**A** recent news editorial in Nature (15 March issue) reminded me of the lectures Louis Aslett gave at the Gregynog Statistical Conference last week, on the advanced use of cryptography tools to analyse sensitive and private data. Lectures that reminded me of a graduate course I took on cryptography and coding, in Paris 6, and which led me to visit a lab at the Université de Limoges during my conscripted year in the French Navy. With no research outcome. Now, the notion of using encrypted data towards statistical analysis is fascinating in that it may allow for efficient inference and personal data protection at the same time. As opposed to earlier solutions of anonymisation that introduced noise and data degradation, not always providing sufficient protection of privacy. Encryption that is also the notion at the basis of the Nature editorial. An issue completely missing from the paper, while stressed by Louis, is that this encryption (like Bitcoin) is costly, in order to deter hacking, and hence energy inefficient. Or limiting the amount of data that can be used in such studies, which would turn the idea into a stillborn notion.

## Archive for information

## bitcoin and cryptography for statistical inference and AI

Posted in Books, Mountains, pictures, Running, Statistics, Travel, University life with tags AI, anonymised data, bitcoin, Britain, cryptography, encryption, Gregynog Hall, Gregynog Statistical Conference, information, Navy, Powys, Tregynon, Wales on April 16, 2018 by xi'an## Conditional love [guest post]

Posted in Books, Kids, Statistics, University life with tags Andrei Kolmogorov, axioms of probability, Bayes rule, Bayesian nonparametrics, Bayesian statistics, bootstrap, Bruno de Finetti, Céline Dion, David Draper, Dirichlet process, Edwin Jaynes, exchangeability, extendibility, information, JSM 2015, MCMC, plausibility, Richard Cox, Series B, Stone-Weierstrass, Theory of Probability on August 4, 2015 by xi'an*[When Dan Simpson told me he was reading Terenin’s and Draper’s latest arXival in a nice Bath pub—and not a nice bath tub!—, I asked him for a blog entry and he agreed. Here is his piece, read at your own risk! If you remember to skip the part about Céline Dion, you should enjoy it very much!!!]*

**P**robability has traditionally been described, as per Kolmogorov and his ardent follower Katy Perry, unconditionally. This is, of course, excellent for those of us who really like measure theory, as the maths is identical. Unfortunately mathematical convenience is not necessarily enough and a large part of the applied statistical community is working with Bayesian methods. These are unavoidably conditional and, as such, it is natural to ask if there is a fundamentally conditional basis for probability.

Bruno de Finetti—and later Richard Cox and Edwin Jaynes—considered conditional bases for Bayesian probability that are, unfortunately, incomplete. The critical problem is that they mainly consider finite state spaces and construct finitely additive systems of conditional probability. For a variety of reasons, neither of these restrictions hold much truck in the modern world of statistics.

In a recently arXiv’d paper, Alexander Terenin and David Draper devise a set of axioms that make the Cox-Jaynes system of conditional probability rigorous. Furthermore, they show that the complete set of Kolmogorov axioms (including countable additivity) can be derived as theorems from their axioms by conditioning on the entire sample space.

This is a deep and fundamental paper, which unfortunately means that I most probably do not grasp it’s complexities (especially as, for some reason, I keep reading it in pubs!). However I’m going to have a shot at having some thoughts on it, because I feel like it’s the sort of paper one should have thoughts on. Continue reading