In this essay, I argue about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. My main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing proportion of Bayesian studies in the applied...

The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true...

Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random fields, relying on a inter-model sufficiency property to show...

In Chib (1995), a method for approximating marginal densities in a Bayesian setting is proposed, with one proeminent application being the estimation of the number of components in a normal mixture. As pointed out in Neal (1999) and Fruhwirth-Schnatter (2004), the approximation often fails short...

We extend the asymmetric, stochastic, volatility model by modeling the return-volatility distribution nonparametrically. The novelty is modeling this distribution with an infinite mixture of Normals, where the mixture unknowns have a Dirichlet process prior. Cumulative Bayes factors show our...

We present a dependent Bayesian nonparametric model for the proba- bilistic modelling of species-by-site data, i.e. population data where observations at different sites are classified into distinct species. We use a dependent version of the Griffiths-Engen-McCloskey distribution, the...