BayesicFitting

Model Fitting and Evidence Calculation

View project on GitHub
Navigation

Global Documentation
Home Manual
Readme Glossary
Notes Design
Examples Classes
Trouble
Style



class UniformErrorDistribution( ScaledErrorDistribution )Source

To calculate a Uniform likelihood, eg. for digitization noise.

For one residual, x, it holds

     L( x ) = 1 / ( 2 * s ) if |x| < s
              0 otherwise

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

The variance of this function is σ2 = s / 6. See: toSigma()

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

     logL = -log( 2 * s ) * N

Note that it is required that all residuals are smaller than s, otherwise the logL becomes -inf.

Using weights this becomes

     logL = -log( 2 * s ) * ∑ w

Author Do Kester.

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

Constructor of Uniform 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 : UniformErrorDistribution
         distribution to be copied.

copy( )

Return copy of this.

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

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

logLikelihood_alt( problem, allpars )
Return the log( likelihood ) for a Uniform distribution.

Alternate calculation.

Outside the range the likelihood is zero, so the logL should be -inf. However for computational reasons the maximum negative value is returned.

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
         parameters of 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
         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
Methods inherited from ErrorDistribution