We present new approaches for analyses of temporally dependent data. The project consists of two parts. In the first part, we consider time-domain models for univariate and multivariate count time series data. Poisson autoregressive (PAR) models and related extensions, such as Poisson ARMA and multivariate versions of these models, including Poisson spatio-temporal ARMA and Poisson network AR models, are often used to analyze count data. However, many inferential approaches fail to incorporate ergodicity conditions for these models. We propose to account for ergodicity conditions by means of structured prior distributions on the model parameters and consider posterior inference in this setting. We also extend this approach to incorporate additional shrinkage on the model parameters. We conduct simulation studies and analyze daily COVID-19 new case data of selected California counties to illustrate our modeling approach. Some future extensions are also discussed, such as adding a zero-inflating latent structure, incorporating covariates, and considering models with time-varying parameters.

In the second part we present frequency-domain models for quantile spectral analysis of multi-dimensional time series data that have a hierarchical structure. Motivated by the need to analyze mouse brain data from fourteen brain function-based regions, where each region consists of several time series, we propose a Bayesian model for inferring multivariate quantile spectra that uses a hierarchical factor model representation that adequately incorporates the labeling information of the time series, extending the work of [Hu, 2022]. We show how the proposed model allows for a parsimonious representation of the data in the frequency domain that leads to dimension reduction. We discuss posterior inference in this setting via MCMC, as well as extensions that include fast approximate algorithms for posterior inference and additional shrinkage priors.

Event Host: Seokjun Choi, Ph.D. Student, Statistical Science

Advisor: Raquel Prado