We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the stick-breaking representation of the Pitman-Yor process or the expression of the finite-dimensional distributions for the normalized-inverse Gaussian process, w...

We study the probability of ruin before time t for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression. These are benchmarked against simulations...

We study the internal intermittency in the inverse energy cascade and in the condensation regime of two-dimensional turbulence, using physical and numerical experimental approaches. The analysis confirms that the velocity increments have nearly Gaussian distributions at all scales in the inverse cascade regime; it moreover shows that, in the condensation regime, the probability distribution fun...

Running Title: Mixture of Inverse GaU88ian Distributions 2 SUMMARY A mixture of Inverse GaU88ian distributions is examined as a model for the lifetime of components. The components differ in one of three ways: in their initial quality, rate of wear, or variability of wear. These three cases are well represented by the parameters of the Inverse GaU88ian model. The mechanistic interpretation of t...

A first-order autoregressive process with inverse gaussian marginals is introduced. The innovation distributions are obtained under certain special cases. The unknown parameters are estimated using different methods and these estimators are shown to be consistent and asymptotically normal. The behavior of the estimators for small samples is studied through simulation experiments. On Sums of Tri...

In this paper, we study the multi-task learning problem with a new perspective of considering the structure of the residue error matrix and the low-rank approximation to the task covariance matrix simultaneously. In particular, we first introduce the Matrix Generalized Inverse Gaussian (MGIG) prior and define a Gaussian Matrix Generalized Inverse Gaussian (GMGIG) model for low-rank approximatio...

There are two major routes to address linear inverse problems. Whereas regularization-based approaches build estimators as solutions of penalized regression optimization problems, Bayesian estimators rely on the posterior distribution of the unknown, given some assumed family of priors. While these may seem radically different approaches, recent results have shown that, in the context of additi...