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Statistical Models Commons

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Statistical Methodology

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Penalized splines

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Full-Text Articles in Statistical Models

Nested Hierarchical Functional Data Modeling And Inference For The Analysis Of Functional Plant Phenotypes, Yuhang Xu, Yehua Li, Dan Nettleton Jul 2019

Nested Hierarchical Functional Data Modeling And Inference For The Analysis Of Functional Plant Phenotypes, Yuhang Xu, Yehua Li, Dan Nettleton

Dan Nettleton

In a plant science Root Image Study, the process of seedling roots bending in response to gravity is recorded using digital cameras, and the bending rates are modeled as functional plant phenotype data. The functional phenotypes are collected from seeds representing a large variety of genotypes and have a three-level nested hierarchical structure, with seeds nested in groups nested in genotypes. The seeds are imaged on different days of the lunar cycle, and an important scientific question is whether there are lunar effects on root bending. We allow the mean function of the bending rate to depend on the lunar …


Implicit Copulas From Bayesian Regularized Regression Smoothers, Nadja Klein, Michael S. Smith Dec 2017

Implicit Copulas From Bayesian Regularized Regression Smoothers, Nadja Klein, Michael S. Smith

Michael Stanley Smith

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors --- a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection --- and both univariate and multivariate function bases. The implicit copulas are high-dimensional and unavailable in closed form. However, we show how to evaluate them by first constructing a Gaussian copula conditional on the regularization parameters, …