# WDmodel.covariance module¶

Parametrizes the noise of the spectrum fit using a Gaussian process.

class WDmodel.covariance.WDmodel_CovModel(errscale, covtype='Matern32', coveps=1e-12)[source]

Bases: object

Parametrizes the noise of the spectrum fit using a Gaussian process.

This class models the covariance of the spectrum fit using a stationary Gaussian process conditioned on the spectrum flux residuals and spectrum flux uncertainties. The class allows the kernel of the Gaussian process to be set in a single location. A few different stationary kernels are supported. These choices are defined in celerite.terms.

Parameters
• errscale (float) – Chracteristic scale of the spectrum flux uncertainties. The kernel amplitude hyperparameters are reported as fractions of this number. If the spectrum flux is rescaled, this must be set appropriately to get the correct uncertainties. The WDmodel package uses the median of the spectrum flux uncertainty internally.

• covtype ({'Matern32', 'SHO', 'Exp', 'White}) – The model to use to parametrize the covariance. Choices are defined in celerite.terms All choices except 'White' parametrize the covariance using a stationary kernel with a characteristic amplitude fsig and scale tau + a white noise component with amplitude fw. Only the white noise component is used to condition the Gaussian process if covtype is 'White'. If not specified or unknown, 'Matern32' is used and a RuntimeWarning is raised.

• coveps (float) – If covtype is 'Matern32' a celerite.terms.Matern32Term is used to approximate a Matern32 kernel with precision coveps. The default is 1e-12. Ignored if any other covtype is specified.

_errscale

The input errscale

Type

float

_covtype

The input covtype

Type

str

_coveps

The input coveps

Type

float

_ndim

The dimensionality of kernel used to parametrize the covariance

Type

int

_k1

The non-trivial stationary component of the kernel

Type

None or a term instance from celerite.terms

_k2

The white noise component of the kernel

Type

celerite.terms.JitterTerm

_logQ

1/sqrt(2) - only set if covtype is 'SHO'

Type

float, conditional

Returns

Return type

Notes

Virtually none of the attributes should be used directly since it is trivially possible to break the model by redefining them. Access to them is best through the functions connected to the models.

__init__(errscale, covtype='Matern32', coveps=1e-12)[source]

Initialize self. See help(type(self)) for accurate signature.

getgp(wave, flux_err, fsig, tau, fw)[source]

Return the celerite.GP instance

Precomputes the covariance matrix of the Gaussian process specified by the functional form of the stationary kernel and the current values of the hyperparameters. Wraps celerite.GP.

Parameters
Returns

gp – The Gaussian process with covariance matrix precomputed at the location of the data

Return type

celerite.GP instance

Notes

fsig, tau and fw all must be > 0. This constraint is not checked here, but is instead imposed by the samplers/optimizers used in the WDmodel.fit methods, and by bounds used to construct the WDmodel.likelihood.WDmodel_Likelihood instance using the WDmodel.likelihood.setup_likelihood() method.

lnlikelihood(wave, res, flux_err, fsig, tau, fw)[source]

Return the log likelihood of the Gaussian process

Conditions the Gaussian process specified by the functional form of the stationary kernel and the current values of the hyperparameters on the data, and computes the log likelihood. Wraps celerite.GP.log_likelihood().

Parameters
• wave (array-like, optional) – Wavelengths at which to condition the Gaussian process

• res (array-like) – Flux residual array on which to condition the Gaussian process. The kernel parametrization assumes that the mean model has been subtracted off.

• flux_err (array-like) – Flux uncertaintyarray on which to condition the Gaussian process

• fsig (float) – The fractional amplitude of the non-trivial stationary kernel. The true amplitude is scaled by WDmodel.covariance.WDmodel_CovModel._errscale

• tau (float) – The characteristic length scale of the non-trivial stationary kernel.

• fw (float) – The fractional amplitude of the white noise component of the kernel. The true amplitude is scaled by WDmodel.covariance.WDmodel_CovModel._errscale

Returns

lnlike – The log likelihood of the Gaussian process conditioned on the data.

Return type

float

predict(wave, res, flux_err, fsig, tau, fw, mean_only=False)[source]

Return the prediction for the Gaussian process

Conditions the Gaussian process specified by the parametrized with the functional form of the stationary kernel and the current values of the hyperparameters on the data, and computes returns the prediction at the same location as the data. Wraps celerite.GP.predict().

Parameters
• wave (array-like, optional) – Wavelengths at which to condition the Gaussian process

• res (array-like) – Flux residual array on which to condition the Gaussian process. The kernel parametrization assumes that the mean model has been subtracted off.

• flux_err (array-like) – Flux uncertaintyarray on which to condition the Gaussian process

• fsig (float) – The fractional amplitude of the non-trivial stationary kernel. The true amplitude is scaled by WDmodel.covariance.WDmodel_CovModel._errscale

• tau (float) – The characteristic length scale of the non-trivial stationary kernel.

• fw (float) – The fractional amplitude of the white noise component of the kernel. The true amplitude is scaled by WDmodel.covariance.WDmodel_CovModel._errscale

• mean_only (bool, optional) – Return only the predicted mean, not the covariance matrix

Returns

• wres (array-like) – The prediction of the Gaussian process conditioned on the data at the same location i.e. the model.

• cov (array-like, optional) – The computed covariance matrix of the Gaussian process using the parametrized stationary kernel evaluated at the locations of the data.