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Noninformative Priors (noninformative + prior)

Distribution by Scientific Domains
Mathematics and Statistics60%

Selected Abstracts

Integrated estimation of measurement error with empirical process modeling,A hierarchical Bayes approach

AICHE JOURNAL, Issue 11 2009
Hongshu Chen
Abstract Advanced empirical process modeling methods such as those used for process monitoring and data reconciliation rely on information about the nature of noise in the measured variables. Because this likelihood information is often unavailable for many practical problems, approaches based on repeated measurements or process constraints have been developed for their estimation. Such approaches are limited by data availability and often lack theoretical rigor. In this article, a novel Bayesian approach is proposed to tackle this problem. Uncertainty about the error variances is incorporated in the Bayesian framework by setting noninformative priors for the noise variances. This general strategy is used to modify the Sampling-based Bayesian Latent Variable Regression (Chen et al., J Chemom., 2007) approach, to make it more robust to inaccurate information about the likelihood functions. Different noninformative priors for the noise variables are discussed and unified in this work. The benefits of this new approach are illustrated via several case studies. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

Probability matching priors for an extended statistical calibration model

THE CANADIAN JOURNAL OF STATISTICS, Issue 1 2001
Daniel R. Eno
Abstract Statistical calibration or inverse prediction involves data collected in two stages. In the first stage, several values of an endogenous variable are observed, each corresponding to a known value of an exogenous variable; in the second stage, one or more values of the endogenous variable are observed which correspond to an unknown value of the exogenous variable. When estimating the value of the latter, it has been suggested that the variability about the regression relationship should not be assumed to be equal for the two stages of data collection. In this paper, the authors present a Bayesian method of analysis based on noninformative priors that takes this heteroscedasticity into account. Le problème de la calibration statistique ou de la prévision inverse concerne des données recueillies en deux temps. La variable endogène est d'abord observée à plusieurs reprises pour des valeurs connues de la variable exogène; puis, la variable endogène est mesurée sur certains individus pour lesquels la variable exogène est indéterminée. Pour estimer la valeur prise par cette dernière, on suppose généralement que la variance du terme d'erreur du modèle de régression n'est pas la même pour les deux phases de cueillette. Dans cet article, les auteurs présentent une méthode d'analyse bayésienne à base de lois a priori non informatives qui tient compte de cette hétéroscédasticité. [source]

Bayesian Multivariate Logistic Regression

BIOMETRICS, Issue 3 2004
Sean M. O'Brien
Summary Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data. The model for individual outcomes has a marginal logistic structure, simplifying interpretation. We follow a Bayesian approach to estimation and inference, developing an efficient data augmentation algorithm for posterior computation. The method is illustrated with application to a neurotoxicology study. [source]

Bayesian Modeling of Age-Specific Survival in Bird Nesting Studies under Irregular Visits

BIOMETRICS, Issue 4 2003
Chong Z. He
Summary. In this article, a Bayesian model for age-specific nest survival rates is presented to handle the irregular visit case. Both informative priors and noninformative priors are investigated. The reference prior under this model is derived, and, therefore, the hyperparameter specification problem is solved to some extent. The Bayesian method provides a more accurate estimate of the total survival rate than the standard Mayfield method, if the age-specific hazard rates are not constant. The Bayesian method also lets the biologist look for high- and low-survival rates during the whole nesting period. In practice, it is common for data of several types to be collected in a single study. That is, some nests may be aged, others are not. Some nests are visited regularly; others are visited irregularly. The Bayesian method accommodates any mix of these sampling techniques by assuming that the aging and visiting activities have no effect on the survival rate. The methods are illustrated by an analysis of the Missouri northern bobwhite data set. [source]