Event Details

Statistics Colloquium: Smooth Regression Modelling (Simon Wood)

Title: Smooth Regression Modelling

Abstract:

Generalized Additive Models (Hastie & Tibshrani, 1990) are generalized linear models in which the linear predictor depends linearly on smooth functions of covariates, and the functions are the target of statistical inference. Estimation of the model and its degree of smoothness is facilitated by using quadratically penalized basis expansions for the smooth terms, and then taking a somewhat Bayesian view of the penalties as log Gaussian priors. However once the resulting machinery for GAM inference is in place, there is little reason to stick with the single parameter exponential families of GLMs: essentially any model with a Fisher-regular likelihood can be employed, and with some more work other loss functions can be used for tasks such as quantile and robust regression. Similarly, quadratically penalized basis expansions cover all sorts of Gaussian random fields and effects, in addition to smooth functions of covariates. This talk will illustrate some of these model generalizations, and discuss the main inferential strategies employed, namely: empirical Bayes, stochastic simulation, INLA and boosting.