New methods for infinite and high-dimensional approximate Bayesian computation

dc.contributor.advisor Sisson, Scott en_US
dc.contributor.advisor Fan, Yanan en_US Rodrigues, Guilherme en_US 2022-03-22T15:45:00Z 2022-03-22T15:45:00Z 2017 en_US
dc.description.abstract The remarkable complexity of modern applied problems often requires the use of probabilistic models where the likelihood is intractable -- in the sense that it cannot be numerically evaluated, not even up to a normalizing constant. The statistical literature provides an extensive array of methods designed to bypass this constraint. Still, inference in this context remains computationally challenging, particularly for high-dimensional models. We focus on the important class of Approximation Bayesian Computation (ABC) methods. Various state-of-the-art ABC techniques are combined to fit an intractable model that describes the epidemiological dynamics of multidrug-resistant tuberculosis. This study addresses a number of important biological questions in a principled manner, providing useful insights to this extraordinarily relevant research topic. We propose a functional regression adjustment ABC procedure that permits the estimation of infinite-dimensional parameters, which effectively launches ABC into the non-parametric framework. Two likelihood-free algorithms are also introduced. The first exploits the principles of ABC and the so-called coverage property to recalibrate an auxiliary approximate posterior estimator. This approach further strengthens the links between ABC and indirect inference, allowing a more comprehensive use of the auxiliary estimator. The second algorithm employs the ABC machinery to build approximate samplers for the intractable full conditional distributions. These samplers are then combined to form a likelihood-free approximate Gibbs sampler. The granular nature of our approach (that comes from breaking down the problem into small pieces) makes it suitable for highly-structured problems. We demonstrate this property by fitting an intractable and very high-dimensional state space model. en_US
dc.language English
dc.language.iso EN en_US
dc.publisher UNSW, Sydney en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri en_US
dc.subject.other Gibbs sampler en_US
dc.subject.other approximate Bayesian computation (ABC) en_US
dc.subject.other Gaussian process prior en_US
dc.subject.other hierarchical models en_US
dc.subject.other indirect inferenceintractable state space models en_US
dc.subject.other likelihood-free inference en_US
dc.subject.other nonparametric density estimation en_US
dc.subject.other regression-adjustment en_US
dc.title New methods for infinite and high-dimensional approximate Bayesian computation en_US
dc.type Thesis en_US
dcterms.accessRights open access
dcterms.rightsHolder Rodrigues, Guilherme
dspace.entity.type Publication en_US
unsw.relation.faculty Science
unsw.relation.originalPublicationAffiliation Rodrigues, Guilherme , Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Sisson, Scott, Mathematics & Statistics, Faculty of Science, UNSW en_US
unsw.relation.originalPublicationAffiliation Fan, Yanan, Mathematics & Statistics, Faculty of Science, UNSW en_US School of Mathematics & Statistics *
unsw.thesis.degreetype PhD Doctorate en_US
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