BayesicFitting

Model Fitting and Evidence Calculation

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class LaplacePrior( Prior )Source

Laplace prior distribution.

     Pr( x ) = 1 / ( 2 s ) exp( - |x - c| / s )

By default: c = center = 0.0 and s = scale = 1.

It can also have a limited domain. By default the domain is [-Inf,+Inf]. In computational practice the domain is limited to about [-36,36] scale units

Equivalent to a double-sided exponential prior

domain2unit:
  u = 0.5 * exp( ( d - c ) / scale ) if d < c
      1.0 - 0.5 * exp( ( c - d ) / scale ) otherwise unit2domain:
  d = c + log( 2 * u ) * scale if u < 0.5
      c - log( 2 * ( 1 - u ) ) * scale otherwise

Examples

pr = LaplacePrior()                         # center=0, scale=1
pr = LaplacePrior( center=1.0, scale=0.5 )
pr = LaplacePrior( limits=[0,None] )        # limites to values >= 0
pr = LaplacePrior( center=1, circular=3 )   # circular between 0.5 and 2.5

Attributes

  • center : float
         center of the Laplace prior
  • scale : float
         scale of the Laplace prior

Attributes from Prior

lowLimit, highLimit, deltaP, _lowDomain, _highDomain

lowLimit and highLimit cannot be used in this implementation.

LaplacePrior( center=0.0, scale=1.0, limits=None, circular=False, prior=None )

Constructor.

Parameters

  • center : float
         of the prior
  • scale : float
         of the prior
  • limits : None or list of 2 float/None
         None : no limits.
         2 limits, resp low and high
  • circular : bool or float
         bool : y|n circular with period from limits[0] to limits[1]
         float :period of circularity
  • prior : LaplacePrior
         prior to copy (with new scale if applicable)

copy( )

domain2Unit( dval )
Return a value in [0,1] given a value within the valid domain of a parameter for a Laplace distribution.

  u = 0.5 * exp( ( d - c ) / s ) if d < c else
      1.0 - 0.5 * exp( ( c - d ) / s )

Parameters

  • dval : float
         value within the domain of a parameter

unit2Domain( uval )
Return a value within the valid domain of the parameter given a value between [0,1] for a Laplace distribution.

  d = c + log( 2 * u ) * scale if u < 0.5 else
      c - log( 2 * ( 1 - u ) ) * scale

Parameters

  • uval : float
         value within [0,1]

result( x )
Return a the result of the distribution function at x.

Parameters

  • x : float
         value within the domain of a parameter

logResult( x )
Return a the log of the result of the distribution function to p.

Parameters

  • x : float
         value within the domain of a parameter

partialLog( x )
Return partial derivative of log( Prior ) wrt parameter.

Parameters

  • x : float
         the value

isBound( )

Return true if the integral over the prior is bound.

shortName( )
Methods inherited from Prior