Does Bayesian statistics have to meet normality assumptions?

startfromzero

I am fairly new to JASP and Bayesian statistics, and this question has been bugging me for some time, so I hope someone is able to give me some advice.

I read from Kruschke's (2010) paper that Bayesian ANOVA does not assume approximations to normality or homogeneity of variance, but I have also come across discussions of using nonparametric Bayesian tests on this forum. This seems rather confusing to me because if those assumptions need not be met, why is it necessary to have some nonparametric versions of the Bayesian tests? Does it apply only to Bayesian ANOVA but not Bayesian t-test or other tests? Or have i misunderstood?

I have also read from his DBDA book that changing the likelihood function to a t distribution (instead of using a normal distribution) will be more robust against outliers because of its long tails. This seems very useful and I wonder if there is any way we can change the likelihood function of Bayesian tests on JASP?

Thank you.

EJ

Dear startfromzero,

I believe that the Bayesian ANOVA does make assumptions, for instance about homogeneity of variance. This is similar to the Bayesian t-test that assumes a common sigma. One may develop a Bayesian Welch test (with two sigma's, one per group) but that will change the result.

I do agree that a t-distribution might be interesting to increase robustness to outliers. We have not implemented this, but we may do so in the future.

Cheers,
E.J.

startfromzero

Dear E.J.

Thank you so much for your prompt response, which helps to clarify an issue that has really puzzled me. I suppose the usual procedures for data screening and cleaning and for outlier detection and exclusion still apply when performing Bayesian statistics.

EJ

Definitely! We are working to develop and include analysis methods based on ranks -- these methods naturally make assumptions that are much weaker.
E.J.