Marginalization example - uncertainty
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- Python
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Description
In this example
https://tinygp.readthedocs.io/en/stable/tutorials/modeling.html#modeling-numpyro
We marginalize hyperparameters with HMC. In the analysis, we plot quantiles of the posterior mean of y found for each state of hyperparameters in the chain.
I'm a bit confused about what the quantiles of the posterior mean are supposed to represent? In my understanding, they show the uncertainty on the mean of y, rather than the uncertainty on y, since they don't account for the (co)variance.
For example, I could know the mean of y exactly. I still wouldn't know y, though, because of the GP has a covariance as well as a mean.
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Research direction
Read the Modeling with NumPyro section at the linked documentation anchor and inspect how the HMC hyperparameter chain is used to plot quantiles of the posterior mean of y. Determine whether the example needs clarification or a different uncertainty visualization, and document the intended interpretation so the treatment of covariance is unambiguous.
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Assessment
- Tech stack
- python
- Domain
- documentation, machine-learning
- Issue type
- Documentation
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100