Additive models for quantile regression: model selection and confidence bandaids

Additive models for conditional quantile functions provide an attractive framework for nonparametric regression applications focused on features of the response beyond its central tendency. Total variation roughness penalities can be used to control the smoothness of the additive components much as squared Sobelev penalties are used for classical L 2 smoothing splines. We describe a general approach to estimation and inference for additive models of this type. We focus attention primarily on selection of smoothing parameters and on the construction of confidence bands for the nonparametric components. Both pointwise and uniform confidence bands are introduced; the uniform bands are based on the Hotelling (1939) tube approach. Some simulation evidence is presented to evaluate finite sample performance and the methods are also illustrated with an application to modeling childhood malnutrition in India.

miRNA Signatures in Sera of Patients with Active Pulmonary Tuberculosis.

Several studies showed that assessing levels of specific circulating microRNAs (miRNAs) is a non-invasive, rapid, and accurate method for diagnosing diseases or detecting alterations in physiological conditions. We aimed to identify a serum miRNA signature to be used for the diagnosis of tuberculosis (TB). To account for variations due to the genetic makeup, we enrolled adults from two study settings in Europe and Africa. The following categories of subjects were considered: healthy (H), active pulmonary TB (PTB), active pulmonary TB, HIV co-infected (PTB/HIV), latent TB infection (LTBI), other pulmonary infections (OPI), and active extra-pulmonary TB (EPTB). Sera from 10 subjects of the same category were pooled and, after total RNA extraction, screened for miRNA levels by TaqMan low-density arrays. After identification of "relevant miRNAs", we refined the serum miRNA signature discriminating between H and PTB on individual subjects. Signatures were analyzed for their diagnostic performances using a multivariate logistic model and a Relevance Vector Machine (RVM) model. A leave-one-out-cross-validation (LOOCV) approach was adopted for assessing how both models could perform in practice. The analysis on pooled specimens identified selected miRNAs as discriminatory for the categories analyzed. On individual serum samples, we showed that 15 miRNAs serve as signature for H and PTB categories with a diagnostic accuracy of 82% (CI 70.2-90.0), and 77% (CI 64.2-85.9) in a RVM and a logistic classification model, respectively. Considering the different ethnicity, by selecting the specific signature for the European group (10 miRNAs) the diagnostic accuracy increased up to 83% (CI 68.1-92.1), and 81% (65.0-90.3), respectively. The African-specific signature (12 miRNAs) increased the diagnostic accuracy up to 95% (CI 76.4-99.1), and 100% (83.9-100.0), respectively. Serum miRNA signatures represent an interesting source of biomarkers for TB disease with the potential to discriminate between PTB and LTBI, but also among the other categories

Densities, spectral densities and modality

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the local adaptivity of the procedures and the method is extended to spectral densities.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000036

The Bayes Lepski's Method and Credible Bands through Volume of Tubular Neighborhoods

For a general class of priors based on random series basis expansion, we develop the Bayes Lepski's method to estimate unknown regression function. In this approach, the series truncation point is determined based on a stopping rule that balances the posterior mean bias and the posterior standard deviation. Equipped with this mechanism, we present a method to construct adaptive Bayesian credible bands, where this statistical task is reformulated into a problem in geometry, and the band's radius is computed based on finding the volume of certain tubular neighborhood embedded on a unit sphere. We consider two special cases involving B-splines and wavelets, and discuss some interesting consequences such as the uncertainty principle and self-similarity. Lastly, we show how to program the Bayes Lepski stopping rule on a computer, and numerical simulations in conjunction with our theoretical investigations concur that this is a promising Bayesian uncertainty quantification procedure.Comment: 42 pages, 2 figures, 1 tabl