Penalized Likelihood and Bayesian Function Selection in Regression Models

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive predictors has been considered only more recently. Several competing suggestions have been developed at about the same time and often do not refer to each other. This article provides a state-of-the-art review on function selection, focusing on penalized likelihood and Bayesian concepts, relating various approaches to each other in a unified framework. In an empirical comparison, also including boosting, we evaluate several methods through applications to simulated and real data, thereby providing some guidance on their performance in practice

Testing silicone digit extensions as a way to suppress natural sensation to evaluate supplementary tactile feedback

Dexterous use of the hands depends critically on sensory feedback, so it is generally agreed that functional supplementary feedback would greatly improve the use of hand prostheses. Much research still focuses on improving non-invasive feedback that could potentially become available to all prosthesis users. However, few studies on supplementary tactile feedback for hand prostheses demonstrated a functional benefit. We suggest that confounding factors impede accurate assessment of feedback, e.g., testing non-amputee participants that inevitably focus intently on learning EMG control, the EMG’s susceptibility to noise and delays, and the limited dexterity of hand prostheses. In an attempt to assess the effect of feedback free from these constraints, we used silicone digit extensions to suppress natural tactile feedback from the fingertips and thus used the tactile feedback-deprived human hand as an approximation of an ideal feed-forward tool. Our non-amputee participants wore the extensions and performed a simple pick-and-lift task with known weight, followed by a more difficult pick-and-lift task with changing weight. They then repeated these tasks with one of three kinds of audio feedback. The tests were repeated over three days. We also conducted a similar experiment on a person with severe sensory neuropathy to test the feedback without the extensions. Furthermore, we used a questionnaire based on the NASA Task Load Index to gauge the subjective experience. Unexpectedly, we did not find any meaningful differences between the feedback groups, neither in the objective nor the subjective measurements. It is possible that the digit extensions did not fully suppress sensation, but since the participant with impaired sensation also did not improve with the supplementary feedback, we conclude that the feedback failed to provide relevant grasping information in our experiments. The study highlights the complex interaction between task, feedback variable, feedback delivery, and control, which seemingly rendered even rich, high-bandwidth acoustic feedback redundant, despite substantial sensory impairment

Generalized structured additive regression based on Bayesian P-splines

Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM's and extensions to generalized structured additive regression based on one or two dimensional P-splines as the main building block. The approach extends previous work by Lang und Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. For the first time, we present Bayesian semiparametric inference for the widely used multinomial logit models. As we will demonstrate through two applications on the forest health status of trees and a space-time analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX

Testing silicone digit extensions as a way to suppress natural sensation to evaluate supplementary tactile feedback

Dexterous use of the hands depends critically on sensory feedback, so it is generally agreed that functional supplementary feedback would greatly improve the use of hand prostheses. Much research still focuses on improving non-invasive feedback that could potentially become available to all prosthesis users. However, few studies on supplementary tactile feedback for hand prostheses demonstrated a functional benefit. We suggest that confounding factors impede accurate assessment of feedback, e.g., testing non-amputee participants that inevitably focus intently on learning EMG control, the EMG's susceptibility to noise and delays, and the limited dexterity of hand prostheses. In an attempt to assess the effect of feedback free from these constraints, we used silicone digit extensions to suppress natural tactile feedback from the fingertips and thus used the tactile feedback-deprived human hand as an approximation of an ideal feed-forward tool. Our non-amputee participants wore the extensions and performed a simple pick-and-lift task with known weight, followed by a more difficult pick-and-lift task with changing weight. They then repeated these tasks with one of three kinds of audio feedback. The tests were repeated over three days. We also conducted a similar experiment on a person with severe sensory neuropathy to test the feedback without the extensions. Furthermore, we used a questionnaire based on the NASA Task Load Index to gauge the subjective experience. Unexpectedly, we did not find any meaningful differences between the feedback groups, neither in the objective nor the subjective measurements. It is possible that the digit extensions did not fully suppress sensation, but since the participant with impaired sensation also did not improve with the supplementary feedback, we conclude that the feedback failed to provide relevant grasping information in our experiments. The study highlights the complex interaction between task, feedback variable, feedback delivery, and control, which seemingly rendered even rich, high-bandwidth acoustic feedback redundant, despite substantial sensory impairment

Penalized additive regression for space-time data: a Bayesian perspective

We propose extensions of penalized spline generalized additive models for analysing space-time regression data and study them from a Bayesian perspective. Non-linear effects of continuous covariates and time trends are modelled through Bayesian versions of penalized splines, while correlated spatial effects follow a Markov random field prior. This allows to treat all functions and effects within a unified general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference can be performed either with full (FB) or empirical Bayes (EB) posterior analysis. FB inference using MCMC techniques is a slight extension of own previous work. For EB inference, a computationally efficient solution is developed on the basis of a generalized linear mixed model representation. The second approach can be viewed as posterior mode estimation and is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to smoothing parameters, are then estimated by using marginal likelihood. We carefully compare both inferential procedures in simulation studies and illustrate them through real data applications. The methodology is available in the open domain statistical package BayesX and as an S-plus/R function

RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]