We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian prior with precision operator of differential form, we show...

We describe a simple, yet efficient, procedure for approximating the Lévy measure of a Gamma(α,1) random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson’s representation of the Dirichlet process. This approximation is written...

In this paper we discuss consistency of the posterior distribution in cases where the Kullback-Leibler condition is not verified. This condition is stated as : for all $\epsilon 0$ the prior probability of sets in the form $\{f ; KL(f0 , f ) \leq \epsilon\}$ where KL(f0 , f ) denotes the...

This paper discuses the application of mixture models for analyzing data with hidden structure. More specifically, we are interested in situations where the structure is due to some unobserved factors. Detecting the latent structures in data is not trivial. On the other hand, since such...

We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both...