Tests de détection de valeurs aberrantes multidimensionnelles
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 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 optimum sequential test of a finite number of hypotheses for statistically dependent observations
The predictive distribution in decision theory: A case study.
The sum-product algorithm: algebraic independence and computational aspects
The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product function whose range is the ground set of a commutative semiring. The algorithm is general enough to include as special cases several classical algorithms developed in information theory and probability theory. We present four results. First, using the sum-product algorithm we show that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of probability-theoretic...
Three methods for constructing reference prior distributions.
Three methods are proposed for constructing reference prior densities for certain biparametric distribution families. These densities represent approximations to the Bayesian concept of noninformative distribution.
Topologies associated to some decision statistical functions
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.