Search results for "Bayesian probability"
showing 10 items of 217 documents
Bayesian survival analysis with BUGS
2020
Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programmin…
Bayesian models for data missing not at random in health examination surveys
2018
In epidemiological surveys, data missing not at random (MNAR) due to survey nonresponse may potentially lead to a bias in the risk factor estimates. We propose an approach based on Bayesian data augmentation and survival modelling to reduce the nonresponse bias. The approach requires additional information based on follow-up data. We present a case study of smoking prevalence using FINRISK data collected between 1972 and 2007 with a follow-up to the end of 2012 and compare it to other commonly applied missing at random (MAR) imputation approaches. A simulation experiment is carried out to study the validity of the approaches. Our approach appears to reduce the nonresponse bias substantially…
Extending conventional priors for testing general hypotheses in linear models
2007
We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are 'proper objective priors' to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full-rank linear models. We extend these priors to deal with general hypotheses in general linear models, not necessarily of full rank. The resulting priors, which we call 'conventional priors', are expressed as a generalizat…
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
2020
We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo-marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelisation and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the sug…
Intrinsic credible regions: An objective Bayesian approach to interval estimation
2005
This paper definesintrinsic credible regions, a method to produce objective Bayesian credible regions which only depends on the assumed model and the available data.Lowest posterior loss (LPL) regions are defined as Bayesian credible regions which contain values of minimum posterior expected loss: they depend both on the loss function and on the prior specification. An invariant, information-theory based loss function, theintrinsic discrepancy is argued to be appropriate for scientific communication. Intrinsic credible regions are the lowest posterior loss regions with respect to the intrinsic discrepancy loss and the appropriate reference prior. The proposed procedure is completely general…
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…
Bayesian Mapping of Lichens Growing on Trees
2001
Suitability of trees as hosts for epiphytic lichens are studied in a forest stand of size 25 ha. Suitability is measured as occupation probabilites which are modelled using hierarchical Bayesian approach. These probabilities are useful for an ecologist. They give smoothed spatial distribution map of suitability for each of the species and can be used in detecting high- and low-probability areas. In addition, suitability is explained by tree-level covariates. Spatial dependence, which is due to unobserved spatially structured covariates, is modelled through an unobserved Markov random field. Markov chain Monte Carlo method has been applied in Bayesian computation. The extensive spatial data …
Exponential and bayesian conjugate families: Review and extensions
1997
The notion of a conjugate family of distributions plays a very important role in the Bayesian approach to parametric inference. One of the main features of such a family is that it is closed under sampling, but a conjugate family often provides prior distributions which are tractable in various other respects. This paper is concerned with the properties of conjugate families for exponential family models. Special attention is given to the class of natural exponential families having a quadratic variance function, for which the theory is particularly fruitful. Several classes of conjugate families have been considered in the literature and here we describe some of their most interesting feat…
Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter
2013
Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is…
Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range
2014
A Bayesian solution is suggested for the modelling of spatial point patterns with inhomogeneous hard-core radius using Gaussian processes in the regularization. The key observation is that a straightforward use of the finite Gibbs hard-core process likelihood together with a log-Gaussian random field prior does not work without penalisation towards high local packing density. Instead, a nearest neighbour Gibbs process likelihood is used. This approach to hard-core inhomogeneity is an alternative to the transformation inhomogeneous hard-core modelling. The computations are based on recent Markovian approximation results for Gaussian fields. As an application, data on the nest locations of Sa…