Bayesian semiparametric inference of complex longitudinal and multiple time series systems




Fan, Jingjing, Ph. D.

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Time series inference differs from traditional statistical analysis in that there is inherent dependence between observations in a time series. In the case of multiple time series, multivariate time series, or panel data, performing inference can become even more complex because of possible interactions between different subjects, variables, or both. We develop three new methodologies capable of performing inference on multiple time series, high dimensional multivariate time series, and panel data respectively. For multiple time series, we combine functional analysis with a Hidden Markov model to create a clustering algorithm that allows each time series to change its cluster membership over time. For high dimensional multivariate time series, we develop a tensor decomposition estimation method for the Vector Autoregressive (VAR) model which greatly reduces the parameter space without sacrificing accuracy. We extend the tensor decomposed VAR into a random effects model to allow for information sharing between subjects in multi-subject panels. For panels with many subjects, we employ a divide-and-conquer strategy with embarrassingly parallel samplers to lessen the computational burden on a single estimation process.



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