Search results for "informative prior"
showing 4 items of 4 documents
Objective Bayesian point and region estimation in location-scale models.
2007
Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this requires the use of an invariant loss function; moreover, an objective solution requires the use of a prior which does not introduce subjective elements. The combined use of an invariant informatio…
Can bayesian models play a role in dental caries epidemiology? Evidence from an application to the BELCAP data set
2012
Objectives The aim of this study was to show the potential of Bayesian analysis in statistical modelling of dental caries data. Because of the bounded nature of the dmft (DMFT) index, zero-inflated binomial (ZIB) and beta-binomial (ZIBB) models were considered. The effects of incorporating prior information available about the parameters of models were also shown. Methods The data set used in this study was the Belo Horizonte Caries Prevention (BELCAP) study (Bohning et al. (1999)), consisting of five variables collected among 797 Brazilian school children designed to evaluate four programmes for reducing caries. Only the eight primary molar teeth were considered in the data set. A data aug…
A Bayesian stable isotope mixing model for coping with multiple isotopes, multiple trophic steps and small sample sizes
2022
We introduce a Bayesian stable isotope mixing model for estimating the relative contributions of different dietary components to the tissues of consumers within food webs. The model is implemented with the probabilistic programming language Stan. The model incorporates isotopes of multiple elements (e.g. C, N, H) for two trophic levels, when the structure of the food web is known. In addition, the model allows inclusion of latent trophic levels (i.e. for which no empirical data are available) intermediate between sources and measured consumers. Running the model in simulations driven by a real dataset from Finnish lakes, we tested the sensitivity of the posterior distributions by altering c…
Bayesian analysis of a disability model for lung cancer survival
2016
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncolog…