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Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... 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 consi ..."
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Cited by 13 (5 self)
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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 plugandplay property. Our work builds on recently developed plugandplay 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. 1. Introduction. A
Monte Carlo inference for statespace models of wild animal populations
, 2007
"... We compare two Monte Carlo procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of statespace models for animal populations. The procedures were applied to both simulated and real pup count data ..."
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Cited by 3 (1 self)
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We compare two Monte Carlo procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of statespace models for animal populations. The procedures were applied to both simulated and real pup count data for the British grey seal metapopulation, as well as to simulated data for a Chinook salmon population. The MCMC implementation was based on tailormade proposal distributions combined with analytical integration of some of the states and parameters. SIS was implemented in a more generic fashion. For the same computing time MCMC tended to yield posterior distributions with less Monte Carlo variation across different runs of the algorithm than did the SIS implementation with the exception in the seal model of some states and one of the parameters which mixed quite slowly. The efficiency of the SIS sampler greatly increased by analytically integrating out unknown parameters in the observation model. We consider that a careful implementation of MCMC for cases where data are informative relative to the priors sets the gold standard, but that SIS samplers are a viable alternative that can be programmed more quickly. Our SIS implementation is particularly competitive in situations where the data are relatively uninformative; in other cases, SIS may require substantially more computer power than an efficient implementation of MCMC to achieve the same level of Monte Carlo error.
Ed Ionides Infectious disease dynamics: a statistical perspective 1 Infectious disease dynamics: a statistical perspective CCMB/Bioinformatics Seminar
, 2009
"... Why do we seek to quantify and understand disease dynamics? • Prevention and control of emerging infectious diseases (SARS, HIV/AIDS, H5N1 influenza “bird flu”) • Understanding the development and spread of drug resistant strains (malaria, tuberculosis, MRSA “the hospital superbug”) Ed Ionides Infe ..."
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Why do we seek to quantify and understand disease dynamics? • Prevention and control of emerging infectious diseases (SARS, HIV/AIDS, H5N1 influenza “bird flu”) • Understanding the development and spread of drug resistant strains (malaria, tuberculosis, MRSA “the hospital superbug”) Ed Ionides Infectious disease dynamics: a statistical perspective 4 Disease dynamics: epidemiology or ecology, or both? • Environmental host/pathogen dynamics are close to predator/prey relationships which are a central topic of ecology. • Analysis of diseases as ecosystems complements more traditional epidemiology (risk factors etc). • Ecologists typically seek to avoid extinctions, whereas epidemiologists typically seek the reverse. Things are not always this simple... – Helicobacter pylori bacteria used to live in the stomach of most humans. Some strains cause stomach ulcers and cancer. It is almost extinct in the developed world due to widespread use of
Ed Ionides The theory and practice of iterated filtering 1 The theory and practice of iterated filtering
, 2008
"... Inference for static parameters in state space models (i.e., unknown model parameters that do not vary in time) • Numerical issues have led to a considerable literature on this topic. • Iterated filtering maximizes the likelihood function via taking an average of filtered “local ” parameter estimate ..."
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Inference for static parameters in state space models (i.e., unknown model parameters that do not vary in time) • Numerical issues have led to a considerable literature on this topic. • Iterated filtering maximizes the likelihood function via taking an average of filtered “local ” parameter estimates obtained by adding noise to the static parameters (which regularizes the numerical issues). This process is recursively repeated while reducing the added noise. • Iterated filtering, implemented by basic SMC, has a plugandplay property: it requires simulation from the state process but not transition densities. Ed Ionides The theory and practice of iterated filtering 3 Plugandplay methods for state space models • Statistical methods are plugandplay if they require simulation from the dynamic model but not explicit likelihood ratios. • Bayesian plugandplay: 1. Artificial parameter evolution (Liu and West, 2001)
RAPIDD: Research and Policy in Infectious Disease Dynamics
, 2008
"... Ed Ionides Time series analysis of infectious disease dynamics 1 Time series analysis of infectious disease dynamics: State of the art and future challenges Epidemic model hierarchies and model validation workshop ..."
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Ed Ionides Time series analysis of infectious disease dynamics 1 Time series analysis of infectious disease dynamics: State of the art and future challenges Epidemic model hierarchies and model validation workshop
Invited Session Discussion
, 2008
"... What is a “mechanistic ” approach to time series analysis? • Write down equations, based on scientific understanding of a dynamic system, which describe how it evolves with time. • Further equations describe the relationship of the state of the system to available observations on it. • Mechanistic t ..."
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What is a “mechanistic ” approach to time series analysis? • Write down equations, based on scientific understanding of a dynamic system, which describe how it evolves with time. • Further equations describe the relationship of the state of the system to available observations on it. • Mechanistic time series analysis concerns drawing inferences from the available data about the hypothesized equations. • Questions of general interest: Are the data consistent with a particular model? If so, for what range of values of model parameters? Does one mechanistic model describe the data better than another? • A defining principle: the model structure should be chosen based on scientific considerations, rather than statistical convenience. Ed Ionides Time series analysis via mechanistic models 3 Example: why quantify biological population dynamics? • Conservation. Mankind is increasingly responsible for managing ecosystems. This requires a quantitative understanding of population behavior. • Public health. Pathogens are also biological populations. Despite successes of vaccination and medical treatment, new diseases are emerging (SARS, HIV/AIDS) and old ones reemerging due to drug resistant strains (malaria, tuberculosis). Treating the pathogen as part of an ecosystem is one approach to understanding and controlling emergent and reemergent diseases. • Basic scientific interest. Ed Ionides Time series analysis via mechanistic models 4 Time series data of sufficient quantity and quality to justify mechanistic modeling are increasingly available: Two recent examples • King, Ionides, Pascual and Bouma. Inapparent infections and cholera dynamics. To appear in Nature.
ITERATED FILTERING 1
"... Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of fi ..."
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Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated filtering algorithms implemented via sequential Monte Carlo filters. This theory complements the growing body of empirical evidence that iterated filtering algorithms provide an effective inference strategy for scientific models of nonlinear dynamic systems. The first step in our theory involves studying a new recursive approach for maximizing the likelihood function of a latent variable model, when this likelihood is evaluated via importance sampling. This leads to the consideration of an iterated importance sampling algorithm which serves as a simple special case of iterated filtering, and may have applicability in its own right. 1. Introduction. Partially observed Markov process (POMP) models are
Iterated Filtering
, 2011
"... Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of fi ..."
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Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated filtering algorithms implemented via sequential Monte Carlo filters. This theory complements the growing body of empirical evidence that iterated filtering algorithms provide an effective inference strategy for scientific models of nonlinear dynamic systems. The first step in our theory involves studying a new recursive approach for maximizing the likelihood function of a latent variable model, when this likelihood is evaluated via importance sampling. This leads to the consideration of an iterated importance sampling algorithm which serves as a simple special case of iterated filtering, and may have applicability in its own right. 1
DEDICATION.................................
, 2010
"... Time series analysis for nonlinear dynamical systems with applications to modeling of infectious diseases by ..."
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Time series analysis for nonlinear dynamical systems with applications to modeling of infectious diseases by