I've been playing around with Bayesian / Probabilistic Programming with PyMC and others. I can't find a ton of great practical examples on the web so I created my own problem and tried to solve it. Can someone sanity check it for me to make sure I'm "doing it right"? (It's short): https://storage.googleapis.com/static-web-1/Risk%20Analysis.html
Here's what it's trying to do:
- I want to model the Probability of a pretend business breaking even every single day.
- The business has 10 customers that can have variable distributions of usage.
- I model the customers' usage as 10 different gamma distributions (first question: are gammas appropriate for this?)
- I assume uniform priors on the alpha & beta for the gammas and then use the observed data (usage_i) to infer what they should be.
- Once, I inferred what the alpha & beta should be for every customer, I randomly sample from that gamma (inf_usage_i).
- Then I combine the sum of the sampled usages with a fixed cost, a variable cost (assumed normal r.v. but presumably this can be inferred from historical data too) and constant price. I sample this to draw a distribution of profits.
Does this make sense? One thing that bothers me is that it seems weird to first infer the alpha & betas and then immediately sample again from the corresponding gammas that they define by creating a new variable. I guess this is a necessary evil when I want to infer the distribution and use it somewhere?