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jacopo-chevallard / BEAGLE-general

Basic information to get started with the galaxy spectral modelling tool Beagle
https://www.iap.fr/beagle/
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Goodness of fit #75

Closed steveschulze closed 6 years ago

steveschulze commented 6 years ago

Hi Jacopo,

The extension "POSTERIOR PDF" in the BEAGLE output has a column "probability" and "ln likelihood". What is the difference between them? Does BEAGLE provide a figure for the goodness of fit?

Cheers,

Steve

jacopo-chevallard commented 6 years ago

Hi Steve, the probability is the posterior probability, defined as in Bayes theorem

P(Theta|M,D) = P(D|M,Theta) * P(Theta|M) / P(D)

While the likelihood is just the term P(Theta|M).

In the case of a Gaussian likelihood (the one assumed by default in Beagle), the likelihood is proportional to the square of the residuals, i.e. to a chi-square goodness-of-fit measure.

It makes sense, however, to also include a chi-square in the Beagle output, as it is a useful quantity when interpreting the results.

steveschulze commented 6 years ago

Thanks a lot! It would be fantastic to add the chi-square to Beagle output.

jacopo-chevallard commented 6 years ago

as @eclake made me noticing, the probability is not exactly what I stated above, it is the weight (they sum up to 1) required to sample from the Multinest output to be able to produce MCMC-like samples (equation 9 of Feroz+2009)

jacopo-chevallard commented 6 years ago

available in version >= 0.19.6

steveschulze commented 6 years ago

Thanks a lot for adding this feature.