Academic

Abstract

Regression analysis is undoubtedly an important tool to understand the relationship between one or more explanatory and independent variables of interest. The problem of estimating a generic regression function in a model with normal errors is considered. For this purpose, a novel objective prior to the regression function is proposed, defined as the distribution maximizing entropy (subject to a suitable constraint) based on the Fisher information on the regression function. This prior is called the I-prior. The regression function is then estimated by its posterior mean under the I-prior, and accompanying hyperparameters are estimated via maximum marginal likelihood. Estimation of I-prior models is simple and inference straightforward, while predictive performances are comparative, and often better, to similar leading state-of-the-art models–as will be illustrated by several data examples. Further plans for research in this area are also presented, including variable selection for interaction effects and extending the I-prior methodology to non-Gaussian errors. Please visit the project website for further details: https://phd.haziqj.ml/ 

Biography

Dr Haziq Jamil is an assistant professor in Statistics at the Faculty of Science, Universiti Brunei Darussalam. His research interests lie in statistical theory, methods, and computation, particularly those inclining toward social science applications. Previously, he was a Research Officer at the Centre of Science & Technology, Research & Development (CSTRAD), Ministry of Defence, Brunei, where his primary task was to provide data analysis and decision support to strategic acquisition projects. He also assisted in statistical analyses for defense-related research.  Dr Haziq graduated from Warwick University, completing the 4-year Mathematics, Operational Research, Statistics and Economics (MORSE) BSc & Masters degree in 2010. He then obtained his MSc and PhD in Statistics from the London School of Economics and Political Science (LSE). His PhD project explored the use of Fisher information-dependent priors in a vector space framework for regression, classification, and variable selection. He was awarded the 2020 Arnold Zellner Thesis Award in Econometrics and Statistics (honourable mention) by the American Statistical Association for this work.