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Projection rank evidence

In the TFrankProjections script the projection/models are ranked by

  1. Projection/model "anti"-evidence is currently calculated as a ratio of estimated cost integral and volume; "anti" because we integrate cost function (negative log-likelihood), not a likelihood function, and only over viable region of parameter space (cf. #31 (closed)). Is that correct?
    Note that in case of known likelihood function, one can always compute negative likelihood integral (to comply to < threshold cut-off criteria), w/o log, and for high enough threshold (large enough viable region) this is a good approximation of the minus evidence.

  2. Error estimation (currently min/max of val+/-err ratios), as @clormeau pointed out, could be done by Taylor's first order approximation of the variance of a ratio of positive-support random variables (cost integral and volume estimators here; cf. derivation PDF by Howard Seltman), i.e.

evidence_error = (OutV.ci/OutV.vol)*sqrt((OutV.cierr/OutV.ci)^2 + (OutV.err/OutV.vol)^2 - 2*estCovCiVol/(OutV.ci*OutV.vol))

This is likely less conservative. What's the covariance here (estCovCiVol; 0 for independent)?