Simulation and Statistical Inference of Stochastic Reaction Networks with Applications to Epidemic Models

Handle URI:
http://hdl.handle.net/10754/344375
Title:
Simulation and Statistical Inference of Stochastic Reaction Networks with Applications to Epidemic Models
Authors:
Moraes, Alvaro ( 0000-0003-4144-1243 )
Abstract:
Epidemics have shaped, sometimes more than wars and natural disasters, demo- graphic aspects of human populations around the world, their health habits and their economies. Ebola and the Middle East Respiratory Syndrome (MERS) are clear and current examples of potential hazards at planetary scale. During the spread of an epidemic disease, there are phenomena, like the sudden extinction of the epidemic, that can not be captured by deterministic models. As a consequence, stochastic models have been proposed during the last decades. A typical forward problem in the stochastic setting could be the approximation of the expected number of infected individuals found in one month from now. On the other hand, a typical inverse problem could be, given a discretely observed set of epidemiological data, infer the transmission rate of the epidemic or its basic reproduction number. Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 4 This PhD thesis is focused on novel fast simulation algorithms and statistical inference methods for SRNs. Our novel Multi-level Monte Carlo (MLMC) hybrid simulation algorithms provide accurate estimates of expected values of a given observable of SRNs at a prescribed final time. They are designed to control the global approximation error up to a user-selected accuracy and up to a certain confidence level, and with near optimal computational work. We also present novel dual-weighted residual expansions for fast estimation of weak and strong errors arising from the MLMC methodology. Regarding the statistical inference aspect, we first mention an innovative multi- scale approach, where we introduce a deterministic systematic way of using up-scaled likelihoods for parameter estimation while the statistical fittings are done in the base model through the use of the Master Equation. In a di↵erent approach, we derive a new forward-reverse representation for simulating stochastic bridges between con- secutive observations. This allows us to use the well-known EM Algorithm to infer the reaction rates. The forward-reverse methodology is boosted by an initial phase where, using multi-scale approximation techniques, we provide initial values for the EM Algorithm.
Advisors:
Tempone, Raul Fidel ( 0000-0003-1967-4446 )
Committee Member:
Knio, Omar; Bisetti, Fabrizio ( 0000-0001-5162-7805 ) ; Genton, Marc; Giles, Michael
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
Jan-2015
Type:
Dissertation
Appears in Collections:
Applied Mathematics and Computational Science Program; Dissertations; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorTempone, Raul Fidelen
dc.contributor.authorMoraes, Alvaroen
dc.date.accessioned2015-02-11T11:53:55Z-
dc.date.available2015-02-11T11:53:55Z-
dc.date.issued2015-01en
dc.identifier.urihttp://hdl.handle.net/10754/344375en
dc.description.abstractEpidemics have shaped, sometimes more than wars and natural disasters, demo- graphic aspects of human populations around the world, their health habits and their economies. Ebola and the Middle East Respiratory Syndrome (MERS) are clear and current examples of potential hazards at planetary scale. During the spread of an epidemic disease, there are phenomena, like the sudden extinction of the epidemic, that can not be captured by deterministic models. As a consequence, stochastic models have been proposed during the last decades. A typical forward problem in the stochastic setting could be the approximation of the expected number of infected individuals found in one month from now. On the other hand, a typical inverse problem could be, given a discretely observed set of epidemiological data, infer the transmission rate of the epidemic or its basic reproduction number. Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 4 This PhD thesis is focused on novel fast simulation algorithms and statistical inference methods for SRNs. Our novel Multi-level Monte Carlo (MLMC) hybrid simulation algorithms provide accurate estimates of expected values of a given observable of SRNs at a prescribed final time. They are designed to control the global approximation error up to a user-selected accuracy and up to a certain confidence level, and with near optimal computational work. We also present novel dual-weighted residual expansions for fast estimation of weak and strong errors arising from the MLMC methodology. Regarding the statistical inference aspect, we first mention an innovative multi- scale approach, where we introduce a deterministic systematic way of using up-scaled likelihoods for parameter estimation while the statistical fittings are done in the base model through the use of the Master Equation. In a di↵erent approach, we derive a new forward-reverse representation for simulating stochastic bridges between con- secutive observations. This allows us to use the well-known EM Algorithm to infer the reaction rates. The forward-reverse methodology is boosted by an initial phase where, using multi-scale approximation techniques, we provide initial values for the EM Algorithm.en
dc.language.isoenen
dc.subjectstochastic numericsen
dc.subjectstochastic processesen
dc.subjectmulti-level monte carloen
dc.subjectstochastic reaction networksen
dc.subjectSimulationen
dc.subjectstatistical inferenceen
dc.titleSimulation and Statistical Inference of Stochastic Reaction Networks with Applications to Epidemic Modelsen
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberKnio, Omaren
dc.contributor.committeememberBisetti, Fabrizioen
dc.contributor.committeememberGenton, Marcen
dc.contributor.committeememberGiles, Michaelen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameDoctor of Philosophyen
dc.person.id102007en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.