Dottorato in SCUOLA DI SCIENZE STATISTICHE

Titolo della tesi: Spatial Point Pattern Estimation Using Integrated Laplace Approximation: Methodology and Applicaions

This thesis presents the primary research projects conducted during my PhD program. All projects focus on the challenges of performing spatial analysis by integrating data from diverse sources, a topic that is receiving increasing attention in statistical research due to the exponential growth of data collection technologies, such as social networks and Citizen Science campaigns. The rising demand for advanced analytical methods is driven by the proliferation of devices capable of recording fine-scale spatial data with high temporal resolution, enabling detailed exploration of phenomena across various fields, including ecology, epidemiology, geology, and economics. The thesis begins with an introduction to spatial statistics, outlining its historical development and core concepts. This section also presents the core principles of Bayesian statistics and outlines the applied context of my research. Chapter 2 explores the spatial analysis of processes, discussing key properties of spatial process analysis with a focus on one of its most widely applied types: spatial point processes. Point process models are a natural choice for species distribution modeling when data are represented as point events (presence-only data). This chapter examines a specific type of point process known as Poisson processes, with a particular focus on Log-Gaussian Cox processes. These processes are widely used in point process modeling because they incorporate the properties of the multivariate normal distribution within the framework of Cox processes. In addition, the chapter addresses the computational challenges inherent in spatial models by analyzing strategies in the Bayesian framework, starting from MCMC-based methods to the latest Integrated Nested Laplace approximation method. Chapter 3 presents three applications of the methodology developed during the research period. These applications are based on the data integration methodology defined by Martino, Pace, et al. (2021), highlighting advancements that enable its use in increasingly diverse contexts. Establishing clear protocols that outline the correct estimates’ methodologies to be followed is crucial for studies related to wildlife conservation. It is essential to utilize modern data sources to address the limitations of traditional protocols. However, non-standard data are difficult to use and are often biased by human activity. Therefore, it is necessary to define accurate estimation procedures that account for all potential sources of bias and produce the most accurate estimates possible. Finally, Chapter 4 summarizes the original contributions of the thesis and emphasizes the evolving role of statistical modeling in addressing modern, datadriven challenges. The thesis underscores the importance of continuously adapting and innovating statistical methodologies in response to technological advancements and the increasing complexity of datasets.