PPC

Name

PPC

Purpose

Computes a Posterior Predictive Check (PPC) on a MCMC Lightning output. Uses the methods described in Rubin (1984) and Gelman et al. (1996).

Calling Sequence

pvalue = ppc(Nrep, Lobs, Lunc, Lpredict, lnprob_chain [, $
             counts_obs = , counts_unc = , counts_predict = , $
             chisqr_obs=chisqr_obs, chisqr_rep=chisqr_rep])

Inputs

Nrepint, float or double scalar

The number of times to replicate the predicted data.

Lobsint, float or double array(Nfilters)

The observed luminosities [arbitrary units].

Luncint, float or double array(Nfilters)

The uncertainties on the observed luminosities in the same units as Lobs.

Lpredictint, float, or double array(Nfilters, Nchain)

The model luminosities predicted by the model given a set of parameters in same units as Lobs.

lnprob_chainint, float, or double array(Nchain)

The log posterior probability values of each SED predicted by the model given a set of parameters. Used to select the replicated data.

Optional Inputs

counts_obsint, float, or double array(Nxray)

The observed X-ray counts. If specified, counts_unc and counts_predict must also be given.

counts_uncint, float, or double array(Nxray)

The uncertainties on the observed X-ray counts. If specified, counts_obs and counts_predict must also be given.

counts_predict: int, float, or double array(Nxray, Nchain)

The X-ray counts predicted by the model. If specified, counts_obs and counts_unc must also be given.

model_uncint, float, or double scalar

The fractional model uncertainty to use in all bands. (Default = 0.d0)

Output

pvaluedouble scalar

The p-value associated with the PPC. Determined as the fraction of chisqr_rep that is greater than chisqr_obs.

Optional Outputs

chisqr_obsdouble array(Nrep)

The resulting \(\chi^2\) values by comparing the predicted data with the observational data.

chisqr_repdouble array(Nrep)

The resulting \(\chi^2\) values by comparing the predicted data with the replicated data.

Notes

• If the X-ray model was fit using fluxes rather than counts, the X-ray luminosities can simply be appended to Lobs, Lunc, and Lpredict.

References

• Rubin D. B., 1984, Ann. Stat., 12, 1151

• Gelman A., Meng X.-L., Stern H., 1996, Stat. Sin., 6, 733

Modification History

• 2022/03/15: Created (Keith Doore)

• 2022/04/18: Added documentation (Keith Doore)

• 2022/04/18: Added error handling (Keith Doore)

• 2022/07/21: Added ability to handle NaNs in lnprob_chain (Keith Doore)

• 2022/07/27: Fixed bug with missing keyword nrand in mrandomn (Keith Doore)

• 2022/07/27: Fixed bug where value_locate maybe selecting -1 when we want 0, force -1 to be 0 (Keith Doore)

• 2022/09/01: Added X-ray emission (Erik B. Monson)

• 2022/09/15: Changed from chi2_chain input to lnprob_chain (Keith Doore)

• 2022/09/30: Added model_unc input to include in uncertainties (Keith Doore)