Best prior for financial expenditures over time?

Questions
1

Hi all,

I’m getting started using PyMC and am going through the bayesian methods for hackers book. For the chapter 1 example I’m trying to recreate the example where Cam Davidson Pilon estimates whether or not there’s been a change in the amount of texts he receives with some different data.

I took my credit card bills from the last 4 years, and want to figure out when / if there were breakpoints where my average credit card bill went up. In the book he used a poisson distribution and an exponential distribution to estimate the parameters.

This is probably not a good choice for me since financial expenditure is continuous and likely to be somewhat right tailed.

I’m wondering if someone has an analogous setup for this problem. Right now I’m thinking of either using a half-cauchy or gamma distribution, and am wondering if anyone has an opinion on either of these for this problem and the best way to parameterize them.

Thank you!

2

Poisson would actually work as well as its log probability function can evaluate on continues data.
I think you would want to model it with something that could be parameterized as location + scale, which you can model the change in average spending or standard deviation of the spending. With that in mind, you can try specifying the likelihood with Gamma, log-Normal, Truncated Normal (not half Cauchy or half Normal as the location parameter is set at 0).

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