Sampling from the posterior distribution in generalized linear mixed models
Statistics and Computing
Nonparametric regression using linear combinations of basis functions
Statistics and Computing
Estimation and variable selection in nonparametric heteroscedastic regression
Statistics and Computing
Generalized Additive Models (Texts in Statistical Science)
Generalized Additive Models (Texts in Statistical Science)
Semiparametric estimation of mean and variance functions for non-Gaussian data
Computational Statistics
Feature significance in generalized additive models
Statistics and Computing
SiZer Map for inference with additive models
Statistics and Computing
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Generic reversible jump MCMC using graphical models
Statistics and Computing
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In parametric regression models the sign of a coefficient often plays an important role in its interpretation. One possible approach to model selection in these situations is to consider a loss function that formulates prediction of the sign of a coefficient as a decision problem. Taking a Bayesian approach, we extend this idea of a sign based loss for selection to more complex situations. In generalized additive models we consider prediction of the sign of the derivative of an additive term at a set of predictors. Being able to predict the sign of the derivative at some point (that is, whether a term is increasing or decreasing) is one approach to selection of terms in additive modelling when interpretation is the main goal. For models with interactions, prediction of the sign of a higher order derivative can be used similarly. There are many advantages to our sign-based strategy for selection: one can work in a full or encompassing model without the need to specify priors on a model space and without needing to specify priors on parameters in submodels. Also, avoiding a search over a large model space can simplify computation. We consider shrinkage prior specifications on smoothing parameters that allow for good predictive performance in models with large numbers of terms without the need for selection, and a frequentist calibration of the parameter in our sign-based loss function when it is desired to control a false selection rate for interpretation.