Bayesian spatial-temporal statistics for epidemic risk estimation and modelling : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University, Manawatū, New Zealand
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2024
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Massey University
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This thesis focuses on employing Bayesian methods for spatiotemporal modeling of various types of epidemiological or health-related spatial-temporal data. Spatial data types include point pattern data, point reference (geostatistical) data, and area-level (lattice) data. Different types of spatial data have different spatial resolution and virtual assumptions. Therefore, the spatial and spatiotemporal modeling approaches for different data types also differ. The thesis introduces spatial modeling methods for three types of epidemiological data, including discrete spatial model, linear geostatistical model, generalized linear geostatistical model, Poisson point process, and log-gaussian Cox process. Additionally, we elaborate on extending spatial modeling to spatiotemporal modeling for various data types. This extension is relatively intuitive to implement due to the flexibility of Bayesian methods and hierarchical Bayesian models. We used two epidemiological datasets as examples; one is Campylobacteriosis cases in the Manawatu region of New Zealand during the period Mar 2005-Sep,2016, and another dataset is from the SARS-CoV-2 wastewater surveillance program launched in 2022 in Aotearoa, New Zealand, which is used to monitor and track potential cases of COVID-19. When modeling COVID-19 using wastewater epidemiology data in New Zealand, we employ the INLA-SPDE method. This approach, a Bayesian analysis method for spatial data on intricate grids, represents a new frontier in Bayesian disease mapping techniques and has practical applications. Regarding Bayesian computational methods, we introduced the traditional Monte Carlo sampling method, the Markov chain Monte Carlo (MCMC) method, and the integrated nested Laplace approximation (INLA), an approximate Bayesian inference method. Compared to commonly used MCMC methods, INLA has a significant advantage in providing precise parameter estimates in less time and is user-friendly through the R-INLA package. R-INLA conducted all the Bayesian-related computations for this thesis. Finally, we discussed the transformation of data types related to the flexible use of spatial epidemiological data and modeling methods. It's crucial to model flexibly according to the problem we aim to solve in epidemiological modeling rather than adhering to specific data formats corresponding to particular models.