Archive for applied Bayesian analysis

moralizing gods drive Nature rejection

Posted in Statistics with tags , , , , , , , on August 29, 2021 by xi'an

simplified Bayesian analysis

Posted in Statistics with tags , , , , , , , , , , , , on February 10, 2021 by xi'an

A colleague from Dauphine sent me a paper by Carlo Graziani on a Bayesian analysis of vaccine efficiency, asking for my opinion. The Bayesian side is quite simple: given two Poisson observations, N~P(μ) and M~P(ν), there exists a reparameterisation of (μ,ν) into

e=1-μ/rν  and  λ=ν(1+(1-e)r)=μ+ν

vaccine efficiency and expectation of N+M, respectively, when r is the vaccine-to-placebo ratio of person-times at risk, ie the ratio of the numbers of participants in each group. Reparameterisation such that the likelihood factorises into a function of e and a function of λ. Using a product prior for this parameterisation leads to a posterior on e times a posterior on λ. This is a nice remark, which may have been made earlier (as for instance another approach to infer about e while treating λ as a nuisance parameter is to condition on N+M). The paper then proposes as an application of this remark an analysis of the results of three SARS-Cov-2 vaccines, meaning using the pairs (N,M) for each vaccine and deriving credible intervals, which sounds more like an exercise in basic Bayesian inference than a fundamental step in assessing the efficiency of the vaccines…

Bayes @ NYT

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , on August 8, 2020 by xi'an

A tribune in the NYT of yesterday on the importance of being Bayesian. When an epidemiologist. Tribune that was forwarded to me by a few friends (and which I missed on my addictive monitoring of the journal!). It is written by , a Canadian journalist writing about mathematics (and obviously statistics). And it brings to the general public the main motivation for adopting a Bayesian approach, namely its coherent handling of uncertainty and its ability to update in the face of new information. (Although it might be noted that other flavours of statistical analysis are also able to update their conclusions when given more data.) The COVID situation is a perfect case study in Bayesianism, in that there are so many levels of uncertainty and imprecision, from the models themselves, to the data, to the outcome of the tests, &tc. The article is journalisty, of course, but it quotes from a range of statisticians and epidemiologists, including Susan Holmes, whom I learned was quarantined 105 days in rural Portugal!, developing a hierarchical Bayes modelling of the prevalent  SEIR model, and David Spiegelhalter, discussing Cromwell’s Law (or better, humility law, for avoiding the reference to a fanatic and tyrannic Puritan who put Ireland to fire and the sword!, and had in fact very little humility for himself). Reading the comments is both hilarious (it does not take long to reach the point when Trump is mentioned, and Taleb’s stance on models and tails makes an appearance) and revealing, as many readers do not understand the meaning of Bayes’ inversion between causes and effects, or even the meaning of Jeffreys’ bar, |, as conditioning.

souvenirs de Luminy

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on July 6, 2020 by xi'an

just in case your summer of British conferences is not yet fully-booked…

Posted in Statistics with tags , , , , , , , , , , , on May 11, 2018 by xi'an