["BayesicFitting"]

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class ExponentialErrorDistribution( ScaledErrorDistribution )	[source]

Also known as generalized gaussian errordistribution.

To calculate an Exponential likelihood.

For one residual, x, it holds

f( x ) = p / ( 2 s Γ( 1 / p ) ) exp( - ( |x| / s )^p )

where Γ is the Gamma-function, s is the scale and p is the power. s and p are hyperparameters, which might be estimated from the data.

The variance of this function is

σ² = s² Γ( 3 / p ) / Γ( 1 / p )

See method

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

logL = log( N p / ( 2 s Γ( 1 / p ) ) ) - ∑( ( |x| / s )^p )

Using weights this becomes

logL = log( ∑( w ) p / ( 2 s Γ( 1 / p ) ) ) - ∑( w ( |x| / s )^p )

Note
The scale s in Exponential is NOT the same as the scale in Gaussian or in Laplace.

Attributes from ErrorDistibution
hyperpar, deltaP, ncalls, nparts, sumweight, ndata, hypar, nphypar

Author Do Kester.

ExponentialErrorDistribution( scale=1.0, power=2.0, limits=None, copy=None )	[source]

Default Constructor.

Parameters

scale : float
noise scale
power : float
power of the distribution
limits : None or [low,high] or [[low],[high]]
     None : no limits implying fixed scale
     low low limit on scale (needs to be >0)
     high high limit on scale
     [low] low limit on [scale,power] (need to be >0)
     [high] high limit on [scale,power]
     when limits are set, the scale cq. power are not fixed.
copy : ExponentialErrorDistribution
distribution to be copied.

copy( )	[source]

Return copy of this.

acceptWeight( )	[source]

True if the distribution accepts weights. Always true for this distribution.

toSigma( hypar )	[source]

Return sigma, the squareroot of the variance.

Parameter

hypar : array_like (2 floats)
the [scale,power] of this Exponential distribution.

logLikelihood_alt( problem, allpars )	[source]

Return the log( likelihood ) for a Gaussian distribution.

Parameters

problem : Problem
to be solved
allpars : array_like
parameters of the problem

logLdata( problem, allpars, mockdata=None )	[source]

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

getChipow( problem, allpars=None, scale=1 )	[source]

Return chisq.

return Sum over the (weighted) powered residuals

Parameters

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

getScale( problem, allpars=None )	[source]

Return the noise scale 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

partialLogL_alt( problem, allpars, fitIndex )	[source]

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

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 )	[source]

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

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