Archive for Ed Jaynes

The Coherence Principle

Posted in The Universe and Stuff with tags , , , , on July 14, 2026 by telescoper

Back into the swing of things in Maynooth, getting ready for the repeat examinations that start next month, I realized that I had forgotten to pass on an interesting paper that I found out about a few weeks ago but was reminded of while in London so I’m remedying my omission now. The title is The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories by Raul Jimenez, Carlos Peña Garay, Fergus Simpson, and Licia Verde. It addresses the issue of how to assign prior probabilities. We know how to do this in cases where the models concerned belong to a family differentiated by relatively simple parameters (as is the case in the standard cosmological framework), but for more complex differences the appropriate prior is difficult to choose. I see the paper as an attempt to extend the work of Ed Jaynes, though I’m not sure the authors see it quite in those terms!

Here is the abstract:

Bayesian model selection in cosmology and particle physics is often performed where posterior odds inherit a strong, often unacknowledged dependence on the prior assigned to competing models. Standard responses — reference priors, hierarchical priors, or appeals to naturalness — ignore relevant theoretical knowledge or rely on criteria hard to define operationally. We propose the Coherence Principle: a reproducible prescription for assigning model priors according to compatibility with the validated structure of an existing theory. This structure, grammar, includes symmetries, conservation laws, locality, Lorentz invariance, and universality patterns. Unmotivated violations of these rules incur a coherence cost, converted into a prior weight through a maximum-entropy exponential form controlled by one calibratable parameter α. The resulting prior is distinct from both the Bayesian Occam factor and naturalness: it penalizes not parameter volume or fine tuning, but departures from validated theoretical grammar. We illustrate the principle with examples from cosmology and fundamental physics: neutrino mass mechanisms, dark energy and modified gravity, inflation, beyond-Standard-Model sectors, and hierarchical astrophysical inference. We test it also on four historical cases — general relativity, Pauli’s neutrino, parity violation, and special relativity — where evidential and theoretical contexts can be reconstructed. These examples show that it favors the historically successful choice when the proper grammar is defined in the correct domain and time. The Coherence Principle makes explicit a common but usually tacit part of physical reasoning: trust in validated structural rules. It turns this judgment into a transparent, testable, and overrulable component of Bayesian inference, leaving empirical likelihoods free to dominate when data are sufficiently constraining.

arXiv:2606.18491v1

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Guest Post – Bayesian Book Review

Posted in Bad Statistics, Books, Talks and Reviews with tags , , , on May 30, 2011 by telescoper

My regular commenter Anton circulated this book review by email yesterday and it stimulated quite a lot of reaction. I haven’t read the book myself, but I thought it would be fun to post his review on here to see whether it provokes similar responses. You can find the book on Amazon here (UK) or here ( USA). If you’re not completely au fait with Bayesian probability and the controversy around it, you might try reading one of my earlier posts about it, e.g. this one. I hope I can persuade some of the email commenters to upload their contributions through the box below!

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The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy

by Sharon Bertsch Mcgrayne

I found reading this book, which is a history of Bayes’ theorem written for the layman, to be deeply frustrating. The author does not really understand what probability IS – which is the key to all cogent writing on the subject. She never mentions the sum and product rules, or that Bayes’ theorem is an easy consequence of them. She notes, correctly, that Bayesian methods or something equivalent to them have been rediscovered advantageously again and again in an amazing variety of practical applications, and says that this is because they are pragmatically better than frequentist sampling theory – ie, she never asks the question: Why do they work better and what deeper rationale explains this? RT Cox is not mentioned. Ed Jaynes is mentioned only in passing as someone whose Bayesian fervour supposedly put people off.

The author is correct that computer applications have catalysed the Bayesian revolution, but in the pages on image processing and other general inverse problems (p218-21) she manages to miss the key work through the 1980s of Steve Gull and John Skilling, and you will not find “Maximum entropy” in the index. She does get the key role of Markov Chain Monte Carlo methods in computer implementation of Bayesian methods, however. But I can’t find Dave Mackay either, who deserves to be in the relevant section about modern applications.

On the other hand, as a historian of Bayesianism from Bayes himself to about 1960, she is full of superb anecdotes and information about
people who are to us merely names on the top of papers, or whose personalities are mentioned tantalisingly briefly in Jaynes’ writing.
For this material alone I recommend the book to Bayesians of our sort and am glad that I bought it.

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