On many occasions it’s handy to have a list of conjugate prior distributions. Several books have it, but if you’re typing away on a beach somewhere, let me provide some links:
John Cook’s summary of univariate conjugate prior relationships:
John links to another two good sources: Wikipedia and to Daniel Fink’s “A Compendium of Conjugate Priors”.
John Cook also has a clickable diagram of distribution relationships, a subset of a much larger one by Leemis and McQueston (click to enlarge):
(Material found via LingPipe’s introduction to Bayesian statistics, thanks Bob.)
I have the Leemis and McQueston chart blown up to 11 by 17 on the glass wall of my office. There's a Chicago Bike Map on another glass wall. Both get close attention from visitors.
Surrounding the Leemis and McQueston chart are various classic illustrations from Alice in Wonderland.
A lot of the work I'm doing lately deals with stretched distributions (e.g. NBD as stretched poisson, Weibull as stretched exponential) and the chart is occasionally helpful in convincing people I'm not just making this stuff up.
Another useful list would be symmetric distributions expressible as scale mixtures of normals — very handy for Gibbs sampling. So far I know of three:
t-distribution – mixing distribution is inverse gamma;
logistic distribution – mixing distribution is Kolmogorov-Smirnov
Laplace distribution – mixing distribution is exponential
Great references– thanks!
Thanks for writing about these distribution diagrams. I find them very helpful in teaching and I hope other people will too.
Very nice, thanks!
Corey, this is interesting – would be definitely cool (unfortunately, don't know of good references on this topic)! I posted before about the connections between distance metrics and distributions at http://www.stat.columbia.edu/~cook/movabletype/ar…