March 24, 2025

About the speaker

Dr. Fahad Mostafa is a tenure-track assistant professor in statistics at the New College Interdisciplinary of Arts and Sciences of Arizona State University. His recent focus has been on identifying patterns in high-dimensional biomedical data, particularly in infectious diseases, Cancer and Alzheimer disease research. Using statistical learning/AI, he aims to enhance disease diagnosis and monitoring, with a special emphasis on EHR, cancer infrared tomography, genomics, and medical imaging. His interdisciplinary approach merges advanced statistical modeling, time series analysis, and machine learning techniques, improving the accuracy and reliability of disease prediction, diagnosis, and treatment. Before joining to ASU, he was a postdoctoral researcher, and ORISE fellow at CU Anschutz, and NCTR, FDA, respectively.

Periodic Mean-Reverting SDE Models for Seasonal Time Series

Seasonal fluctuations are evident across a wide range of environmental and biological systems. These variations impact diverse phenomena, including the growth cycles of plants, the dynamics of animal populations, and the occurrence of disease outbreaks. Such periodic changes are integral to understanding the natural patterns and behaviors within ecosystems and human health. Periodic mean-reverting stochastic differential equations (SDEs) effectively capture these seasonal patterns. We explore periodic mean- reverting SDE models and apply them to influenza and temperature data, given by \( dX(t) = r(\beta(t) - X(t)) \, dt + d\beta(t) + \sigma X^p(t) \, dW(t) \) for \( p = 0, \frac{1}{2}, 1 \), with periodic mean \(\beta(t)\). For \( p = 0 \), the SDE corresponds to the Ornstein- Uhlenbeck process with an asymptotic normal distribution. The models with \( p = \frac{1}{2} \) and \( p = 1 \) relate to the Cox-Ingersoll-Ross (CIR) process and geometric Brownian motion (GBM), respectively, demonstrating periodic higher-order moments, if they exist. We address missing influenza data using a modified MissForest algorithm. Model parameters are estimated in two steps: first, fitting the mean function \(\beta(t)\) via least squares, and second, fitting \( r \) and \(\sigma\) to the SDE model using maximum likelihood estimation, with bootstrap confidence interval regions computed for both parameters