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

BAYESIAN CURVE ESTIMATION BY MODEL AVERAGING

A bayesian approach is used to estimate a nonparametric regression model. The main features of the procedure are, first, the functional form of the curve is approximated by a mixture of local polynomials by Bayesian Model Averaging (BMA); second, the model weights are approximated by the BIC criterion, and third, a robust estimation procedure is incorporated to improve the smoothness of the estimated curve. The models considered at each sample points are polynomial regression models of order smaller that four, and the parameters of each model are estimated by a local window. The estimated value is computed by BMA, and the posterior probability of each model is approximated by the exponential of the BIC criterion. The robustness is achieved by assuming that the noise follows a scale contaminated normal model so that the effect of possible outliers is downweighted. The procedure provides a smooth curve and allows a straightforward prediction and quantification of the uncertainty. The method is illustrated with several examples and some Monte Carlo experiments.

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;

A note on detecting statistical outliers in psychophysical data

This paper considers how to identify statistical outliers in psychophysical datasets, where the underlying sampling distributions are unknown. Eight methods are described, and each is evaluated using Monte Carlo simulations of a typical psychophysical experiment. The best method is shown to be one based on a measure of spread known as S n . This is shown to be more sensitive than popular heuristics based on standard deviations from the mean, and more robust than non-parametric methods based on percentiles or interquartile range. MATLAB code for computing S n is included

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

Practical Concepts of Quality Control

This book aims to provide a concise account of the essential elements of quality control. It is designed to be used as a text for courses on quality control for students of industrial engineering at the advanced undergraduate, or as a reference for researchers in related fields seeking a concise treatment of the key concepts of quality control. It is intended to give a contemporary account of procedures used to design quality 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.