Fully Bayesian spline smoothing and intrinsic autoregressive priors By PAUL
نویسنده
چکیده
There is a well-known Bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors. The limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form, which we call partially informative normal. We derive necessary and sufficient conditions for the propriety of the posterior for this class of partially informative normal priors with noninformative priors on the variance components, a condition crucial for successful implementation of the Gibbs sampler. The results apply for fully Bayesian smoothing splines, thin-plate splines and L-splines, as well as models using intrinsic autoregressive priors.
منابع مشابه
Bayesian hierarchical linear mixed models for additive smoothing splines
Bayesian hierarchical models have been used for smoothing splines, thin-plate splines, and L-splines. In analyzing high dimensional data sets, additive models and backfitting methods are often used. A full Bayesian analysis for such models may include a large number of random effects, many of which are not intuitive, so researchers typically use noninformative improper or nearly improper priors...
متن کاملBayesian Analysis of Multivariate Smoothing Splines
A general version of multivariate smoothing splines with correlated errors and correlated curves is proposed. A suitable symmetric smoothing parameter matrix is introduced, and practical priors are developed for the unknown covariance matrix of the errors and the smoothing parameter matrix. An efficient algorithm for computing the multivariate smoothing spline is derived, which leads to an effi...
متن کاملLocally adaptive Bayesian P-splines with a Normal-Exponential-Gamma prior
The necessity to replace smoothing approaches with a global amount of smoothing arises in a variety of situations such as effects with highly varying curvature or effects with discontinuities. We present an implementation of locally adaptive spline smoothing using a class of heavy-tailed shrinkage priors. These priors utilize scale mixtures of normals with locally varying exponential-gamma dist...
متن کاملSpatially Adaptive Bayesian Penalized Splines With Heteroscedastic Errors
Penalized splines have become an increasingly popular tool for nonparametric smoothing because of their use of low-rank spline bases, which makes computations tractable while maintaining accuracy as good as smoothing splines. This article extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. This combina...
متن کاملPartially Improper Gaussian Priors for Nonparametric Logistic Regression
A \partially improper" Gaussian prior is considered for Bayesian inference in logistic regression. This includes generalized smoothing spline priors that are used for nonparametric inference about the logit, and also priors that correspond to generalized random e ect models. Necessary and su cient conditions are given for the posterior to be a proper probability measure, and bounds are given fo...
متن کامل