use biased autocorrelation estimate by default (resolves #1785) #1877
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numpyro/diagnostics.py
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| @@ -96,12 +96,13 @@ def _fft_next_fast_len(target): | |||
| target += 1 | |||
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| def autocorrelation(x, axis=0): | |||
| def autocorrelation(x, axis=0, unbiased=False): | |||
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maybe change unbiased to bias and set bias=True by default.
numpyro/diagnostics.py
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| """ | ||
| Computes the autocorrelation of samples at dimension ``axis``. | ||
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| :param numpy.ndarray x: the input array. | ||
| :param int axis: the dimension to calculate autocorrelation. | ||
| :param unbiased: use an unbiased estimator of the autocorrelation. |
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whether to use a biased estimator
It will change it for sure, my experience with the current ESS was that it was too erratic to even be useful, which is why I started looking into this in the first place. If it is a concern we could always make |
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Actually, the biased/unbiasedness refers to the autocovariance, not the autocorrelation. Maybe the parameter names need a rethink. |
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I think we should go with the biased version by default if the unbiased one is not practical. |
This changes the autocorrelation function to use the same (biased) estimate as Stan by default. The unbiased estimate is known to have "wild" tails, with variance that is O(1) at longer lags regardless of the length of the chain. See Priestley (1981, Section 5.3) for a discussion of the properties of these estimators. Note that the old (unbiased) estimator is only strictly unbiased when the mean is known, but I have followed Priestley (1981) in referring to it as unbiased.
I have added two checks to
test_autocorrelationthat highlight the difference in the tail behaviour.