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Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models

Andrzej Michalski (2009)

Discussiones Mathematicae Probability and Statistics

The paper deals with construction of exact confidence intervals for the variance component σ₁² and ratio θ of variance components σ₁² and σ² in mixed linear models for the family of normal distributions t ( 0 , σ ₁ ² W + σ ² I t ) . This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two classes of bayesian interval estimators depending on a prior distribution on (σ₁², σ²) for: 1) the variance components ratio...

Bayesian estimation of AR(1) models with uniform innovations

Hocine Fellag, Karima Nouali (2005)

Discussiones Mathematicae Probability and Statistics

The first-order autoregressive model with uniform innovations is considered. In this paper, we propose a family of BAYES estimators based on a class of prior distributions. We obtain estimators of the parameter which perform better than the maximum likelihood estimator.

Bayesian estimation of mixtures with dynamic transitions and known component parameters

Ivan Nagy, Evgenia Suzdaleva, Miroslav Kárný (2011)

Kybernetika

Probabilistic mixtures provide flexible “universal” approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs “naturally” in one-pass mode. This is important in on-line applications and/or extensive databases. It even copes with dynamic nature of components forming the mixture. However, the quasi-Bayesian estimation relies on mixing via constant...

Bayesian estimation of the 3-parameter inverse Gaussian distribution.

Mohamed Mahmoud (1991)

Trabajos de Estadística

The three-parameter inverse Gaussian distribution is used as an alternative model for the three parameter lognormal, gamma and Weibull distributions for reliability problems. In this paper Bayes estimates of the parameters and reliability function of a three parameter inverse Gaussian distribution are obtained. Posterior variance estimates are compared with the variance of their maximum likelihood counterparts. Numerical examples are given.

Bayesian estimation of the intraclass correlation coefficients in the mixed linear model

Teresa H. Jelenkowska (1998)

Applications of Mathematics

The method of determining Bayesian estimators for the special ratios of variance components called the intraclass correlation coefficients is presented. The exact posterior distribution for these ratios of variance components is obtained. The approximate posterior mean of this distribution is also derived. All computations are non-iterative and avoid numerical integration.

Bayesian estimation of the mean holding time in average semi-Markov control processes

J. Adolfo Minjárez-Sosa, José A. Montoya (2015)

Applicationes Mathematicae

We consider semi-Markov control models with Borel state and action spaces, possibly unbounded costs, and holding times with a generalized exponential distribution with unknown mean θ. Assuming that such a distribution does not depend on the state-action pairs, we introduce a Bayesian estimation procedure for θ, which combined with a variant of the vanishing discount factor approach yields average cost optimal policies.

Bayesian inference and optimal release times. For two software failure models

W. P. Wiper, D. Ríos Insua, R. Hierons (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

We carry out Bayesian inference for the Jelinski-Moranda and Littlewood software failure models given a sample of failure times. Furthermore, we illustrate how to assess the optimal length of an additional pre-release testing period under each of these models. Modern Bayesian computational methods are used to estimate the posterior expected utility of testing for and additional time.

Bayesian inference in group judgement formulation and decision making using qualitative controlled feedback.

S. James Press (1980)

Trabajos de Estadística e Investigación Operativa

This paper considers the problem of making statistical inferences about group judgements and group decisions using Qualitative Controlled Feedback, from the Bayesian point of view. The qualitative controlled feedback procedure was first introduced by Press (1978), for a single question of interest. The procedure in first reviewed here including the extension of the model to the multiple question case. We develop a model for responses of the panel on each stage. Many questions are treated simultaneously...

Bayesian inference in life tests based on exponential model with outliers when sample size is a random variable.

G. S. Lingappaiah (1990)

Trabajos de Estadística

This paper deals with the problem of prediction of the order statistics in a future sample. Underlying model is exponential. Outlier is present in the sample drawn and the sample size is considered a random variable. Firstly, an outlier of type θδ in the exponential model, is treated. Actual predictive distribution of the order statistics is obtained. As an extension, the two-sample problem is also taken up. Finally, an outlier of type θ + δ is dealt with and now the predictive distribution is expressed...

Bayesian joint modelling of the mean and covariance structures for normal longitudinal data.

Edilberto Cepeda-Cuervo, Vicente Nunez-Anton (2007)

SORT

We consider the joint modelling of the mean and covariance structures for the general antedependence model, estimating their parameters and the innovation variances in a longitudinal data context. We propose a new and computationally efficient classic estimation method based on the Fisher scoring algorithm to obtain the maximum likelihood estimates of the parameters. In addition, we also propose a new and innovative Bayesian methodology based on the Gibbs sampling, properly adapted for longitudinal...

Bayesian like R- and M- estimators of change points

Jaromír Antoch, Marie Husková (2000)

Discussiones Mathematicae Probability and Statistics

The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.

Bayesian MCMC estimation of the rose of directions

Michaela Prokešová (2003)

Kybernetika

The paper concerns estimation of the rose of directions of a stationary fibre process in R 3 from the intersection counts of the process with test planes. A new approach is suggested based on Bayesian statistical techniques. The method is derived from the special case of a Poisson line process however the estimator is shown to be consistent generally. Markov chain Monte Carlo (MCMC) algorithms are used for the approximation of the posterior distribution. Uniform ergodicity of the algorithms used is...

Bayesian methods in hydrology: a review.

David Ríos Insua, Raquel Montes Díez, Jesús Palomo Martínez (2002)

RACSAM

Hydrology and water resources management are inherently affected by uncertainty in many of their involved processes, including inflows, rainfall, water demand, evaporation, etc. Statistics plays, therefore, an essential role in their study. We review here some recent advances within Bayesian statistics and decision analysis which will have a profound impact in these fields.

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