# Stretched beta prior width in Bayesian correlation (Pearson's vs Kendall's)

I am running some correlations, and want to provide the Bayesian alternatives in the analysis. Some correlations are on normally distributed variables, so I am using Pearson's, others are non-parametric, so I'm using Kendall's tau-b. I have a query regarding uninformed priors in these cases.

Why is the prior flat for Pearson's at width 1, but only flat for Kendall's at width 2?

## Comments

Hi arran_reader,

This is because of the connection between Pearson's rho and Kendall's tau. See the section on "parametric yoking" here: http://www.ejwagenmakers.com/inpress/VanDoornEtAlBayesianKendallsTauinpress.pdf

Cheers,

E.J.

Hi EJ,

Thanks for your quick response. I had a look at the article you linked. Whilst I don't really understand the maths, can I check that I understand the conceptual implications?

Is the curved prior in Kendall's at width 1 conceptually similar to the flat Pearson's prior, in that it assumes all results are equally likely? If so, why is this the case? Why is a uniform prior in Kendall's more suitable for 'parameter estimation instead of hypothesis testing'?

Arran

Hi Arran,

The flat Pearson prior translates to a curved Kendall prior. So if you repeatedly generate large fake data sets by values of rho drawn from a flat Pearson prior, and you estimate Kendall's tau for those fake data sets, the point estimates will yield a curved distribution. And do we argue that a uniform prior for Kendall's tau?!

Cheers,

E.J.