Interpreting posterior with Half-Hormal shape

[Johannes]

Hi all,

I am building a Marketing Mix Model in PyMC and am not sure how to interpret the posteriors, especially those with half-normal priors (sigma=1). I’ve chosen this prior because media could not have a negative effect on the revenue. After sampling, the posteriors for some beta’s look like this:

Is there a non-zero effect here at all? and how can I test this? Furthermore, I am curious how to determine the effect size. I feel that the mean and median are positively biased here, as the the posterior cannot take on negative values.

All variables are 0-1 transformed.

Kind regards.

[OriolAbril]

If you have a somewhat clear idea about what you consider to be 0 effect, you can compute the probability that the posterior variable is above that threshold (e.g. 1e-3) and take that as the probability of the effect not being zero.

In general I’d recommend plotting the ecdf so it is easier to see how much mass is above 1e-3, and above 1e-2, and above 0.2… you can use az.plot_ecdf for this. The only trick is that for now (and for 1-2 more weeks until the next arviz release) you need to install the arviz development version