Wang, Zhongzhen; (2021) Statistical modelling approaches with Bayesian tensor factorisations. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

We propose a flexible nonparametric Bayesian modelling of univariate and multivariate time series of count data based on conditional tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with non-linear serial dependence or, with an introduction of appropriate latent variables, as a Bayesian hierarchical model with conditionally independent Poisson distributed observations. Inference about the important lags and their complex interactions is achieved via Markov chain Monte Carlo. When the observed counts are large, we deal with the resulting computational complexity of the model by performing an initial analysis in a training set of the data that is not used further in the inference and prediction. Our methodology is illustrated using simulation experiments and real-world data. Our Bayesian tensor factorisations model can have a good performance in inference and prediction on time series of count data that tends to be non-linear, and in the meanwhile, can deal with Markov chains of linear or log-linear count data. Moreover, our Bayesian tensor factorisations model can capture higher-order interactions among the lags and then, maximal orders, in time series where the actual order of Markov chain of count data and serial dependence are unknown.

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