Bayesian Methods in the Analysis of the General Linear Model.
Bayesian nonparametric estimation of hazard rate in monotone Aalen model
This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the...
Bayesian parameter estimation and adaptive control of Markov processes with time-averaged cost
This paper considers Bayesian parameter estimation and an associated adaptive control scheme for controlled Markov chains and diffusions with time-averaged cost. Asymptotic behaviour of the posterior law of the parameter given the observed trajectory is analyzed. This analysis suggests a "cost-biased" estimation scheme and associated self-tuning adaptive control. This is shown to be asymptotically optimal in the almost sure sense.
Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size
2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.We consider the problem of predictive interval for future observations from Weibull distribution. We consider two cases they are: (i) fixed sample size (FSS), (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation...
Bayesian rank estimation with application to factor analysis
Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution
This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy...
Bayesian reliability analysis when multiple early failures may be present.
This paper discusses the Bayesian reliability analysis for an exponential failure mode on the basis of some ordered observations when the first p observations may represent early failures or outliers. The Bayes estimators of the mean life and reliability are obtained for the underlying parametric model referred to as the SB(p) model under the assumption of the squared error loss function, the inverted gamma prior for scale parameter and a generalized uniform prior for the nuisance parameter.
Bayesian Shrinkage Estimation of Reliability in the Exponential Distribution
Bayesian stopping rule in discrete parameter space with multiple local maxima
The paper presents the stopping rule for random search for Bayesian model-structure estimation by maximising the likelihood function. The inspected maximisation uses random restarts to cope with local maxima in discrete space. The stopping rule, suitable for any maximisation of this type, exploits the probability of finding global maximum implied by the number of local maxima already found. It stops the search when this probability crosses a given threshold. The inspected case represents an important...
Bayesian sufficient statistics and invariance
Bayesian survival analysis based on the Rayleigh model.
In this paper, the Bayesian analysis of the survival data arising from a Rayleigh model is carried out under the assumption that the clinical study based on n patients is terminated at the dth death, for some preassigned d (0 < d ≤ n), resulting in the survival times t1 ≤ t2 ≤ ... ≤ td, and (n - d) survivors. For the prior knowledge about the Rayleigh parameter, the gamma density, the inverted gamma density, and the beta density of the second kind are respectively assumed, and for each of...
Bayesian testing of fuzzy parametric hypotheses from fuzzy information
Behaviour of higher-order approximations of the tests in the single parameter Cox proportional hazards model
Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the Wald test, or the score test. In addition to standard tests, appropriate higher-order approximations...
Behaviour of sign test and one sample median test against changes in the model
Belief functions induced by multimodal probability density functions, an application to the search and rescue problem
In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...
Belief functions induced by multimodal probability density functions, an application to the search and rescue problem
In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension n. We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...
Bemerkung zur Lösung der Yule-Walker-Gleichungen.
Bemerkungen über die zentralen unvollständigen und absoluten Momente der Pólya-Verteilung
Bemerkungen zum Vergleich linearer normaler Experimente.
Bemerkungen zur Saisonbereinigung von ökonomischen Zeitreihen