["BayesicFitting"]

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class Gauss2dErrorDistribution( GaussErrorDistribution )	Source

To calculate a Gauss likelihood in case of errors in X and Y

For one residual in x and y it holds

L = 1 / ( 2 π √ det ) exp( - 0.5 ( x / s )² )

where s is the scale. s is a hyperparameter, which might be estimated from the data.

The scale s is also the square root of the variance of this error distribution.

The function is mostly used to calculate the likelihood L over N residuals, or easier to use log likelihood, logL.

logL = log( N / ( √( 2 π ) s ) ) - 0.5 ∑( x / s )²

Using weights this becomes

logL = log( ∑( w ) / ( √( 2 π ) s ) ) - 0.5 ∑( w ( x / s )² )

Author Do Kester.

Gauss2dErrorDistribution( scale=1.0, limits=None, copy=None )

Default Constructor.

Parameters

scale : float
noise scale
limits : None or list of 2 floats [low,high]
     None : no limits implying fixed scale
     low low limit on scale (needs to be >0)
     high high limit on scale
     when limits are set, the scale is not fixed.
copy : GaussErrorDistribution
distribution to be copied.

copy( )

Return copy of this.

TBDgetScale( problem, allpars=None )

Return the noise scale.

Parameters

problem : Problem
to be solved
allpars : array_like
None take parameters from problem.model
list of all parameters in the problem

updateDeterminant( problem, scale )

Update the determinant of the covar matrix with scale

Parameters

problem : ErrorsInXandYProblem
problem at hand
scale : float
present vale for the cale

logLikelihood_alt( problem, allpars )

Return the log( likelihood ) for a Gaussian distribution.

Alternate calculation

Parameters

problem : Problem
to be solved
allpars : array_like
list of all parameters in the problem

logLdata( problem, allpars, mockdata=None )

Return the log( likelihood ) for each residual

logL = sum( logLdata )

Parameters

problem : Problem
to be solved
allpars : array_like
list of all parameters in the problem
mockdata : array_like
as calculated by the model

partialLogL_alt( problem, allpars, fitIndex )

Return the partial derivative of log( likelihood ) to the parameters in fitIndex.

Alternate calculation

Parameters

problem : Problem
to be solved.
allpars : array_like
(hyper)parameters of the problem
fitIndex : array_like
indices of parameters to be fitted

nextPartialData( problem, allpars, fitIndex, mockdata=None )

Return the partial derivative all elements of the log( likelihood ) to the parameters in fitIndex.

Parameters

problem : Problem
to be solved
allpars : array_like
(hyper)parameters of the problem
fitIndex : array_like of int
indices of allpars to fit
mockdata : array_like
as calculated for the problem

Methods inherited from GaussErrorDistribution

Methods inherited from ScaledErrorDistribution

setLimits( limits )

Methods inherited from ErrorDistribution