This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors.

Published nearly seventy years ago, Jeffreys' Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the...

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density f(λ) can be written as f(λ)=|λ|−2dg(|λ|), where 0d1/2 (resp., −1/2d0), and g is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation...

A Monte Carlo algorithm is said to be adaptive if it can adjust automatically its current proposal distribution, using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for a good performance. We treat the problem of constructing...

A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for a good performance. In this paper, we present such a...

We consider the generic problem of performing sequential Bayesian inference in a state-space model with observation process y, state process x and fixed parameter theta. An idealized approach would be to apply the iterated batch importance sampling (IBIS) algorithm of Chopin (2002). This is a...

Gaussian time-series models are often specified through their spectral density. Such models pose several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We use importance sampling...