Comparing probabilistic methods for outlier detection

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived

A Bayesian look at diagnostics in the univariate linear model

This paper develops diagnostics for data thought to be generated in accordance with the general univariate linear model. A first set of diagnostics is developed by considering posterior probabilities of models that dictate which of k observations form a sample of n observations (k < n/2) are spuriously generated, giving rise to the possible outlyingness of the k observations considered. This in turn gives rise to diagnostics to help assess (estimate) the value of k. A second set of diagnostics is found by using the Kullback-Leibler symmetric divergence, which is found to generate measures of outlyingness and influence. Both sets of diagnostics are compared and related to each other and to other diagnostic statistics suggested in the literature. An example to illustrate to the use of these diagnostic procedures is included

A Bayesian look at diagnostics in the univariate linear model.

This paper develops diagnostics for data thought to be generated in accordance with the general univariate linear model. A first set of diagnostics is developed by considering posterior probabilities of models that dictate which of k observations form a sample of n observations (kspurious and outlying observations; posteriors of models; leverage; Kullback-Leibler measures; outlying and influential observations;

Comparing probabilistic methods for outlier detection.

This paper compares the use of two posterior probability methods to deal with outliers in linear models. We show that putting together diagnostics that come from the mean-shift and variance-shift models yields a procedure that seems to be more effective than the use of probabilities computed from the posterior distributions of actual realized residuals. The relation of the suggested procedure to the use of a certain predictive distribution for diagnostics is derived.Diagnostic; Posterior and Predictive distributions; Leverage; Linear models;

A bayesian approach for predicting with polynomial regresión of unknown degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data

A Bayesian Approach for Predicting with Polynomial Regresión of Unknown Degree.

This article presents a comparison of four methods to compute the posterior probabilities of the possible orders in polynomial regression models. These posterior probabilities are used for forecasting by using Bayesian model averaging. It is shown that Bayesian model averaging provides a closer relationship between the theoretical coverage of the high density predictive interval (HDPI) and the observed coverage than those corresponding to selecting the best model. The performance of the different procedures are illustrated with simulations and some known engineering data.

A high-resolution map of human evolutionary constraint using 29 mammals.

The comparison of related genomes has emerged as a powerful lens for genome interpretation. Here we report the sequencing and comparative analysis of 29 eutherian genomes. We confirm that at least 5.5% of the human genome has undergone purifying selection, and locate constrained elements covering ∼4.2% of the genome. We use evolutionary signatures and comparisons with experimental data sets to suggest candidate functions for ∼60% of constrained bases. These elements reveal a small number of new coding exons, candidate stop codon readthrough events and over 10,000 regions of overlapping synonymous constraint within protein-coding exons. We find 220 candidate RNA structural families, and nearly a million elements overlapping potential promoter, enhancer and insulator regions. We report specific amino acid residues that have undergone positive selection, 280,000 non-coding elements exapted from mobile elements and more than 1,000 primate- and human-accelerated elements. Overlap with disease-associated variants indicates that our findings will be relevant for studies of human biology, health and disease

A High-Resolution Map of Human Evolutionary Constraint Using 29 Mammals

The comparison of related genomes has emerged as a powerful lens for genome interpretation. Here we report the sequencing and comparative analysis of 29 eutherian genomes. We confirm that at least 5.5% of the human genome has undergone purifying selection, and locate constrained elements covering ~4.2% of the genome. We use evolutionary signatures and comparisons with experimental data sets to suggest candidate functions for ~60% of constrained bases. These elements reveal a small number of new coding exons, candidate stop codon readthrough events and over 10,000 regions of overlapping synonymous constraint within protein-coding exons. We find 220 candidate RNA structural families, and nearly a million elements overlapping potential promoter, enhancer and insulator regions. We report specific amino acid residues that have undergone positive selection, 280,000 non-coding elements exapted from mobile elements and more than 1,000 primate- and human-accelerated elements. Overlap with disease-associated variants indicates that our findings will be relevant for studies of human biology, health and disease.National Human Genome Research Institute (U.S.)National Institute of General Medical Sciences (U.S.) (Grant number GM82901)National Science Foundation (U.S.). Postdoctural Fellowship (Award 0905968)National Science Foundation (U.S.). Career (0644282)National Institutes of Health (U.S.) (R01-HG004037)Alfred P. Sloan Foundation.Austrian Science Fund. Erwin Schrodinger Fellowshi