Expected Sample Size

[Michele]

Hello,

I wonder if in webPPL there is a method to directly obtain the Expected Sample Size (ESS) of the particles' weights {w_i} at the end of a SMC simulation.  

ESS=(\sum_i w_i)^2 / (\sum_i w_i^2).

Thanks,

Michele

[null-a]

I don't recall a built-in way of getting at this, but I could be wrong.

SMC does resampling, which I think means that in the end each particle has the same weight:

https://github.com/probmods/webppl/blob/daabd60361f72eef53f69005751facce34c7f916/src/inference/smc.js#L193-L195

This (or rather the log of it) is available as the `normalizationConstant` property on the returned distribution:

https://github.com/probmods/webppl/blob/daabd60361f72eef53f69005751facce34c7f916/src/inference/smc.js#L343

So, perhaps you can use this to compute ESS like so?

```

N = 100;

var dist = Infer({particles: N, ...});

var w_i = Math.exp(dist.normalizationConstant);

var ess = ((N*w)^2) /  (N*(w^2))

```

This is completely untested and I'm not at all confident that it's correct, but perhaps it will help!

Best,

Paul