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Marginal Posterior Distributions (marginal + posterior_distribution)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

A Bayesian approach to the transmission/disequilibrium test for binary traits

GENETIC EPIDEMIOLOGY, Issue 1 2002
Varghese George
Abstract The transmission/disequilibrium test (TDT) for binary traits is a powerful method for detecting linkage between a marker locus and a trait locus in the presence of allelic association. The TDT uses information on the parent-to-offspring transmission status of the associated allele at the marker locus to assess linkage or association in the presence of the other, using one affected offspring from each set of parents. For testing for linkage in the presence of association, more than one offspring per family can be used. However, without incorporating the correlation structure among offspring, it is not possible to correctly assess the association in the presence of linkage. In this presentation, we propose a Bayesian TDT method as a complementary alternative to the classical approach. In the hypothesis testing setup, given two competing hypotheses, the Bayes factor can be used to weigh the evidence in favor of one of them, thus allowing us to decide between the two hypotheses using established criteria. We compare the proposed Bayesian TDT with a competing frequentist-testing method with respect to power and type I error validity. If we know the mode of inheritance of the disease, then the joint and marginal posterior distributions for the recombination fraction (,) and disequilibrium coefficient (,) can be obtained via standard MCMC methods, which lead naturally to Bayesian credible intervals for both parameters. Genet. Epidemiol. 22:41,51, 2002. © 2002 Wiley-Liss, Inc. [source]

GSEVM v.2: MCMC software to analyze genetically structured environmental variance models

JOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 3 2010
N. Ibáñez-Escriche
Summary This note provides a description of software that allows to fit Bayesian genetically structured variance models using Markov chain Monte Carlo (MCMC). The gsevm v.2 program was written in Fortran 90. The DOS and Unix executable programs, the user's guide, and some example files are freely available for research purposes at http://www.bdporc.irta.es/estudis.jsp. The main feature of the program is to compute Monte Carlo estimates of marginal posterior distributions of parameters of interest. The program is quite flexible, allowing the user to fit a variety of linear models at the level of the mean and the logvariance. [source]

Bayesian inference in a piecewise Weibull proportional hazards model with unknown change points

JOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 4 2007
J. Casellas
Summary The main difference between parametric and non-parametric survival analyses relies on model flexibility. Parametric models have been suggested as preferable because of their lower programming needs although they generally suffer from a reduced flexibility to fit field data. In this sense, parametric survival functions can be redefined as piecewise survival functions whose slopes change at given points. It substantially increases the flexibility of the parametric survival model. Unfortunately, we lack accurate methods to establish a required number of change points and their position within the time space. In this study, a Weibull survival model with a piecewise baseline hazard function was developed, with change points included as unknown parameters in the model. Concretely, a Weibull log-normal animal frailty model was assumed, and it was solved with a Bayesian approach. The required fully conditional posterior distributions were derived. During the sampling process, all the parameters in the model were updated using a Metropolis,Hastings step, with the exception of the genetic variance that was updated with a standard Gibbs sampler. This methodology was tested with simulated data sets, each one analysed through several models with different number of change points. The models were compared with the Deviance Information Criterion, with appealing results. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation data. Moreover, results showed that the piecewise baseline hazard function could appropriately fit survival data, as well as other smooth distributions, with a reduced number of change points. [source]

The seasonal forecast of electricity demand: a hierarchical Bayesian model with climatological weather generator

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 2 2006
Sergio Pezzulli
Abstract In this paper we focus on the one year ahead prediction of the electricity peak-demand daily trajectory during the winter season in Central England and Wales. We define a Bayesian hierarchical model for predicting the winter trajectories and present results based on the past observed weather. Thanks to the flexibility of the Bayesian approach, we are able to produce the marginal posterior distributions of all the predictands of interest. This is a fundamental progress with respect to the classical methods. The results are encouraging in both skill and representation of uncertainty. Further extensions are straightforward at least in principle. The main two of those consist in conditioning the weather generator model with respect to additional information like the knowledge of the first part of the winter and/or the seasonal weather forecast. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Bayesian Case Influence Diagnostics for Survival Models

BIOMETRICS, Issue 1 2009
Hyunsoon Cho
Summary We propose Bayesian case influence diagnostics for complex survival models. We develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the Kullback,Leibler divergence (K,L divergence). We present a simplified expression for computing the K,L divergence between the posterior with the full data and the posterior based on single case deletion, as well as investigate its relationships to the conditional predictive ordinate. All the computations for the proposed diagnostic measures can be easily done using Markov chain Monte Carlo samples from the full data posterior distribution. We consider the Cox model with a gamma process prior on the cumulative baseline hazard. We also present a theoretical relationship between our case-deletion diagnostics and diagnostics based on Cox's partial likelihood. A simulated data example and two real data examples are given to demonstrate the methodology. [source]