The AstroStat Slog » priors

coin toss with a twist

vlk — Sun, 26 Dec 2010 22:27:50 +0000

Here’s a cool illustration of how to use Bayesian analysis in the limit of very little data, when inferences are necessarily dominated by the prior. The question, via Tom Moertel, is: suppose I tell you that a coin always comes up heads, and you proceed to toss it and it does come up heads — how much more do you believe me now?

He also has the answer worked out in detail.

(h/t Doug Burke)

[ArXiv] 4th week, Apr. 2008

hlee — Sun, 27 Apr 2008 15:29:48 +0000

The last paper in the list discusses MCMC for time series analysis, applied to sunspot data. There are six additional papers about statistics and data analysis from the week.

[astro-ph:0804.2904]M. Cruz et al.
The CMB cold spot: texture, cluster or void?
[astro-ph:0804.2917] Z. Zhu, M. Sereno
Testing the DGP model with gravitational lensing statistics
[astro-ph:0804.3390] Valkenburg, Krauss, & Hamann
Effects of Prior Assumptions on Bayesian Estimates of Inflation Parameters, and the expected Gravitational Waves Signal from Inflation
[astro-ph:0804.3413] N.Ball et al.
Robust Machine Learning Applied to Astronomical Datasets III: Probabilistic Photometric Redshifts for Galaxies and Quasars in the SDSS and GALEX (Another related publication [astro-ph:0804.3417])
[astro-ph:0804.3471] M. Cirasuolo et al.
A new measurement of the evolving near-infrared galaxy luminosity function out to z~4: a continuing challenge to theoretical models of galaxy formation
[astro-ph:0804.3475] A.D. Mackey et al.
Multiple stellar populations in three rich Large Magellanic Cloud star clusters
[stat.ME:0804.3853] C. R\”over , R. Meyer, N. Christensen
Modelling coloured noise (MCMC & sunspot data)

“you are biased, I have an informative prior”

vlk — Wed, 10 Oct 2007 16:26:27 +0000

Hyunsook drew attention to this paper (arXiv:0709.4531v1) by Brad Schaefer on the underdispersed measurements of the distances to LMC. He makes a compelling case that since 2002 published numbers in the literature have been hewing to an “acceptable number”, possibly in an unconscious effort to pass muster with their referees. Essentially, the distribution of the best-fit distances are much more closely clustered than you would expect from the quoted sizes of the error bars.

To be sure, there are other possible reasons for this underdispersion, such as correlations in how the data are gathered and analyzed, and an overly conservative estimation of error bars, etc. In fact, the most benign explanation is probably in how people carry out “sanity checks” and tend to discard or explain away or correct the data that give odd results.

While this is indeed worrisome, I am inclined to think that this is not wrong per se, but rather a case where a fully Bayesian analysis would give the “right” coverage. After all, there does exist a strong prior that people are bringing into the analysis, but are not including in the calculations of the widths of the posterior probability distributions. Including such a highly informative prior will of course shrink the sizes of the error bars and make everything consistent. i.e., I think that the assumption needs to be explicit, that is all. Is that bias? bandwagon? or prior belief?

Wrong Priors?

vlk — Mon, 10 Sep 2007 16:15:31 +0000

arXiv:0709.1067v1 : Wrong Priors (Carlos C. Rodriguez)

This came through today on astro-ph, suggesting that we could be choosing priors better than we do, and in fact that we generally do a very bad job of it. I have been brought up to believe that, like points in Whose Line Is It Anyway, priors don’t matter (unless you have very little data), so I am somewhat confused. What is going on here?