Testing a precise null hypothesis using reference posterior odds.
The Bayes choice of an experiment in estimating a success probability
A Bayesian method of estimation of a success probability p is considered in the case when two experiments are available: individual Bernoulli (p) trials-the p-experiment-or products of r individual Bernoulli (p) trials-the -experiment. This problem has its roots in reliability, where one can test either single components or a system of r identical components. One of the problems considered is to find the degree r̃ of the -experiment and the size m̃ of the p-experiment such that the Bayes estimator...
The Bayes estimator of the variance components and its admissibility
The Bayes sequential estimation of a normal mean from delayed observations
The problem of estimating the mean of a normal distribution is considered in the special case when the data arrive at random times. Certain classes of Bayes sequential estimation procedures are derived under LINEX and reflected normal loss function and with the observation cost determined by a function of the stopping time and the number of observations up to this time.
The Bayesian approach to the combination of forecasts: some extensions into a skewed environment.
Where a decision-maker has to rely on expert opinions a need for a normative model to combine these forecasts appears. This can be done using Bayes' formula and by making some assumptions on the prior distribution and the distribution of the expert assessments. We extend the case to skewed distributions of these assessments. By using an Edgeworth expansion of the density function including the skewness parameter, we are able to obtain the formula to combine the forecasts in a Bayesian way.
The Bayesian sequential model with the range-based probability estimation
The effect of loss functions on empirical Bayes reliability analysis.
The importance of being the upper bound in the bivariate family.
Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric...
The optimal control chart procedure
The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span is specified by a partition of the space into three disjoint parts. We call this partition as the control chart frame of span A shift in the process parameter is signalled at time by having the vector of the last sample characteristics fall out of the...
The optimum sequential test of a finite number of hypotheses for statistically dependent observations
The posterior predictive p-value: An alternative to the classical p-value.
Theoretical and practical considerations regarding bonus-malus system.
Two-point priors and minimax estimation of a bounded parameter under convex loss
The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.