BayesicFitting

Model Fitting and Evidence Calculation

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class LaplaceErrorDistribution( ScaledErrorDistribution )Source

To calculate a Laplace likelihood.

For one residual, x, it holds

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

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

The variance of this function is σ2 = 2 s2. See: toSigma()

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

     logL = log( N / ( 2 s ) ) - ∑( |x| / s )

Using weights this becomes

     logL = log( ∑( w ) / ( 2 s ) ) - ∑( w |x| / s )

Using this error distribution results in median-like solutions.

Author Do Kester.

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

Constructor of Laplace Distribution.

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 : LaplaceErrorDistribution
         distribution to be copied.

copy( )

Return copy of this.

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

toSigma( scale )
Return sigma, the squareroot of the variance. Parameter
  • scale : float
         the scale of this Laplace distribution.

getScale( 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

getSumRes( problem, allpars=None, scale=1 )
Return the sum of the absolute values of the residuals.

     sum ( | res | )

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
         scale of residuals (from accuracies or noisescale of errdis)

logLikelihood_alt( problem, allpars )
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 )
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.

dL/ds is not implemented for problems with accuracy

Parameters

  • problem : Problem
         to be solved
  • allpars : array_like
         list of all parameters in the problem
  • fitIndex : array_like
         indices of parameters to be fitted

nextPartialData( problem, allpars, fitIndex, mockdata=None )
Return the partial derivative of 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
         list of all parameters in the problem
  • fitIndex : array_like
         indices of parameters to be fitted
  • mockdata : array_like
         as calculated by the model
Methods inherited from ScaledErrorDistribution
Methods inherited from ErrorDistribution