Comments on: Bayesian Counterpart to Fisher Exact Test on Contingency Tables

By: Mehran Aflakparast

Mehran Aflakparast — Sat, 04 Jun 2011 11:05:10 +0000

It is definitly related to my problem.
What I’m looking for is a 2*L version of the method you presented here. But I have an other prior information which considers ordered probabilities for celles in contingency table (i.e. P1<=P2<=P3…<=Pl).

By: Bob Carpenter

Bob Carpenter — Wed, 01 Jun 2011 21:27:31 +0000

I don’t see how it relates to this post per se, but what you’re looking for is perhaps ordinal logistic regression. If you compute a Bayesian posterior via sampling, you can then do whatever you want with statistics over the posterior samples.

By: Mehran Aflakparast

Mehran Aflakparast — Tue, 31 May 2011 08:02:42 +0000

Your method sounds great! I wonder If I can use your method in my problem or not.
I am working on a data set with a binary response variable and discrete predictor variables (each has three state: 0,1,2).
I am willing to test independence between response variable and all combinations of predictor variable in a Bayesian framework.
I think it would be logical to assign a similarity between two adjacent categories (e.g. x1=0 , x2=0, x3=0, x4=0, x5=0 & x1=0 , x2=0, x3=0, x4=0, x5=1).
Thus, I want to use the property of similarity of probabilities in adjacent categories, when the categories are ordered.

Kindly give me a clue.

By: lingpipe

lingpipe — Tue, 30 Nov 2010 22:51:02 +0000

I’m toying with writing such a book myself. But I’d just steer clear of the whole frequentist notion of hypothesis testing. I got distracted with the LingPipe book, which is much less mathematical.

I’ve never really studied Bayes factors or model selection problems.

I like the analysis of the actual Fisher exact test with the oddball improper priors Beta(0,1) and Beta(1,0). I’ll have to look that up and work through it.

There must be better things to cite than Andrew’s and my blog posts here! There’s pretty extensive discussion in Andrew’s book and in the multiple comparisons paper I linked in the previous comment.

By: Kevin Murphy

Kevin Murphy — Tue, 30 Nov 2010 21:43:54 +0000

I like this example, and have incorporated it into a book
I am writing called “Machine learning: a probabilistic approach”.
I thought readers of this blog might be interested to see
the relevant pages, which can be accessed here
http://people.cs.ubc.ca/~murphyk/MLbook/pmlBFcoin.pdf
(A version with all the cross references fixed should
be ready in a year or so :)
In particular, I compare Gelman’s p(delta|D) method
to a more standard Bayes factor analysis.
The latter has a simple closed form solution which might be of
interest to Luke Hutchinson and others.

Please let me know your comments.

Kevin

PS. would “psirusteam” please translate his Spanish posting
(at http://predictive.files.wordpress.com/2009/10/binder2.pdf )
to English?

By: lingpipe

lingpipe — Tue, 30 Nov 2010 19:26:32 +0000

No! Don't cite me. I didn't make this up -- it's just the standard Bayesian posterior inference. I was just working through the details for Andrew Gelman's blog post. Andrew didn't make this up, either, though his (co-authored) book Bayesian Data Analysis is my favorite general reference for the basics of Bayesian inference. In general, you want to build a hierarchical model of the population, which sensibly adjusts for data size relative to a population and can handle multiple comparisons. See Andrew, Masanao and Jennifer's paper and my blog post.

By: Beth Biller

Beth Biller — Tue, 30 Nov 2010 14:44:40 +0000

This is super-useful… enough so that I’d like to use this Bayesian method to replace the Fisher exact test method I have been using in the paper I am currently writing (in this particular astronomical application, I’m comparing binarity fractions between two different samples of brown dwarfs)

How should I cite you?

By: lingpipe

lingpipe — Fri, 19 Nov 2010 20:25:35 +0000

I didn’t write one, but it’d be pretty simple. Just translate all the binomials to multinomials and betas to Dirichlets.

By: Andrew

Andrew — Fri, 19 Nov 2010 08:47:17 +0000

Very useful analysis and R code.

Is there an extension of it to handle larger r x c tables – e.g. 2 x 3?

By: lingpipe

lingpipe — Sat, 30 Oct 2010 05:05:14 +0000

For a quick look at Bayesian multiple comparisons, you can check out my baseball batting ability analysis:

http://lingpipe-blog.com/2009/11/04/hierarchicalbayesian-batting-ability-with-multiple-comparisons/

For more depth, check out Andrew, Jennifer and Masanao’s paper and presentation, linked from this blog post:

http://www.stat.columbia.edu/~cook/movabletype/archives/2008/03/why_i_dont_usua_1.html

I’ve been spending lots of time with RNA-Seq data lately, specifically differential gene or splice-variant of gene expression, as described here:

http://lingpipe-blog.com/2010/02/05/inferring-splice-variant-mrna-expression-rna-seq/

Of course, I had to reimplment the sampler — BUGS won’t scale to RNA-Seq size data sets!