Statistique bayésienne, théorie de la décision et méthodes de simulation par chaînes de Markov

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I want to develop an algorithm that is going to help the companies when they have to offer new products to the customers. The algorithm is a Bayesian procedure giving predictive probabilities on rank statistics. The theory of copula is used in the model and a Markov Chain Monte Carlo simulation is going to be constructed for the numerical evaluations.******The acceptance-rejection sampler is an algorithm for sampling from a target density f using a proposal density g. In this algorithm some of the sample values generated by g will be rejected when they fail a test. When the rejection rate is large the sampling is slow. I want to develop better samplers. In particular, I propose to use a Markov chain related to the acceptance-rejection sampler. In want to work on an existing variation of the acceptance-rejection sampler showing that this variation works under weaker conditions than the ones proposed in Caffo, Booth and Davison (2002).******In the theory of copula I want to answer the questions raised in Carley's (2002) paper. These questions are about copula extensions of a subcopula.******In the theory of extreme values the copula is characterized by a function called the Pickands function. The Pickands function is also related to something called the spectral measure. In Guillotte and Perron (2016) we have characterized all of the polynomial Pickands functions for a 2-dimensional problem. I want to do the same for the spectral measure in a 3-dimensional problem. I want to develop a Bayesian nonparametric estimator for the spectral measure in a 3-dimensional problem. This problem is related to the estimation of a cumulative distribution function. The solution will be based on Polya trees.******In Pham Gia, Turkkan and Marchand (2006) the density of the ration X_1/X_2 where the distribution of (X_1,X_2) is a mixture of normal distributions is expressed through special functions like the 1F1 function. I want to exploit a new representation involving a mixture. In the mixture the weights follow a mixed Poisson distribution. The mixed Poisson distributions are very important in mathematical finance.*****