Is it possible to model an observed random variable as a range or interval? In my case, the likelihood function has a deterministic part (which happens to be a black-box simulation), and I’d like the inference to consider a range of values as possible observations. For example, the simulation output is 0.15 and the observation is in the range [0.12, 0.18], so that’s a good output from the simulation. But if the simulation output is 0.15 and the observed range is [0.16, 0.2] or [0.08, 0.12], then the simulation output is not good.
You might consider using pm.Potential() to directly, if perhaps inelegantly, crafting a likelihood that reproduces whatever you think “good” and “not good” matches are. You might check out this notebook to see if it helps.
That’s certainly helpful! But I’m getting the following warning when calling sample_prior_predictive:
C:\Users\username\Miniconda3\envs\myenv\lib\site-packages\pymc3\sampling.py:1944: UserWarning: The effect of Potentials on other parameters is ignored during prior predictive sampling. This is likely to lead to invalid or biased predictive samples.
warnings.warn(
Should I be worried?
As the warning states, the potential is going to be ignored when sampling from your prior. Whether you should be worried depends on what you are expecting/wanting out of your prior samples.
Got it. I should be fine then. I’m sampling from the priors just to plot a histogram and compare that to the posterior samples.
Always a smart move!