Regression modelling using I-priors


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 for 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.

16 Nov 2022 3:00 PM — 1 Feb 2018 4:00 PM
Department of Statistics & Data Science Seminar
Faculty of Science, NUS, Singapore
Haziq Jamil
Haziq Jamil
Assistant Professor in Statistics

My research interests include statistical theory, methods and computation, with applications towards the social sciences.