The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the parameters are obtained using the asymptotic theory and bootstrap method. The coverage of the confidence intervals is also examined.

On the Folded Normal Distribution

Genomic selection refers to the use of dense, genome-wide markers for the prediction of breeding values (BV) and subsequent selection of breeding individuals. It has become a standard tool in livestock and plant breeding for accelerating genetic gain. The core of genomic selection is the prediction of a large number of marker effects from a limited number of observations. Various Bayesian methods that successfully cope with this challenge are known. Until now, the main research emphasis has been on additive genetic effects. Dominance coefficients of quantitative trait loci (QTLs), however, can also be large, even if dominance variance and inbreeding depression are relatively small. Considering dominance might contribute to the accuracy of genomic selection and serve as a guide for choosing mating pairs with good combining abilities. A general hierarchical Bayesian model for genomic selection that can realistically account for dominance is introduced. Several submodels are proposed and compared with respect to their ability to predict genomic BV, dominance deviations and genotypic values (GV) by stochastic simulation. These submodels differ in the way the dependency between additive and dominance effects is modelled. Depending on the marker panel, the inclusion of dominance effects increased the accuracy of GV by about 17% and the accuracy of genomic BV by 2% in the offspring. Furthermore, it slowed down the decrease of the accuracies in subsequent generations. It was possible to obtain accurate estimates of GV, which enables mate selection programmes.

Bayesian models with dominance effects for genomic evaluation of quantitative traits.

https://perso.uclouvain.be/michel.verleysen/papers/neuralnetworks13bf.pdf

Neural networks letter: Is mutual information adequate for feature selection in regression?

The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly, and Bayesian meta-analysis has been suggested as a potential solution. The Bayesian approach, however, requires the sensible specification of prior distributions. While non-informative priors are commonly used for the overall mean effect, the use of weakly informative priors has been suggested for the heterogeneity parameter, in particular in the setting of (very) few studies. To date, however, a consensus on how to generally specify a weakly informative heterogeneity prior is lacking. Here we investigate the problem more closely and provide some guidance on prior specification.

On weakly informative prior distributions for the heterogeneity parameter in Bayesian random-effects meta-analysis

Measurements are frequently recorded without their algebraicsign. As a consequence the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is t the resulting distribution is called the “folded-t distribution”. Here we study this distribution, we find the relationship between the folded-t distribution and a special case of the folded normal distribution and we derive relationships of the folded-t distribution to other distributions pertaining to computer generation. Also tables are presented which give areas of the folded-t distribution.

J. Panaretoes

Papers

The folded t distribution