lsst::meas::modelfit::Prior Class Reference

Base class for Bayesian priors. More...

#include <Prior.h>

Inheritance diagram for lsst::meas::modelfit::Prior:

Public Member Functions
std::string const &	getTag () const
virtual Scalar	evaluate (ndarray::Array< Scalar const, 1, 1 > const &nonlinear, ndarray::Array< Scalar const, 1, 1 > const &amplitudes) const =0
	Evaluate the prior at the given point in nonlinear and amplitude space.
virtual void	evaluateDerivatives (ndarray::Array< Scalar const, 1, 1 > const &nonlinear, ndarray::Array< Scalar const, 1, 1 > const &amplitudes, ndarray::Array< Scalar, 1, 1 > const &nonlinearGradient, ndarray::Array< Scalar, 1, 1 > const &amplitudeGradient, ndarray::Array< Scalar, 2, 1 > const &nonlinearHessian, ndarray::Array< Scalar, 2, 1 > const &amplitudeHessian, ndarray::Array< Scalar, 2, 1 > const &crossHessian) const =0
	Evaluate the derivatives of the prior at the given point in nonlinear and amplitude space.
virtual Scalar	marginalize (Vector const &gradient, Matrix const &hessian, ndarray::Array< Scalar const, 1, 1 > const &nonlinear) const =0
	Return the -log amplitude integral of the prior*likelihood product.
virtual Scalar	maximize (Vector const &gradient, Matrix const &hessian, ndarray::Array< Scalar const, 1, 1 > const &nonlinear, ndarray::Array< Scalar, 1, 1 > const &amplitudes) const =0
	Compute the amplitude vector that maximizes the prior x likelihood product.
virtual void	drawAmplitudes (Vector const &gradient, Matrix const &hessian, ndarray::Array< Scalar const, 1, 1 > const &nonlinear, afw::math::Random &rng, ndarray::Array< Scalar, 2, 1 > const &amplitudes, ndarray::Array< Scalar, 1, 1 > const &weights, bool multiplyWeights=false) const =0
	Draw a set of Monte Carlo amplitude vectors.
virtual	~Prior ()
	Prior (const Prior &)=delete
Prior &	operator= (const Prior &)=delete
	Prior (Prior &&)=delete
Prior &	operator= (Prior &&)=delete

Protected Member Functions
	Prior (std::string const &tag="")

Detailed Description

Base class for Bayesian priors.

Definition at line 36 of file Prior.h.

Constructor & Destructor Documentation

~Prior()

virtual lsst::meas::modelfit::Prior::~Prior ( )

inlinevirtual

Definition at line 161 of file Prior.h.

{}

Prior() [1/3]

lsst::meas::modelfit::Prior::Prior ( const Prior & )

delete

Prior() [2/3]

lsst::meas::modelfit::Prior::Prior ( Prior && )

delete

Prior() [3/3]

lsst::meas::modelfit::Prior::Prior ( std::string const & tag = "" )

inlineexplicitprotected

Definition at line 173 of file Prior.h.

: _tag(tag) {}

Member Function Documentation

drawAmplitudes()

virtual void lsst::meas::modelfit::Prior::drawAmplitudes ( Vector const & gradient, Matrix const & hessian, ndarray::Array< Scalar const, 1, 1 > const & nonlinear, afw::math::Random & rng, ndarray::Array< Scalar, 2, 1 > const & amplitudes, ndarray::Array< Scalar, 1, 1 > const & weights, bool multiplyWeights = false ) const

pure virtual

Draw a set of Monte Carlo amplitude vectors.

This provides a Monte Carlo approach to extracting the conditional amplitude distribution that is integrated by the marginalize() method.

Parameters

[in]	gradient	Gradient of the -log likelihood in \(\alpha\) at fixed \(\theta\).
[in]	hessian	Second derivatives of of the -log likelihood in \(\alpha\) at fixed \(\theta\).
[in]	nonlinear	The nonlinear parameters \(\theta\) at which we are evaluating the conditional distribution \(P(\alpha|\theta)\).
[in,out]	rng	Random number generator.
[out]	amplitudes	The Monte Carlo sample of amplitude parameters \(\alpha\). The number of rows sets the number of samples, while the number of columns must match the dimensionality of \(\alpha\).
[out]	weights	The weights of the Monte Carlo samples; should asymptotically average to one.
[in]	multiplyWeights	If true, multiply weight vector instead of overwriting it.

Implemented in lsst::meas::modelfit::MixturePrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::SoftenedLinearPrior.

evaluate()

virtual Scalar lsst::meas::modelfit::Prior::evaluate ( ndarray::Array< Scalar const, 1, 1 > const & nonlinear, ndarray::Array< Scalar const, 1, 1 > const & amplitudes ) const

pure virtual

Evaluate the prior at the given point in nonlinear and amplitude space.

Parameters

[in]	nonlinear	Vector of nonlinear parameters
[in]	amplitudes	Vector of linear parameters

Implemented in lsst::meas::modelfit::MixturePrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::SoftenedLinearPrior.

evaluateDerivatives()

virtual void lsst::meas::modelfit::Prior::evaluateDerivatives ( ndarray::Array< Scalar const, 1, 1 > const & nonlinear, ndarray::Array< Scalar const, 1, 1 > const & amplitudes, ndarray::Array< Scalar, 1, 1 > const & nonlinearGradient, ndarray::Array< Scalar, 1, 1 > const & amplitudeGradient, ndarray::Array< Scalar, 2, 1 > const & nonlinearHessian, ndarray::Array< Scalar, 2, 1 > const & amplitudeHessian, ndarray::Array< Scalar, 2, 1 > const & crossHessian ) const

pure virtual

Evaluate the derivatives of the prior at the given point in nonlinear and amplitude space.

Note that while the model is linear in the amplitudes, the prior is not necessarily linear in the amplitudes, so we do care about second derivatives w.r.t. amplitudes.

Parameters

[in]	nonlinear	Vector of nonlinear parameters
[in]	amplitudes	Vector of linear parameters
[in]	nonlinearGradient	First derivative w.r.t. nonlinear parameters
[in]	amplitudeGradient	First derivative w.r.t. linear parameters parameters
[in]	nonlinearHessian	Second derivative w.r.t. nonlinear parameters
[in]	amplitudeHessian	Second derivative w.r.t. linear parameters parameters
[in]	crossHessian	Second derivative cross term of d(nonlinear)d(amplitudes); shape is [nonlinearDim, amplitudeDim].

Implemented in lsst::meas::modelfit::MixturePrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::SoftenedLinearPrior.

getTag()

std::string const & lsst::meas::modelfit::Prior::getTag ( ) const

inline

Definition at line 39 of file Prior.h.

{ return _tag; }

marginalize()

virtual Scalar lsst::meas::modelfit::Prior::marginalize ( Vector const & gradient, Matrix const & hessian, ndarray::Array< Scalar const, 1, 1 > const & nonlinear ) const

pure virtual

Return the -log amplitude integral of the prior*likelihood product.

If \(\alpha\) are the amplitudes, \(\theta\) are the nonlinear parameters, and \(D\) is the data, then this method represents \(P(\alpha,\theta)\) by computing

\[ -\ln\left[\int\!P(D|\alpha,\theta)\,P(\alpha,\theta)\,d\alpha\right] \]

at fixed \(\theta\). Because \(\alpha\) are linear parameters, \(P(D|\alpha,\theta)\) is Gaussian in \(\alpha\), and because \(\theta\) is fixed, it's usually convenient to think of the integral as:

\[ -ln\left[P(\theta)\int\!P(D|\alpha,\theta)\,P(\alpha|\theta)\,d\alpha\right] \]

Thus, we marginalize the likelihood in \(\alpha\) at fixed \(\theta\), and then multiply by the prior on \(\theta\).

We also assume the likelihood \(P(D|\alpha,\theta)\) is Gaussian in \(\alpha\), which is generally true because \(\alpha\) defined such that the model is linear in them, and the noise on the data is generally Gaussian. In detail, we represent the likelihood at fixed \(\theta\) as

\[ P(D|\alpha,\theta) = A e^{-g^T\alpha - \frac{1}{2}\alpha^T H \alpha} \]

The normalization \(A\) can be brought outside the integral as a constant to be added to the return value, so it is not passed as an argument to this function.

Parameters

[in]	gradient	Gradient of the -log likelihood in \(\alpha\) at fixed \(\theta\); the vector \(g\) in the equation above.
[in]	hessian	Second derivatives of of the -log likelihood in \(\alpha\) at fixed \(\theta\); the matrix \(H\) in the equation above.
[in]	nonlinear	The nonlinear parameters \(\theta\).

Implemented in lsst::meas::modelfit::MixturePrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::SoftenedLinearPrior.

maximize()

virtual Scalar lsst::meas::modelfit::Prior::maximize ( Vector const & gradient, Matrix const & hessian, ndarray::Array< Scalar const, 1, 1 > const & nonlinear, ndarray::Array< Scalar, 1, 1 > const & amplitudes ) const

pure virtual

Compute the amplitude vector that maximizes the prior x likelihood product.

Parameters

[in]	gradient	Gradient of the -log likelihood in \(\alpha\) at fixed \(\theta\); the vector \(g\) in the equation above.
[in]	hessian	Second derivatives of of the -log likelihood in \(\alpha\) at fixed \(\theta\); the matrix \(H\) in the equation above.
[in]	nonlinear	The nonlinear parameters \(\theta\).
[out]	amplitudes	The posterior-maximum amplitude parameters \(\alpha\).

Returns

The -log(posterior) at the computed amplitude point.

Implemented in lsst::meas::modelfit::MixturePrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::SoftenedLinearPrior.

operator=() [1/2]

Prior & lsst::meas::modelfit::Prior::operator= ( const Prior & )

delete

operator=() [2/2]

Prior & lsst::meas::modelfit::Prior::operator= ( Prior && )

delete

---

The documentation for this class was generated from the following file:

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-9.0.0/Linux64/meas_modelfit/ga5288a1d22+2903d499ea/include/lsst/meas/modelfit/Prior.h