## Bayes vs the virial theorem

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### 4 Responses to Bayes vs the virial theorem

1. One update to my thoughts on non-parametric error models for semi-parametric Bayesian analyses: one limitation of the Dirichlet Process is that its concentration parameter controls both the ‘spike-iness’ of its realisations *and* their allowed ‘deviation’ from the reference distribution, so it may be worth exploring the more general class of Chinese restaurant processes reviewed thoroughly and explained (at a rather sophisticated level) by Zhou and Carin in “Negative Binomial Process Count and Mixture Modelling”.

2. Thanks Drew! I’ll need to dig into that some time soon. (At least I’ll try.) Doesn’t really look too bad … I’m familiar with Polya urns, and stick-breaking processes are the heart of the Bayesian bootstrap which, in my immediate world, finds its way into Bayesian approaches for finite population sampling (Ghosh and Meeden).

I have SO many things to read, meaning study! Doing a lot of writing, too.

On the error in all variables problem, there’s a major paper on the climate science front,

A. Hannart, A. Ribes, and P. Naveau, “Optimal fingerprinting under multiple sources of uncertainty”, GEOPHYSICAL RESEARCH LETTERS, http://dx.doi.org/10.1002/2013GL058653

which I need to give priority.

There’s also one with an intriguing title and abstract, but I don’t know if it’s special or not:

D. Williamson, A. T. Blaker, “Evolving Bayesian Emulators for Structured Chaotic Time Series, with Application to Large Climate Models”, http://dx.doi.org/10.1137/120900915, 2014.

3. Hi Jan,
The maximum likelihood, errors-in-variable method with selection of predictor variables by profile likelihood ratios described by Hannart et al is (as they acknowledge) quite an ‘old-fashioned’ statistical technique. There’s nothing ‘wrong’ with it per se, but I imagine due to the availability of fast codes for implementing the equivalent Bayesian model (e.g. R or STAN) many (perhaps most?) statisticians outside geophys would go Bayes. Bayesian model selection (or, for the prediction problem, model averaging) of course requires some care to check for sensitivity of the output to the parameter priors. But I would think it could have a lot of potential here owing to its flexibility: e.g. the errors don’t have to be assumed Normal (perhaps fat-tailed distributions make more sense), and/or the predictor variable set could be expanded to include variables for which one might not have observations at all places / time-points via data augmentation (e.g. http://amstat.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10518?src=recsys ).
cheers, Ewan (not Drew: but i get the confusion from my username which omits the periods in dr.ewan.cameron)

4. Apologies for the name confounding, Ewan!

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