"Numerical" Integration in Statistical Problems

When and Where

Thursday, February 06, 2025 11:00 am to 12:00 pm

Speakers

Alex Stringer, University of Waterloo

Description

When numerical integration is used to approximate a likelihood function, the resulting maximum likelihood estimators are not guaranteed to have the same statistical properties as they would if based on the exact likelihood. For two-level generalized linear and additive mixed models for longitudinal repeated measures data, using the default Laplace approximation recommended in standard software leads to estimators for the regression coefficients/function and variance components which exhibit nonzero bias and decreasing coverage of confidence intervals as more subjects are sampled. We give results that suggest when to use more accurate but more intensive adaptive quadrature estimators. Since these estimators incur substantially increased computational burden compared to those based on the Laplace approximation, we also discuss recent progress in improving the computational feasibility of these both in terms of speed and in their extension to models with multivariate random effects. This is based on joint work with Yanbo Tang and Blair Bilodeau.

About Alex Stringer

Alex StringerI am an assistant professor in the Department of Statistics and Actuarial Science at the University of Waterloo. My research area is computational statistics. I completed my PhD in the Department of Statistical Sciences at the University of Toronto in 2021, under the supervision of Jamie Stafford and Patrick Brown.