This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an assumed model (Gelman 2008). The Bayesian perspective is thus...

Our aim is to analyze the link between optimism and risk aversion in a subjective expected utility setting and to estimate the average level of optimism when weighted by risk tolerance. Its estimation leads to a non-trivial statistical problem. We start from a large lottery survey (1536...

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.

Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some...

. The Adaptive Multiple Importance Sampling algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling (IS) scheme. The difference with earlier adaptive IS implementations like Population Monte Carlo is that the importance weights of all simulated values,...

While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures. Recent innovations like Monte Carlo Markov chain, sequential...

Many authors have considered the problem of estimating a covariance matrix in small samples. In this framework the sample covariance matrix is not robust, the solution is to impose some ad hoc structure on the covariance matrix to force it to be well-conditioned. This method is known as...

When testing a null hypothesis H0: θ=θ0 in a Bayesian framework, the Savage–Dickey ratio (Dickey, 1971) is known as a specific representation of the Bayes factor (O’Hagan and Forster, 2004) that only uses the posterior distribution under the alternative hypothesis at θ0, thus allowing for...

For numerous models, it is impossible to conduct an exact Bayesian inference. There are many cases where the derivation of the posterior distribution leads to intractable calculations (due to the fact that this generally involves intractable integrations). The Bayesian computational literature...