BFMI is inconsistent with the paper
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Description
Summary:
The BFMI implementation is inconsistent with the original paper.
Description:
The numerator in get_bfmi is divided by the length of x
https://github.com/stan-dev/rstan/blob/f79dae16e3bc187601520a165916b4d39d83af8d/rstan/rstan/R/check_hmc_diagnostics.R#L231
This is consistent with the paper's equation (bottom of page 7) if var gives the maximum likelihood estimate, but it gives the unbiased estimator instead. The resulting BFMI is off by a factor of (length(x) - 1) / length(x)
PyStan's implementation agrees with the paper (numpy.var defaults to the maximum likelihood estimate).
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Research direction
Start in rstan/R/check_hmc_diagnostics.R at get_bfmi, then compare its variance calculation with the equation on page 7 of the linked paper and the referenced PyStan implementation. Done means BFMI uses the estimator specified by the paper and no longer differs by the reported length-dependent factor.
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Assessment
- Tech stack
- r
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- data
- Issue type
- Bug
- Difficulty
- 2/5
- Estimated time
- 1-3 hours
- Activity status
- Stale
- Clarity
- Clearly specified
- Newbie friendliness
- 35/100