A Bayesian approach to discovery of latent dependency in point-referenced data

In spatial statistics where data usually was observed as point-referenced, classical and parametric spatial models were assumed and used to describe real-world phenomena. This is generally due to the large number of spatial locations that the spatial models should cover. However, such classical methods usually rely strongly on unrealistic assumptions that real-world data do not follow. Due to this limitation, this dissertation focuses on developing statistics models that are more flexible and lead to a better understanding and explanation for the latent dependency in the real-world point-referenced data. This dissertation begins with a statistical model accounting for collective animal movement. The model highlights how to incorporate the ecological perspective into the hierarchical modeling structure, motivating the need of considering the underlying ecological structure to better understand the driving dynamics in the animal behaviors. Then, a statistical model is proposed to explain a real-world phenomenon, lightning strikes. Starting with an exploratory analysis, we found that the lightning strikes data do not follow classical assumptions in spatial models. Thus, a data-driven statistics approach is proposed, where the latent spatio-temporal dependency considered in the Log-Gaussian Cox process (LGCP) is not only non-stationary but also time-varying. The proposed method relaxes the standard assumption in spatial models (stationarity and isotropy) and thus is able to better account for the latent spatio-temporal dependency for the real-world data. Last, we propose using a novel neural-network method to overcome the computational burden in LGCP computations for posterior inference. The proposed neural-networkbased method provides faster and accurate parameter estimation as well as reliable uncertainty quantification for inference.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Statistics (MU)

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2024

Author dc:creator

• Wang, Shuwan

Advisors dc:contributor.advisor

• Wikle, Christopher K.
• Micheas, Athanasios C.

Language dc:language.iso

eng, English

DOI

https://doi.org/10.32469/10355/105052

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/105052