOMP models, analyzing data using existing methods, and developing new inference approaches. Our presentation of spatPomp reviews various methodologies in a unifying notational framework. We demonstrate the package on a simple Gaussian system and on a nontrivial epidemiological model for measles transmission within and between cities. We show how to construct user-specified SpatPOMP models within spatPomp.

stat.ME↗

arXiv2024

Inference on spatiotemporal dynamics for networks of biological populations

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference due to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been developed which enables effective likelihood-based inference for the high-dimensional partially observed stochastic dynamic models arising in metapopulation systems. The COVID-19 pandemic provides a situation where mathematical models and their policy implications were widely visible, and we use the new inferential technology to revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model limitations, and leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on January 23, 2020 in China was more effective than previously thought. We proceed to recommend statistical analysis standards for future metapopulation system modeling.

stat.AP↗

arXiv2022

Markov Genealogy Processes

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

math.PR↗

arXiv2021

Bagged filters for partially observed interacting systems

Bagging (i.e., bootstrap aggregating) involves combining an ensemble of bootstrap estimators. We consider bagging for inference from noisy or incomplete measurements on a collection of interacting stochastic dynamic systems. Each system is called a unit, and each unit is associated with a spatial location. A motivating example arises in epidemiology, where each unit is a city: the majority of transmission occurs within a city, with smaller yet epidemiologically important interactions arising from disease transmission between cities. Monte Carlo filtering methods used for inference on nonlinear non-Gaussian systems can suffer from a curse of dimensionality as the number of units increases. We introduce bagged filter (BF) methodology which combines an ensemble of Monte Carlo filters, using spatiotemporally localized weights to select successful filters at each unit and time. We obtain conditions under which likelihood evaluation using a BF algorithm can beat a curse of dimensionality, and we demonstrate applicability even when these conditions do not hold. BF can out-perform an ensemble Kalman filter on a coupled population dynamics model describing infectious disease transmission. A block particle filter also performs well on this task, though the bagged filter respects smoothness and conservation laws that a block particle filter can violate.

stat.ME↗

arXiv2021

A guide to state-space modeling of ecological time series

State-space models (SSMs) are an important modeling framework for analyzing ecological time series. These hierarchical models are commonly used to model population dynamics, animal movement, and capture-recapture data, and are now increasingly being used to model other ecological processes. SSMs are popular because they are flexible and they model the natural variation in ecological processes separately from observation error. Their flexibility allows ecologists to model continuous, count, binary, and categorical data with linear or nonlinear processes that evolve in discrete or continuous time. Modeling the two sources of stochasticity separately allows researchers to differentiate between biological variation (e.g., in birth processes) and imprecision in the sampling methodology, and generally provides better estimates of the ecological quantities of interest than if only one source of stochasticity is directly modeled. Since the introduction of SSMs, a broad range of fitting procedures have been proposed. However, the variety and complexity of these procedures can limit the ability of ecologists to formulate and fit their own SSMs. We provide the knowledge for ecologists to create SSMs that are robust to common, and often hidden, estimation problems, and the model selection and validation tools that can help them assess how well their models fit their data. In this paper, we present a review of SSMs that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications. The review is accompanied by an in-depth tutorial that demonstrates how SSMs models can be fitted and validated in R. Together, the review and tutorial present an introduction to SSMs that will help ecologists to formulate, fit, and validate their models.

stat.ME↗

arXiv2020

The Sampled Moran Genealogy Process

We define the Sampled Moran Genealogy Process, a continuous-time Markov process on the space of genealogies with the demography of the classical Moran process, sampled through time. To do so, we begin by defining the Moran Genealogy Process using a novel representation. We then extend this process to include sampling through time. We derive exact conditional and marginal probability distributions for the sampled process under a stationarity assumption, and an exact expression for the likelihood of any sequence of genealogies it generates. This leads to some interesting observations pertinent to existing phylodynamic methods in the literature. Throughout, our proofs are original and make use of strictly forward-in-time calculations and are exact for all population sizes and sampling processes.

q-bio.PE↗

arXiv2019

Panel data analysis via mechanistic models

Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared parameters while also having unit-specific parameters. To give the scientist flexibility in model specification, we are motivated to develop a framework for inference on panel data permitting the consideration of arbitrary nonlinear, partially observed panel models. We build on iterated filtering techniques that provide likelihood-based inference on nonlinear partially observed Markov process models for time series data. Our methodology depends on the latent Markov process only through simulation; this plug-and-play property ensures applicability to a large class of models. We demonstrate our methodology on a toy example and two epidemiological case studies. We address inferential and computational issues arising due to the combination of model complexity and dataset size.

stat.ME↗

arXiv2017

Monte Carlo profile confidence intervals

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As data become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present three examples arising in the study of infectious disease transmission. These three examples demonstrate our methodology for inference on nonlinear dynamic models using genetic sequence data, panel time series data, and spatiotemporal data. We also discuss applicability to nonlinear time series analysis.

stat.ME↗

arXiv2016

Cholera forecast for Dhaka, Bangladesh, with the 2016 El Niño

A substantial body of work supports a teleconnection between the El Niño Southern Oscillation (ENSO) and cholera incidence in Bangladesh. In particular, high positive anomalies during the winter (Dec-Feb) in Sea Surface Temperatures (SST) in the Tropical Pacific have been shown to exacerbate the seasonal outbreak of cholera following the monsoons from Aug to Nov, and climate studies have indicated a role of regional precipitation over Bangladesh in mediating this long-distance effect. Thus, the current strong El Niño has the potential to significantly increase cholera risk this year in Dhaka, Bangladesh, where the last five years have experienced low seasons of the disease. To examine this possibility and produce a forecast for the city, we considered two models for the transmission dynamics of cholera: a statistical model previously developed for the disease in this region, and a process-based model presented here that includes the effect of SST anomalies in the force of infection and is fitted to extensive cholera surveillance record between 1995 and 2010. Prediction accuracy was evaluated with 'out-of-fit' data from the same surveillance efforts, by comparing the total number of cholera cases observed for the season to those predicted by model simulations 8 to 12 months ahead, starting in January each year. Encouraged by accurate forecasts for the low risk of cholera for this period, we then generated a prediction for this coming season. An increase above the third quantile in cholera cases is expected for the period of Aug - Dec 2016 with 92% and 87% probability respectively for the two models. This alert warrants the preparedness of the public health system. We discuss the possible limitations of our approach, including variations in the impact of El Niño events, and the importance of this large, warm event for further informing an early-warning system for cholera in Dhaka

q-bio.PE↗

arXiv2015

Statistical Inference for Partially Observed Markov Processes via the R Package pomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.

stat.ME↗

arXiv2015

Detecting adaptive evolution in phylogenetic comparative analysis using the Ornstein-Uhlenbeck model

Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and more detailed evolutionary hypotheses, including adaptive hypotheses with multiple selective optima and hypotheses with rate variation within and across lineages. The statistical performance of these sophisticated models has received relatively little systematic attention, however. We conducted an extensive simulation study to quantify the statistical properties of a class of models toward the simpler end of the spectrum that model phenotypic evolution using Ornstein-Uhlenbeck processes. We focused on identifying where, how, and why these methods break down so that users can apply them with greater understanding of their strengths and weaknesses. Our analysis identifies three key determinants of performance: a discriminability ratio, a signal-to-noise ratio, and the number of taxa sampled. Interestingly, we find that model-selection power can be high even in regions that were previously thought to be difficult, such as when tree size is small. On the other hand, we find that model parameters are in many circumstances difficult to estimate accurately, indicating a relative paucity of information in the data relative to these parameters. Nevertheless, we note that accurate model selection is often possible when parameters are only weakly identified. Our results have implications for more sophisticated methods inasmuch as the latter are generalizations of the case we study.

q-bio.PE↗

arXiv2015

Avoidable errors in the modeling of outbreaks of emerging pathogens, with special reference to Ebola

As an emergent infectious disease outbreak unfolds, public health response is reliant on information on key epidemiological quantities, such as transmission potential and serial interval. Increasingly, transmission models fit to incidence data are used to estimate these parameters and guide policy. Some widely-used modeling practices lead to potentially large errors in parameter estimates and, consequently, errors in model-based forecasts. Even more worryingly, in such situations, confidence in parameter estimates and forecasts can itself be far over-estimated, leading to the potential for large errors that mask their own presence. Fortunately, straightforward and computationally inexpensive alternatives exist that avoid these problems. Here, we first use a simulation study to demonstrate potential pitfalls of the standard practice of fitting deterministic models to cumulative incidence data. Next, we demonstrate an alternative based on stochastic models fit to raw data from an early phase of 2014 West Africa Ebola Virus Disease outbreak. We show not only that bias is thereby reduced, but that uncertainty in estimates and forecasts is better quantified and that, critically, lack of model fit is more readily diagnosed. We conclude with a short list of principles to guide the modeling response to future infectious disease outbreaks.

q-bio.PE↗

arXiv2009

Time series analysis via mechanistic models

The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plug-and-play property. Our work builds on recently developed plug-and-play inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae.

math.ST↗