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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?


  • Hi arran_reader,

    This is because of the connection between Pearson's rho and Kendall's tau. See the section on "parametric yoking" here:


  • 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'?


  • 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?!


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