MCMC

GalPaK3D allows the user to select several samplers for the MCMC as described in the run_mcmc method which has the following options:

mcmc_method: ‘galpak’ [default] | ‘emcee_walkers’| ‘emcee_MH’ | ‘dynesty’ | ‘multinest’
The MCMC method.

  • galpak: for the original MCMC algorithm using Cauchy proposal distribution

  • emcee_MH: emcee v2.x classic MH; no longer supported

  • emcee_walkers: emcee v3.x multi-Walkers algorithms with Moves

  • dynesty: unsupported

  • multinest: still experimental

  • pymc3: to be implemented

mcmc_sampling:

  • galpak: ‘Cauchy’ [default] | ‘Normal’ | ‘AdaptiveCauchy’

  • emcee_walkers: ‘walkers’ [default] | ‘walkersCauchy’ | ‘DE’ | ‘Snooker’ | ‘Cauchy’ | ‘Normal’

  • multinest: None

  • pymc3: to be implemented

The proposal sampling methods

_images/GalPaK_MCMC.png

GalPaK3D uses an internal MCMC class which extend the galpak class. This can be used to call its likelihood such as:

li = gk(params)

using a self.__call__() method which returns the lnprob

Here is a full example:

import galpak
gk=galpak.GalPaK3D('data/input/GalPaK_cube_1101_from_paper.fits',model=galpak.DefaultModel())
p=gk.model.Parameters()
params=p.from_ndarray([15,15,15,1e-16,5,60,90,1,100,10])
li=gk(params)

You can always check that the log-likelihood is finite :

print(li)
-16117.55742040931

If it is not finite, this is probably caused by the priors when the parameter values are outside the min and max boundaries.

class galpak.MCMC[source]

An extension of the galpak class with the galpak MH algorithm (myMCMC class) and method used for emcee and external algorithm

the following methods are for external samplers such as emcee:

  • lnprob: returned by __call__ / the full log-probability function: Ln = Priors x L(p)

  • loglike: the log L(p)

  • logpriors: the log priors with uniform priors.

the following methods are for multinest:

  • pyloglike: the log L(p)

  • pycube: transforms unit cube to uniform priors.

the following methods are for dynesty:

  • loglike: the log L(p)

  • ptforms: transforms unit cube to uniform priors.

the following methods are for the internal galpak MH algorithm

  • myMCMC