what does it mean by "autocorrelation"?

[Juan Wu]

Hi, all,

In the demo, there is a command to show the posterior plots: m.plot_posteriors(['a', 't', 'v', 'a_std'])

Following the plots, it is noted that "there are no drifts or large jumps in the trace. The autocorrelation is also very low". Could any one explain what is the "autocorrelation" and what larger is "large"? Also how jump is a "large" jump for the drifts?

I was thinking that the "autocorrelation" means the correlation between last (e.g, trial, N-1) and current trials (trial N). If so, why the higher correlation between them is problematic? Does it mean a problem of convergence?

Thanks so much,

J

[Michael J Frank]

Hi Juan,

Autocorrelation implies that locally (within a restricted set of samples), the posteriors are not sampled from the full posterior distribution - ie the samples from one trial to the next (or with various lags) are not independent but come from similar parts of the distribution.  With limited samples this is bad because we may not get good estimates of posteriors. It used to be advised to do thinning (ie to take only one of every X sample) which can reduce autocorrelation. But actually this is mostly just wasting a bunch of samples: even though local samples are autocorrelated that just means that each sample is not as informative as it could be if they were independent, but it is still more informative than not using it at all. Autocorrelation does mean that you should make sure to have enough samples so that eventually the full posterior is constructed. So it can be used as a clue that you might want to check what happens if you sampled a lot more to see if the distributions change much. In any case you should always look at convergence using R-hat etc.

Michael

 

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[Juan]

Hi, Michael,

Thanks a lot. It is very nice of you to give me such a patient illustration. It makes sense to me.

Best,

J