# Basic question regarding simple groups differences, credibility and evidence

Hi! I am new in Bayesian Statistics and I’m trying to perform some analysis using brms. However, I’m facing some difficulties. I have two really basic questions and I would be grateful if you could give me your opinion. They can be simplified as follows:

1. Consider the following model:
m <- brm(y ~ Group + (1|Subj), data=dat)
where y is count data and Group is a categorical variable with two levels, A and B. Since y has underdispersion and currently brms has no specific family for underdispersion, may I trust the results from this model when convergence is achieved?

2. Suppose I can trust these results. I want to assess the differences between the two groups. I thought about assessing the difference by analyzing the (Bayesian) 95%CI and the Evidence Ratio (ER).

-95%CI: The output of model m gives me an estimate, x=.61, and a 95% Bayesian CI = [-0.04, 1.29].

-ER: I specified the model
m_prime <- brm(y ~ 0+Group + (1|Subj), data=dat, save_all_pars = TRUE, sample_prior=TRUE);
and used the ‘hypothesis’ function [that is, hypothesis(m_prime, “GroupB - GroupA > 0”)], and obtained the same estimate (x) and ER = 26.97.

So, it seems to me that the concepts of ‘credibility’ and ‘evidence’ are very different. Can you please tell me an opinion about how to report this between-groups difference? Is there a better way to assess this difference using Bayesian tools?

1. brms currently does not have a family for underdispered count data. You may check model fit graphically via the pp_check method. Convergence does not tell you anything about whether the distribution is reasonable for your data.

2. Can you tell me why you think the results you obtain are inconsitent with each other? Perhaps the “Details” section of `?hypothesis`

Professor Paul Buerkner,