Search results for "Bayesian probability"
showing 10 items of 217 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…
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…
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…
Bayesian Essentials with R, 2nd edn. J.-M. Marin and C. P. Robert (2014). New York: Springer/Springer Texts in Statistics. 296 pages, ISBN: 978-1-461…
2015
Bayesian hierarchical models in manufacturing bulk service queues
2006
In this paper, Queueing Theory and Bayesian statistical tools are used to analyze the congestion of various manufacturing bulk service queues with the same characteristics that are working independently of one another and in equilibrium. Hierarchical models are discussed in order to develop the whole inferential process for the parameters governing the system. Markov Chain Monte Carlo methods and numerical inversion of transforms are addressed to compute the posterior predictive distributions of the usual measures of performance in practice.