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Activity Number: 112 - Smoothing for Spatially and Temporally Indexed Data
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 8:30 AM to 10:20 AM
Sponsor: Royal Statistical Society
Abstract #328627 Presentation
Title: Some Model-Building Tools for Gaussian Processes, Using an Approximate Form of the Restricted Likelihood
Author(s): Maitreyee Bose and James S. Hodges* and Sudipto Banerjee
Companies: University of Washington and University of Minnesota and UCLA School of Public Health
Keywords: Gaussian Processes; mixed linear models; diagnostics; restricted likelihood; spectral approximation

Gaussian processes (GPs) are widely used in statistical modeling as the distribution of a random effect in a mixed linear model. The GP's unknowns are commonly estimated using the restricted likelihood (RL) or the closely related Bayesian analysis. It is unclear how the error variance and the GP's variance and range parameters are fit to features in the data because the RL does not have a closed form. To clarify this, we need a simple, interpretable form of the RL. We use the spectral approximation to obtain a simple approximate RL, which is identical to the likelihood arising from a gamma-errors generalized linear model (GLM) with the identity link. We use this GLM to conjecture about how GP parameters are fit to data and investigate those conjectures by introducing features into simulated data, e.g., outliers and mean shifts, and observing how those features affect parameter estimates. We describe briefly how this representation can be used to derive diagnostic tools to identify potential covariates, to examine whether and how the data support their inclusion, and to assess how their inclusion will affect the fit of the GP and error parts of the mixed linear model.

Authors who are presenting talks have a * after their name.

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