ROI Error

Hi, I am trying to calculate the errors for my ROI figure from targeted marketing campaigns. At the end of a campaign I have the amounts spent by the targeted customers as well as the control group. I have also been developing a Bayesian hierarchical model into which I can feed in all the spend amounts, and do the whole parameter estimation process (using a Bernoulli->Exponential model for customer purchase->amount). We already have an ROI figure that we report.

My question is simply - how do I calculate the errors/bounds on this ROI figure?

This is my first attempt at Bayesian hierarchical modelling and I believe my model is working, but I am not sure how to quote an error.
P.S. the error is particularly important in my case as the control groups can be quite small sometimes (~100 people).

Thanks for your help!


TS Contributor
Define ROI as a function of stochastic variables described by the posterior, then you should be able to calculate error bounds by for example simulating the ROI distribution using MCMC procedures.