No time today to read those as I am preparing for the course this afternoon but there are two interesting new entries on arXiv, one by Madeleine Thompson and Radford Neal on covariance-adaptive slice sampling
We describe two slice sampling methods for taking multivariate steps using the crumb framework. These methods use the gradients at rejected proposals to adapt to the local curvature of the log-density surface, a technique that can produce much better proposals when parameters are highly correlated. We evaluate our methods on four distributions and compare their performance to that of a non-adaptive slice sampling method and a Metropolis method. The adaptive methods perform favourably on low-dimensional target distributions with highly-correlated parameters.
and one by Brian Shea and Galin Jones on consequential evaluation of default priors
We consider evaluating improper priors in a formal Bayes setting according to consequences of their use. This approach bridges the frequentist concern of evaluating a decision rule and the Bayesian concern of evaluating a prior. We generalize Eaton’s method, which exploits a connection between admissibility and a Markov chain defined by the sampling distribution and posterior. This generalization leads us to introduce the idea of
-admissibility, itself a generalization of strong admissibility. To illustrate the method, we establish
There have been very few extensions of Eaton’s (1992) great characterisation of admissible Bayes procedures so this sounds quite exciting!
