Exclusion of 0 in 95% Credible Interval In Bayesian regression, does the exclusion of null value (0 or 1, depending on difference or ratio) in the 95% HDI implies significance (like in frequentist), and what's the relation with ROPE? Is it possible for a null to be excluded but the ROPE to be large? Or for a null to be included but the ROPE to be small?
Ref for ROPE:
https://dominiquemakowski.github.io/publication/makowski2019indices/
 A: In bayesian regression, the marginal posterior distributions are probability distributions of possible regression coefficients. So a marginal posterior distribution for a given IV that does not include 0 in the 95% HDI just shows that 95% of the most likely parameter values based on the data do not include zero. The 'significance' or the importance of that effect depends on the context.
The ROPE is the range of values that would be considered to be practically equivalent to no effect. Classic example is an intervention that aims to increase IQ (mean = 100, SD = 15). You might decide that an intervention that changes IQ by 10 points is not important and is therefore practically equivalent to no effect - e.g. if you have posterior mean = 105 and 95% HDI = 103-107 with ROPE = 90-110, then there appears to be an effect (the 'null' is not in HDI), but it is not practically important.
So because the ROPE can be set, it is theoretically possible to have a posterior distribution that doesn't include 0 in 95% HDI but falls within the ROPE (the above example), or for there to be a small ROPE and for 0 to be included in 95% HDI.
