Tests de détection de valeurs aberrantes multidimensionnelles
Tests optimaux sur les paramètres des lois de von Mises
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 Necessity of Strongly Subadditive Capacities for Neyman-Pearson Minimax Tests.
The optimum sequential test of a finite number of hypotheses for statistically dependent observations
The predictive distribution in decision theory: A case study.
The Restricted Regularity of Admissible Minimax Criteria for many well known Parametric Statistical Problems.
The revolution of testimonies in the calculus of probabilities. (La révolution des témoignages dans le calcul des probabilités.)
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...
Third-Order Optimum Properties of Estimator-Sequences.
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
Toward Optimal Feature Selection Using Ranking Methods and Classification Algorithms
Towards a notion of testability
The problem of testability has been undertaken many times in the context of linear hypotheses. Almost all these considerations restricted to some algebraical conditions without reaching the nature of the problem. Therefore, a general and commonly acceptable notion of testability is still wanted. Our notion is based on a simple and natural decision theoretic requirement and is characterized in terms of the families of distributions corresponding to the null and the alternative hypothesis. Its consequences...
Two problems of minimax estimation
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.