Statistical Models Commons^™

Likelihood-Based Inference For The Poisson–Tweedie Family, Si Chen

Theses and Dissertations (Comprehensive)

This thesis develops likelihood-based methodology for flexible modeling and inference for heterogeneous count data within and adjacent to the Poisson–Tweedie family. A mean–dispersion regression framework is introduced to jointly relate the mean and dispersion to covariates, enabling separation of covariate-driven heterogeneity from distributional parameters. Likelihood inference is implemented using recursive probability mass function evaluation, and performance is assessed through simulation and applications including RNA-sequence counts. The framework is extended to accommodate excess zeros via zero-inflated Poisson–Tweedie models, with full likelihood-based estimation and improved risk estimation illustrated using insurance claim data. Finally, boundary behaviour is investigated through the discrete stable distribution …

Multivariate Quantile Autoregression-Mixed Data Sampling (Mvqar-Midas) Modeling Of Cost Of Living And Supply Chain Dynamics In Canada., Patrick Gbolonyo

Theses and Dissertations (Comprehensive)

In recent years, the rising cost of living as a result of persistent inflationary pressures, disruptions in the global supply chains, and changes in the macroeconomic landscape has become a critical topic of discussion. To address this, we move beyond a mean-based framework and employ a quantile regression approach. This allows the persistence of each series and the transmis- sion of shocks between the Consumer Price Index (CPI) (the total CPI which is a percentage change over the past 12 months), the Interest Rate (IR)(the target for the overnight rate), the New Housing Price Index (NHPI), and high-frequency supply chain …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Last Passage Time And Excursion Theory For Solvable Diffusions With Applications In Mathematical Finance, Yaode Sui

Theses and Dissertations (Comprehensive)

In this dissertation, we investigate the properties of last passage times and excursion theory in one-dimensional solvable diffusions, emphasizing their applications in financial modeling, particularly in option pricing. We derive closed-form formulas for the marginal distribution of last passage times and their joint distribution with process values, including the maximum and minimum of the process value. The focus is on time-homogeneous diffusions with various boundaries and imposed killing. Employing spectral expansion theory, we derive explicit formulas for distributions of last passage times in common processes such as Drifted Brownian Motion (BM), Squared Bessel (SQB), Ornstein-Uhlenbeck (OU), and Cox-Ingersoll-Ross (CIR) models. …

Self-Exciting Point Processes In Real Estate, Ian Fraser

Theses and Dissertations (Comprehensive)

This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …

Statistical Models For Decision-Making In Professional Soccer, Sean Hellingman

Theses and Dissertations (Comprehensive)

As soccer is widely regarded as the most popular sport in the world there is high interest in methods of improving team performances. There are many ways teams and individual athletes can influence their own performances during competition. This thesis focuses on developing statistical methodologies for improving competition-based decision-making for soccer so as to allow professional soccer teams to make better informed decisions regarding player selection and in-game decision-making.

To properly capture the dynamic actions of professional soccer, Markov chains with increasing complexity are proposed. These models allow for the inclusion of potential changes in the process caused by goals …

Modeling Multivariate Hopfield-Transformer Hawkes Process: Application To Sovereign Credit Default Swaps, Mohsen Bahremani

Theses and Dissertations (Comprehensive)

Hawkes process was evolved so that the past events contribute to the occurrence time of future events by self-exciting or mutually exciting. However, many real-world data do not follow the Hawkes process's assumptions (i.e., positivity, additivity, and exponential decay) and become more complex to be modeled by the traditional Hawkes processes, so the neural Hawkes process was developed to tackle the challenges. However, Recurrent Neural Networks (RNN) fail to capture long-term dependencies among multiple point processes, and Transformer Hawkes processes only address temporal characteristics of Hawkes processes. In this thesis, we proposed a combination of neural networks and Hawkes processes …

Aggregate Loss Model With Poisson-Tweedie Loss Frequency, Si Chen

Theses and Dissertations (Comprehensive)

The aggregate loss model has applications in various areas such as financial risk management and actuarial science. The aggregate loss is the summation of all random losses occurred in a period, and it is governed by both the loss severity and the loss frequency. While the impact of the loss severity on aggregate loss is well studied, less focus is paid on the influence of loss frequency on aggregate loss, which motivates our study. In this thesis, we enrich the aggregate loss framework by introducing the Poisson-Tweedie distribution as a candidate for modelling loss frequency, prove the closedness of Poisson-Tweedie …

Spatial Modelling And Wildlife Health Surveillance: A Case Study Of White Nose Syndrome In Ontario, Lauren Yee

Theses and Dissertations (Comprehensive)

Wildlife data is often limited by survey effort, small sample sizes, and spatial biases associated with collection and missing data. These factors can create unique challenges from a surveillance perspective when trying to extract spatial patterns of habitat suitability and disease distributions for conservation and management purposes. This thesis examined data quality from a wildlife health database in the context of spatial analysis of wildlife disease. Spatial analysis of the data to predict habitat suitability of bats and white nose syndrome afflicted bats was examined by using the MaxEnt modelling method. Methods to reduce spatial bias were examined and specific …

Space-Time Modelling Of Emerging Infectious Diseases: Assessing Leptospirosis Risk In Sri Lanka, Cameron C F Plouffe

Theses and Dissertations (Comprehensive)

In this research, models were developed to analyze leptospirosis incidence in Sri Lanka and its relation to rainfall. Before any leptospirosis risk models were developed, rainfall data were evaluated from an agro-ecological monitoring network for producing maps of total monthly rainfall in Sri Lanka. Four spatial interpolation techniques were compared: inverse distance weighting, thin-plate splines, ordinary kriging, and Bayesian kriging. Error metrics were used to validate interpolations against independent data. Satellite data were used to assess the spatial pattern of rainfall. Results indicated that Bayesian kriging and splines performed best in low and high rainfall, respectively. Rainfall maps generated from …