Denys Pommeret

Likelihood-free parallel tempering

Approximate Bayesian Computational (ABC) methods, or likelihood-free methods, have appeared in the past fifteen years as useful methods to perform Bayesian analysis when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: MCMC methods have been developed by Marjoram et al. (2003) and by Bortot et al. (2007) for instance, and sequential methods have been proposed among others by Sisson et al. (2007), Beaumont et al. (2009) and Del Moral et al. (2012). Recently, sequential ABC methods have appeared as an alternative to ABC-PMC methods (see for instance McKinley et al., 2009; Sisson et al., 2007). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the parallel tempering algorithm (Geyer 1991). Performance is compared with existing ABC algorithms on simulations and on a real example.

A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model

A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model. The defective density function associated to the ruin probability is projected in an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to a Natural Exponential Family with Quadratic Variance Function (NEF-QVF). The method is convenient in at least four ways. Firstly, it leads to a simple analytical expression of the ultimate ruin probability. Secondly, the implementation does not require strong computer skills. Thirdly, our approximation method does not necessitate any preliminary discretization step of the claim sizes distribution. Finally, the coefficients of our formula do not depend on initial reserves.

Data driven smooth test of comparison for dependent sequences

In this paper we propose a smooth test of comparison for the marginal distributions of strictly stationary dependent bivariate sequences. We first state a general test procedure and several cases of dependence are then investigated. The test is applied to both simulated data and real datasets.

Nonparametric comparison of several transformations of distribution functions

This paper considers two random variables such that there exists a monotone transformation between their distribution functions. The problem is to test if there is a change in this transformation when these two variables are observed under K different conditions. The approach considered is a CUSUM test based on the cumulative sum of the residuals and a test statistic is proposed for testing the equality of the K transformations. The asymptotic distribution of the test statistic is derived and its finite sample properties are examined by simulation. As a further illustration, an analysis of a real data set concerning the impact of the financial crisis of September 2008 is given.

A two-sample test when data are contaminated

In this paper we consider the problem of testing whether two samples of contaminated data arise from the same distribution. Is is assumed that the contaminations are additive noises with known, or estimated moments. This situation can also be viewed as two signals observed before and after perturbations. The problem is then to test the equality of both perturbations. The test statistic is based on the polynomials moments of the difference between observations and noises. The test is very simple and allows one to compare two independent as well as two paired contaminated samples. A data driven selection is proposed to choose automatically the number of involved polynomials. We present a simulation study in order to investigate the power of the proposed test within discrete and continuous cases. Real-data examples are presented to illustrate the method.