The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.

In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model $𝐭=𝐗\beta +ϵ$, $𝐄\left(𝐭\right)=𝐗\beta$, $\mathrm{𝐕𝐚𝐫}\left(𝐭\right)={\mathbf{0}}_{\mathbf{1}}{𝐔}_{\mathbf{1}}+{\mathbf{0}}_{\mathbf{2}}{𝐔}_{\mathbf{2}}+{\mathbf{0}}_{\mathbf{3}}{𝐔}_{\mathbf{3}}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.

In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model $𝐭=𝐗\beta +ϵ$, $𝐄\left(𝐭\right)=𝐗\beta$, $𝐃\left(𝐭\right)={\mathbf{0}}_{\mathbf{1}}{𝐔}_{\mathbf{1}}+{\mathbf{0}}_{\mathbf{2}}{𝐔}_{\mathbf{2}}$ with the unknown variance componets in the normal case. The matrices ${𝐔}_{\mathbf{1}}$, ${𝐔}_{\mathbf{2}}$ may be singular. Applications to two examples of the analysis of variance are given.

The method of least wquares is usually used in a linear regression model $𝐘=𝐗\beta +ϵ$ for estimating unknown parameters $\beta$. The case when $ϵ$ is an autoregressive process of the first order and the matrix $𝐗$ corresponds to a linear trend is studied and the Bayes approach is used for estimating the parameters $\beta$. Unbiased Bayes estimators are derived for the case of a small number of observations. These estimators are compared with the locally best unbiased ones and with the usual least squares estimators.

Structural change for the Koyck Distributed Lag Model is analyzed through the Bayesian approach. The posterior distribution of the break point is derived with the use of the normal-gamma prior density and the break point, ν, is estimated by the value that attains the Highest Posterior Probability (HPP). Simulation study is done using R. Given the parameter values ϕ = 0.2 and λ = 0.3, the full detection of the structural change when σ² = 1 is generally attained at ν + 1. The after...

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.This paper is concerned with the problem of deriving Bayesian prediction bounds for the future observations (two-sample prediction) from the inverse Weibull distribution based on generalized order statistics (GOS). Study the two side interval Bayesian prediction, point prediction under symmetric and asymmetric loss functions and the maximum likelihood (ML) prediction using "plug-in" procedure for future observations from the inverse...

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.

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...

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.

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.

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.

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...

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...