## at CIRM

Thanks to a very early start from Paris, and despite horrendous traffic jams in Marseilles, I managed to reach CIRM with ten minutes to spare before my course. After my one-hour class, I was suddenly made aware of the (simplistic) idea that the slice sampling uniforms are simply auxiliary, meaning they can be used in many different ways.

I noticed Natesh Pillai just arXived an extension of his earlier Cauchy paper with XL. He proves that the result on the Cauchy distribution of any convex combination of normal ratios still holds when the pair of vectors is distributed from a product of elliptically symmetric functions. Some of Natesh’s remarks reminded me of the 1970 Sankhyã paper by Kelker on spherically symmetric variables. Especially because of Kelker’s characterisation of elliptically symmetric functions as scale mixtures of normals, which makes perfect sense since the scale cancels.

As I skimmed through my slides yesterday, fearing everyone knew about the MCMC basics, I decided to present today the Rao-Blackwellisation slides I gave in Warwick a few months ago.

March 1, 2016 at 4:07 am

Thank you Christian!

Your observation is quite nice. In fact, any mixtures of Gaussian clearly satisfies my result, and the closure of mixtures of Gaussians also satisfy my result. The other observation I make is that the product of such densities also satisfy my result.