1. Towards Robust Prediction Using The Elliptical Process for Regression

   A.B. Al Khabori*, M.T. Alodat and Amadou Sarr

   Department of Statistics, Sultan Qaboos University, Al-Khod Muscat, Sultanate of Oman
   

   Abstract:

   We present a novel Bayesian family of models, Elliptical Processes (EPs), designed to extend regression modeling framework. Unlike the widely used Gaussian Process (GP) Regression, EPs generalize the GP framework by accommodating non-normal tail distributions and outlier-prone data, where Gaussian assumptions often fail. In this paradigm, the GP is still a special case, but EPs are more accurate, especially when dealing with heavy-tailed data. We use the Laplace approximation technique to ensure scalability and computational efficiency while addressing the analytical complexity inherent in EP inference. We derive the predictive distribution for EPs at new input points and provide a comprehensive performance comparison with GP, T-Process, and other EP models. The proposed EP, particularly under non-Gaussian assumptions, outperform the GP by demonstrating superior performance and flexibility in handling complex data structures across both simulated and real-world scenarios.

   Keywords: Bayesian Inference, Elliptical Process, Gaussian Process, Laplace approximation, Predictive distribution, Regression.

   Pages: 47 – 85 | Full PDF Paper

2. Model-Free Organization of Patient Reported Outcomes Data: Geometrical Rep-resentation of the Modified Compartmen-talization Method

   Manasi Sheth^1,2, N. Rao Chaganty³

   1. Department of Mathematics, University of Wisconsin – Whitewater, WI, USA.
   2. Department of Computer Science, University of Wisconsin – Whitewater,WI, USA.
   3. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, USA.
   

   Abstract:

   There is a recent advancement in the field of mathematics and statistics to understand the geometry or connectedness of the data due to the massive amounts of data being generated. The data provided for analyses are usually very large and need to be organized and minimized in order to make it more useful and meaningful. In biostatistics or medical field, it is important for patients to have access to high-quality, safe and effective and/ or efficacious medical products. It is quite necessary to ascertain that the patients and their care-partners stay at the center of the regulatory decision-making process. In order to do so, it becomes necessary to partner with the patients by incorporating the patient perspective as evidence in the decision-making process, including patient-reported outcomes (PROs). PROs are often relevant in assessing diagnostic evaluations and can be used to capture a patient’s everyday experience with a medical product, including experience outside of the clinician’s office and the effects of the treatment on a patient’s activities of daily living and functionality. In some cases, PRO measures enable us to measure important health status information that cannot yet be detected by other measures, such as pain and mobility. Here, we present the geometrical representations of a novel approach of analyzing PROs using Modified Compartmentalization Method.

   Keywords: Compartmentalization Method, Patient Reported Outcomes, Geom-etry, Transition Proportion Matrix, Repeated Measures, Longitudinal Data.

   Pages: 87 – 96 | Full PDF Paper