BayesicFitting

Model Fitting and Evidence Calculation

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class MixedErrorDistribution( ErrorDistribution )Source

To calculate a mixture of two likelihoods.

For one residual, x, it holds

     L( x ) = f * L1( x ) + ( 1 - f ) * L2( x )

where f is the contributing fraction while L, L1 and L2 are likelihoods f is a hyperparameter between [0..1]

The likelihood over N datapoints is

     L = Π L( x ) = Π( f * L1( x ) + ( 1 - f ) * L2( x ) )

And the log of L is

     logL = ∑ logL( x ) = ∑( log( f * L1(x) + ( 1 - f ) * L2(x) ) )

Note

The mixture, i.e. the weighted sum of 2 distributions for each residual, is the raison-d'etre for the methods logLdata and nextPartialData, so individual contributions can be weighted, added, log-ged and summed.

Author Do Kester.

MixedErrorDistribution( errdis1, errdis2, fraction=0.5, limits=None, copy=None )

Constructor.

Make a new error distribution as a fraction of errdis1 plus the rest of errdis2.

Parameters

  • errdis1 : ErrorDistribution
         First error distribution

  • errdis2 : ErrorDistribution
         Second error distribution (might be of the same class as errdis1)
         It must have the same xdata, data, weights as errdis1.

  • fraction : float
         contributing fraction

  • limits : None or list of 2 floats [low,high]
         None : no limits implying fixed fraction
         low low limit on fraction ( >0)
         high high limit on fraction ( <1)
         when limits are set, the scale is not fixed.

  • copy : MixedErrorDistribution
         distribution to be copied.

copy( )

Return copy of this.

acceptWeight( )
True if the distribution accepts weights. Always true for this distribution.

logLdata( problem, allpars, mockdata=None )
Return the log( likelihood ) for a Mixedian distribution.

Parameters

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

nextPartialData( problem, allpars, fitIndex, mockdata=None )
Return the partial derivative of log( likelihood ) to the parameters in fitIndex.

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 for the problem
Methods inherited from ErrorDistribution