Show simple item record

dc.contributor.advisorTempone, Raul
dc.contributor.authorMoraes, Alvaro
dc.date.accessioned2015-02-11T11:53:55Z
dc.date.available2016-02-11T00:00:00Z
dc.date.issued2015-01
dc.identifier.doi10.25781/KAUST-532M8
dc.identifier.urihttp://hdl.handle.net/10754/344375
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.
dc.language.isoen
dc.subjectstochastic numerics
dc.subjectstochastic processes
dc.subjectmulti-level monte carlo
dc.subjectstochastic reaction networks
dc.subjectSimulation
dc.subjectstatistical inference
dc.titleSimulation and Statistical Inference of Stochastic Reaction Networks with Applications to Epidemic Models
dc.typeDissertation
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.rights.embargodate2016-02-11
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberKnio, Omar
dc.contributor.committeememberBisetti, Fabrizio
dc.contributor.committeememberGenton, Marc G.
dc.contributor.committeememberGiles, Michael B.
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameDoctor of Philosophy
dc.rights.accessrightsAt the time of archiving, the student author of this dissertation opted to temporarily restrict access to it. The full text of this dissertation became available to the public after the expiration of the embargo on 2016-02-11.
refterms.dateFOA2016-02-11T00:00:00Z


Files in this item

Thumbnail
Name:
Alvaro_Moraes_ PhD_Thesis copy.pdf
Size:
9.312Mb
Format:
PDF
Description:
Thesis

This item appears in the following Collection(s)

Show simple item record