Search results for "Bay"
showing 10 items of 1187 documents
Deriving Reference Decisions
1998
To solve a statistical decision problem from a Bayesian viewpoint, the decision maker must specify a probability distribution on the parameter space, his prior distribution. In order to analyze the influence of this prior distribution on the solution of the problem, Bernardo (1981) proposed to compare the results with those that one would obtain by using that prior distribution which maximizes the useful experimental information, thus introducing the concept of reference decision. This definition is too involved for most of the problems usually found in practice. Here we analyze situations in which it is possible to simplify the definition of the reference decision, and we provide condition…
Bayesian Smoothing in the Estimation of the Pair Potential Function of Gibbs Point Processes
1999
A flexible Bayesian method is suggested for the pair potential estimation with a high-dimensional parameter space. The method is based on a Bayesian smoothing technique, commonly applied in statistical image analysis. For the calculation of the posterior mode estimator a new Monte Carlo algorithm is developed. The method is illustrated through examples with both real and simulated data, and its extension into truly nonparametric pair potential estimation is discussed.
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models
2008
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]
PValues for Composite Null Models
2000
Abstract The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters, p values are not uniquely defined. The proposals for computing a p value in such a situation include the plug-in and similar p values on the frequentist side, and the predictive and posterior predictive p values on the Bayesian side. We propose two alternatives, the conditional predictive p value and the partial…
Gaussian component mixtures and CAR models in Bayesian disease mapping
2012
Hierarchical Bayesian models involving conditional autoregression (CAR) components are commonly used in disease mapping. An alternative model to the proper or improper CAR is the Gaussian component mixture (GCM) model. A review of CAR and GCM models is provided in univariate settings where only one disease is considered, and also in multivariate situations where in addition to the spatial dependence between regions, the dependence among multiple diseases is analyzed. A performance comparison between models using a set of simulated data to help illustrate their respective properties is reported. The results show that both in univariate and multivariate settings, both models perform in a comp…
Some links between conditional and coregionalized multivariate Gaussian Markov random fields
2020
Abstract Multivariate disease mapping models are attracting considerable attention. Many modeling proposals have been made in this area, which could be grouped into three large sets: coregionalization, multivariate conditional and univariate conditional models. In this work we establish some links between these three groups of proposals. Specifically, we explore the equivalence between the two conditional approaches and show that an important class of coregionalization models can be seen as a large subclass of the conditional approaches. Additionally, we propose an extension to the current set of coregionalization models with some new unexplored proposals. This extension is able to reproduc…
Prospective surveillance of multivariate spatial disease data
2012
Surveillance systems are often focused on more than one disease within a predefined area. On those occasions when outbreaks of disease are likely to be correlated, the use of multivariate surveillance techniques integrating information from multiple diseases allows us to improve the sensitivity and timeliness of outbreak detection. In this article, we present an extension of the surveillance conditional predictive ordinate to monitor multivariate spatial disease data. The proposed surveillance technique, which is defined for each small area and time period as the conditional predictive distribution of those counts of disease higher than expected given the data observed up to the previous t…
Analisis bayesiano de los contrastes de hipotesis parametricos
1985
Classical solutions to parametric hypothesis testing are shown to be particular instances of the Bayesian solution to a decision problem with two alternatives, in which the increase in utility for rejecting a false null is a linear function of the discrepancy between the accepted parametric model and the more likely model under the null.
Statistical relationship between hardness of drinking water and cerebrovascular mortality in Valencia: a comparison of spatiotemporal models
2003
The statistical detection of environmental risk factors in public health studies is usually difficult due to the weakness of their effects and their confounding with other covariates. Small area geographical data bring the opportunity of observing health response in a wide variety of exposure values. Temporal sequences of these geographical datasets are crucial to gaining statistical power in detecting factors. The spatiotemporal models required to perform the statistical analysis have to allow for spatial and temporal correlations, which are more easily modelled via hierarchical structures of hidden random factors. These models have produced important research activity during the last deca…
Frequentist and Bayesian approaches for a joint model for prostate cancer risk and longitudinal prostate-specific antigen data
2015
The paper describes the use of frequentist and Bayesian shared-parameter joint models of longitudinal measurements of prostate-specific antigen (PSA) and the risk of prostate cancer (PCa). The motivating dataset corresponds to the screening arm of the Spanish branch of the European Randomized Screening for Prostate Cancer study. The results show that PSA is highly associated with the risk of being diagnosed with PCa and that there is an age-varying effect of PSA on PCa risk. Both the frequentist and Bayesian paradigms produced very close parameter estimates and subsequent 95% confidence and credibility intervals. Dynamic estimations of disease-free probabilities obtained using Bayesian infe…