[Estragon]

The model you describe in your post seems to be assuming identifiability across customers regardless of when the relationship started. If you are not making inferences about new customers based on similar customers with prior attributes, how are you doing it? The ways I can think to would force great naivete on the inferences about new customers.

[aaronjg]

We use the gamma prior and assume that shape parameter remains constant across time, and the scale parameter varies month to month. For each new month there are only two parameters that need to be estimated, one for the attrition rate and one for the purchase rate, so we rarely run into identifiability issues.