Online Batch-Means ESS estimator

[miguelbiron]

Idea

• Use the round-based approach: at the start of each round, we know the number of scans that will occur. Therefore, we can select an adequate batch size beforehand.
• We can then use this online estimator
• To keep the estimator synced with the round-based scheme, at each empty! call we can double an internal value for the number of scans.

Difficulties

• Since the Shared object is not seen by recorder constructors, there is no way of knowing if we are starting from round 1 or round > 1. So we can only keep the estimator in sync if it started in sync.

[miguelbiron]

yay, bots in Github issues. The enshittification of the internet marches on.

[miguelbiron]

RE the issue with not knowing the initial number of scans: we can learn after the first mistake. So perhaps the first round the estimate is NaN, but the following round should work.