We study the one-sided testing problem for the exponential distribution via the empirical Bayes (EB) approach. Under a weighted linear loss function, a Bayes test is established. Using the past samples, we construct an EB test and exhibit its optimal rate of convergence. When the past samples are not directly observable, we work out an EB test by using the deconvolution kernel method and obtain its asymptotic optimality.

An upper bound for the Kolmogorov distance between the posterior distributions in terms of that between the prior distributions is given. For some likelihood functions the inequality is sharp. Applications to assessing Bayes robustness are presented.

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.

A complete algorithm is presented for the sharpening of imprecise information, based on the methodology of kernel estimators and the Bayes decision rule, including conditioning factors. The use of the Bayes rule with a nonsymmetrical loss function enables the inclusion of different results of an under- and overestimation of a sharp value (real number), as well as minimizing potential losses. A conditional approach allows to obtain a more precise result thanks to using information entered as the...

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.

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...

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...

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.