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Arak::ArakPosteriorBernoulliObs Class Reference

#include <point_obs.hpp>

Inheritance diagram for Arak::ArakPosteriorBernoulliObs:

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Detailed Description

An posterior Arak process conditioned on color measurements with Bernoulli noise.

The posterior potential is given by

\[ F(\chi) = F_{\textit{prior}}(\chi) + \sum_{i = 1}^n (\mu_{\chi(t_i)} - y_i)^2 / 2\sigma_{\chi(t_i)}^2 \]

where $t_i$ is the location of a test point, $\chi(t_i)$ is its true color, $y_i$ is the observed value, and $\mu_c$ and $\sigma_c^2$ are the conditional mean and variance of the observation given the true color is $c$.

This potential is additively decomposable so the posterior Arak process has the spatial Markov property.

Definition at line 251 of file point_obs.hpp.

Public Member Functions

 ArakPosteriorBernoulliObs (const ArakProcess &prior, const Arak::Util::PropertyMap &props)
 Stream constructor.

virtual ~ArakPosteriorBernoulliObs ()
 Destructor.

virtual double scale () const
 Returns the scale of this Arak process.

virtual double logMeasure () const
 Computes the (log) measure associated with the Arak process for the coloring.

virtual double potential () const
 Computes the potential associated with this posterior Arak process.

virtual void visualize (CGAL::Qt_widget &widget) const
 Renders a graphical representation of this Arak posterior using the supplied widget.


Protected Attributes

const ArakProcess & prior
 The prior process.

std::vector< Geometry::Point > points
 A vector of points for which observations are available.

std::vector< QueryPointPotential * > potentials
 A vector of potentials, one per observation.

std::vector< bool > obs
 A vector of the observations for each point.

double blackProb
 The conditional probability a black point will be observed as black.

double whiteProb
 The conditional probability a white point will be observed as white.

double lp
 The current potential arising from observations.

Constructor & Destructor Documentation

ArakPosteriorBernoulliObs::ArakPosteriorBernoulliObs (  const ArakProcess &  prior,
const Arak::Util::PropertyMap &  props
) 
 

Stream constructor.

The parameters of the posterior are read from a file with the following format:


     * n
     * point-1-x point-1-y point-1-obs
     * point-2-x point-2-y point-2-obs
     * ...
     * point-n-x point-n-y point-n-obs
     *

Parameters:
c The coloring whose probability is evaluated. This is fixed for each process object so that likelihood changes due to coloring updates can be processed efficiently.
props the property map defining the posterior

Definition at line 82 of file point_obs.cpp.

References Arak::Coloring::addQueryPoints(), blackProb, Arak::ln(), Arak::Geometry::Point, Arak::Util::PropertyMap, and whiteProb.

ArakPosteriorBernoulliObs::~ArakPosteriorBernoulliObs (   )  [virtual]
 

Destructor.

Definition at line 123 of file point_obs.cpp.

Member Function Documentation

double ArakPosteriorBernoulliObs::logMeasure (   )  const [virtual]
 

Computes the (log) measure associated with the Arak process for the coloring.

(This is actually multiplied by an elementary Poisson measure over the vertex locations to yield the coloring measure.)

Returns:
the measure of the coloring

Implements Arak::ArakProcess.

Definition at line 115 of file point_obs.cpp.

References Arak::ArakProcess::logMeasure().

double ArakPosteriorBernoulliObs::potential (   )  const [virtual]
 

Computes the potential associated with this posterior Arak process.

Returns:
the current potential
See also:
ArakProcess

Implements Arak::ArakProcess.

Definition at line 119 of file point_obs.cpp.

References Arak::ArakProcess::potential().

virtual double Arak::ArakPosteriorBernoulliObs::scale (   )  const [inline, virtual]
 

Returns the scale of this Arak process.

Implements Arak::ArakProcess.

Definition at line 324 of file point_obs.hpp.

References Arak::ArakProcess::scale().

void ArakPosteriorBernoulliObs::visualize (  CGAL::Qt_widget &  widget  )  const [virtual]
 

Renders a graphical representation of this Arak posterior using the supplied widget.

The Bernoulli observations are rendered as disks of varying gray level.

Parameters:
widget the widget on which to visualize the process

Reimplemented from Arak::ArakProcess.

Definition at line 128 of file point_obs.cpp.

Member Data Documentation

double Arak::ArakPosteriorBernoulliObs::blackProb [protected]
 

The conditional probability a black point will be observed as black.

Definition at line 280 of file point_obs.hpp.

Referenced by ArakPosteriorBernoulliObs().

double Arak::ArakPosteriorBernoulliObs::lp [protected]
 

The current potential arising from observations.

Definition at line 291 of file point_obs.hpp.

std::vector<bool> Arak::ArakPosteriorBernoulliObs::obs [protected]
 

A vector of the observations for each point.

The indices used in points index into this vector.

Definition at line 274 of file point_obs.hpp.

std::vector<Geometry::Point> Arak::ArakPosteriorBernoulliObs::points [protected]
 

A vector of points for which observations are available.

Definition at line 263 of file point_obs.hpp.

std::vector<QueryPointPotential*> Arak::ArakPosteriorBernoulliObs::potentials [protected]
 

A vector of potentials, one per observation.

Definition at line 268 of file point_obs.hpp.

const ArakProcess& Arak::ArakPosteriorBernoulliObs::prior [protected]
 

The prior process.

Definition at line 258 of file point_obs.hpp.

double Arak::ArakPosteriorBernoulliObs::whiteProb [protected]
 

The conditional probability a white point will be observed as white.

Definition at line 286 of file point_obs.hpp.

Referenced by ArakPosteriorBernoulliObs().

The documentation for this class was generated from the following files:
Generated on Wed May 25 14:41:27 2005 for Arak by doxygen 1.3.6