Sampling Deterministic Random Variables

Questions
1

I have a very simple model:

I have a Uniform prior, p; a Binomial Likelihood that uses the prior as parameter p. I make an observation (e.g. a success) to obtain my posterior belief of p.

This is easily achieved in PyMC3. However, I wish to define a new Random Variable, say, q, that is the reciprocal of p.

I (naively) thought I could just define a new variable q = p**-1, but this does not allow me to see the trace or sample from q when I call

trace = pm.sample(500)

Is there a way for me to take samples from a RV that is not explicitly used in the model but is deterministically related to a RV that IS in the model?

import pymc3 as pm
from scipy import optimize

basic_model = pm.Model()
with basic_model:
     p = pm.Uniform('p', lower=0, upper=1)
     q = p**-1       # THIS IS WHAT I WISH TO BE ABLE TO SEE IN THE TRACE
     out = pm.Binomial('out', n=1, p=p, observed=1)
     trace = pm.sample(500)
     _ = pm.traceplot(trace)
1 Like
2

pm.Deterministic exists for just that!

with pm.Model() as basic_model:
     p = pm.Uniform('p', lower=0, upper=1)
     q = pm.Deterministic('q', 1 / p)
     out = pm.Binomial('out', n=1, p=p, observed=1)
     trace = pm.sample(500)
pm.traceplot(trace)

image
image.jpg856×280 70.6 KB

3 Likes
3

Wow, that’s an awful lot simpler than I was expecting! Classic newbie overcomplicating things :slight_smile:

Thanks!