Changing beta channel prior distributions from weakly to informative

[BahgatN]

I'm relatively new to pymc_marketing, and I've observed a significant decrease in sampling algorithm speed when I switched the beta media channel priors from Halfnormal to a beta distribution. Can someone please shed light on why this might be happening?

[williambdean]

Hello @BahgatN

What are your parameters estimates when the prior is HalfNormal? Is much of there density >1?
Restricting the domain to (0, 1) might impact the MCMC
How are the sampling diagnostics before and after?

[BahgatN]

Hi @wd60622

The estimates show notable differences between the models using beta distribution compared to HalfNormal. This discrepancy arises because I re-parameterized the distribution to incorporate highly informative priors, which align with my beliefs.

In both models there are convergence and the trace plots for all parameters are good, but with beta priors, I had to adjust the tune size and acceptance rate to prevent algorithm divergence

[williambdean]

What do you mean by notably different? Can you through out ball park values? Is the distribution mainly above 1?

How does the sampling perform if you set the prior to distribution with (0, \inf) domain but with most of the prior mass between 0 and 1.
(This could be gamma prior and found initially pm.find_constrained_prior)

[BahgatN]

@wd60622
The shift to Beta priors from HalfNormal resulted in notably different means for the contribution of each media channel. The Beta distribution, bounded between 0 and 1, facilitates informative priors and is well-suited for pymc_marketing package, especially due to its utilization of the MaxAbs Scalar.
See How can i use prior to specific the beta parameter of a channel variable?
I did not get your piont about the zero infinity domain

[williambdean]

Based on the information you've provided, I suspect that the sampling is slower due to parameters being more likely outside of the domain of the Beta distribution