Tsokos, Alkeos; (2020) Exploiting smoothness in regression and joint models: estimation, inference, and interpretation for models with smooth components. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

In this thesis we explore various aspects of smooth modelling. We make contributions in two main areas. The first is in generalized additive modelling, for which we propose an approach that allows for the estimation of functions in a locally adaptive way that does not require the estimation of tuning parameters, and consequently scales well with the number of predictors. This is achieved through the use of a particular sparsity inducing prior on the coefficients of b-splines that are used to represent smooth functions. In addition, we propose a method to determine the individual and relative importance of predictors in generalized additive models, aiding in their interpretation and explanatory power. The second topic we explore is a scenario in which multiple associated variables vary smoothly as a function of some argument, and the objective is to estimate the associations between them. To tackle this problem we propose a general framework that we name structural smooth modelling. Our approach allows us to model multiple stochastic processes jointly, estimating associations between them, without assuming that each process has been observed at the same set of argument values. The general model is flexible and potentially applicable in a variety of disciplines. As a use case we apply the model to data obtained from British Cycling, demonstrating strong potential for the framework to be used as a way to track athlete performance and estimate associations between performance in different types of training efforts.

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