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Bayesian inference methods for latent variable modelling

Vamvourellis, Konstantinos (2021) Bayesian inference methods for latent variable modelling. PhD thesis, London School of Economics and Political Science.

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Identification Number: 10.21953/lse.00004380

Abstract

This thesis develops novel Bayesian Inference methodology for a wide range of factor analysis models. The contributions consist of new Bayesian modelling approaches and the associated Bayesian inference methodology, novel model assessment frameworks and proposed applications of these models in clinical pharmacology. The first section focuses on developing a generalised framework for Bayesian Structural Equation Modelling (SEM) that can be applied to a variety of data types. It extends the previously available framework enhancing the available capabilities in two ways: it can handle binary and ordinal data, in addition to continuous data, which was known before, and it allows the errors to follow any distribution possible, removing the previously imposed restriction of Gaussianity. Moreover, it proposes a novel model assessment paradigm aiming to address shortcomings of posterior predictive p-values, which provide the default metric of fit for Bayesian SEM. The second section extends this framework to the sequential setting utilising techniques from the area of Sequential Monte Carlo. Sequential frameworks are powerful tools that can be used in dynamic settings where statistical inference is performed recursively on a continuous stream of data. In addition, this sequential approach is used for hypothesis testing, where it has been proven superior to the traditional null hypothesis (NHST) paradigm. Sequential Bayesian Factor (SBF) do not suffer from bias associated with the stopping rule, the practice of stopping the processing of new data only when conclusive evidence can be reached. The third section, extends these frameworks to data of mixed type, combining categorical and continuous types, to be used in clinical trial analysis where data is commonly of such mixed type. It develops a novel sequential modelling paradigm to inform regulatory evaluation of new drugs in real time while incorporating all the data available as well as clinical weights of importance relative to patient outcomes.

Item Type: Thesis (PhD)
Additional Information: © 2021 Konstantinos Vamvourellis
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Statistics
Supervisor: Kalogeropoulos, Konstantinos
URI: http://etheses.lse.ac.uk/id/eprint/4380

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