["BayesicFitting"]

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class CauchyErrorDistribution( ScaledErrorDistribution )	Source

To calculate a Cauchy or Lorentz likelihood.

f( x ) = s / ( π * ( s² + x² ) )

where x = residual and s = scale

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

logL = N ( log( s ) - log( π ) ) - ∑( log( x² + s² ) )

Weights are not possible in this error distribution. They are silently ignored.

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

Author Do Kester.

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

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 : CauchyErrorDistribution
distribution to be copied.

copy( )

Return copy of this.

acceptWeight( )

True if the distribution accepts weights. False for this distribution.

getScale( problem, allpars=None )

Return the noise scale as calculated from the residuals.

Parameters

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

funct( scale )

Internal use, only.

logLikelihood_alt( problem, allpars )

Return the log( likelihood ) for a Cauchy distribution.

Cauchy distr : f( x ) = s / ( π * ( s² + x² ) )

where x = residual and s = scale

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

dL/ds is not implemented for problems with accuracy

Parameters

problem : Problem
to be solved
allpars : array_like
parameters of the problem
fitIndex : array_like
indices of parameters to be fitted

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

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

dL/ds is not implemented for problems with accuracy

Parameters

problem : Problem
to be solved
allpars : array_like
parameters of the problem
fitIndex : array_like
indices of parameters to be fitted
mockdata : array_like
as calculated by the model

Methods inherited from ScaledErrorDistribution

setLimits( limits )

Methods inherited from ErrorDistribution