Monte Carlo Methods for Adaptive Disorder Problems

Ludkovski, Michael

doi:10.1007/978-3-642-25746-9_3

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…In contrast, we consider multiple underlying population pools each with a distinct, but co-dependent information channel. In terms of explicitly accounting for spatial propagation, our work is closest to [38] who considered a spatial "wave" model for an epidemic. In the present article, we connect this framework to the SIR context, modeling epidemic spread across geographically-based population pools.…”

Section: Spatial Stochastic Epidemic Modelsmentioning

confidence: 99%

Computational Method for Epidemic Detection in Multiple populations

Shatskikh¹,

Ludkovski²

2015

OJPHI

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Section: Spatial Stochastic Epidemic Modelsmentioning

confidence: 99%

Computational Method for Epidemic Detection in Multiple populations

Shatskikh¹,

Ludkovski²

2015

OJPHI

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“…As we have seen before, {Z t } is finite dimensional if at least one of {M t } or Θ is observed, but is infinite-dimensional in the main case of interest (c) requiring joint inference. Using the Markov structure, the optimal policy response φ * t at time t is a function of the posterior state Z t , φ * t = Φ(I t , Z t , φ t− ), for some strategy rule Φ. Analytic treatment of such infinite-dimensional control problems is generally intractable; see Ludkovski and Niemi [2010], Ludkovski [2012b] for flexible numerical approximations that also rely on SMC.…”

Section: Optimized Policy Responsementioning

confidence: 99%

Sequential Bayesian inference in hidden Markov stochastic kinetic models with application to detection and response to seasonal epidemics

Lin

Ludkovski

2013

Stat Comput

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We study sequential Bayesian inference in continuous-time stochastic kinetic models with latent factors. Assuming continuous observation of all the reactions, our focus is on joint inference of the unknown reaction rates and the dynamic latent states, modeled as a hidden Markov factor. Using insights from nonlinear filtering of jump Markov processes we develop a novel sequential Monte Carlo algorithm for this purpose. Our approach applies the ideas of particle learning to minimize particle degeneracy and exploit the analytical jump Markov structure. A motivating application of our methods is modeling of seasonal infectious disease outbreaks represented through a compartmental epidemic model. We demonstrate inference in such models with several numerical illustrations and also discuss predictive analysis of epidemic countermeasures using sequential Bayes estimates.

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Bayesian Quickest Detection in Sensor Arrays

Ludkovski¹

2012

Sequential Analysis

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Abstract:We study Bayesian quickest detection problems with sensor arrays. An underlying signal is assumed to gradually propagate through a network of several sensors, triggering a cascade of inter-dependent change-points. The aim of the decision-maker is to centrally fuse all available information to find an optimal detection rule that minimizes Bayes risk. We develop a tractable continuous-time formulation of this problem focusing on the case of sensors collecting point process observations and monitoring the resulting changes in intensity and type of observed events. Our approach uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with Monte Carlo based approach to dynamic programming. The developed models and algorithms are illustrated with plenty of numerical examples.

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Monte Carlo Methods for Adaptive Disorder Problems

Cited by 5 publications

References 29 publications

Computational Method for Epidemic Detection in Multiple populations

Computational Method for Epidemic Detection in Multiple populations

Sequential Bayesian inference in hidden Markov stochastic kinetic models with application to detection and response to seasonal epidemics

Bayesian Quickest Detection in Sensor Arrays

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