Bayesian priors

The Conversion of Subjective Bayesian, Colin Howson, & the problem of old evidence (i)

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“The subjective Bayesian theory as developed, for example, by Savage … cannot solve the deceptively simple but actually intractable old evidence problem, whence as a foundation for a logic of confirmation at any rate, it must be accounted a failure.” (Howson, (2017), p. 674)

What? Did the “old evidence” problem cause Colin Howson to recently abdicate his decades long position as a leading subjective Bayesian? It seems to have. I was so surprised to come across this in a recent perusal of Philosophy of Science that I wrote to him to check if it is really true. (It is.) I thought perhaps it was a different Colin Howson, or the son of the one who co-wrote 3 editions of Howson and Urbach: Scientific Reasoning: The Bayesian Approach espousing hard-line subjectivism since 1989.[1] I am not sure which of the several paradigms of non-subjective or default Bayesianism Howson endorses (he’d argued for years, convincingly, against any one of them), nor how he handles various criticisms (Kass and Wasserman 1996), I put that aside. Nor have I worked through his, rather complex, paper to the extent necessary, yet. What about the “old evidence” problem, made famous by Clark Glymour 1980?  What is it? Continue reading

Categories: Bayesian priors, objective Bayesians, Statistics | Tags: | 25 Comments

Can You Change Your Bayesian Prior? The one post whose comments (some of them) will appear in my new book

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I blogged this exactly 2 years ago here, seeking insight for my new book (Mayo 2017). Over 100 (rather varied) interesting comments ensued. This is the first time I’m incorporating blog comments into published work. You might be interested to follow the nooks and crannies from back then, or add a new comment to this.

This is one of the questions high on the “To Do” list I’ve been keeping for this blog.  The question grew out of discussions of “updating and downdating” in relation to papers by Stephen Senn (2011) and Andrew Gelman (2011) in Rationality, Markets, and Morals.[i]

“As an exercise in mathematics [computing a posterior based on the client’s prior probabilities] is not superior to showing the client the data, eliciting a posterior distribution and then calculating the prior distribution; as an exercise in inference Bayesian updating does not appear to have greater claims than ‘downdating’.” (Senn, 2011, p. 59)

“If you could really express your uncertainty as a prior distribution, then you could just as well observe data and directly write your subjective posterior distribution, and there would be no need for statistical analysis at all.” (Gelman, 2011, p. 77)

But if uncertainty is not expressible as a prior, then a major lynchpin for Bayesian updating seems questionable. If you can go from the posterior to the prior, on the other hand, perhaps it can also lead you to come back and change it.

Is it legitimate to change one’s prior based on the data? Continue reading

Categories: Bayesian priors, Bayesian/frequentist | 14 Comments

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