Class Likelihood

Inheritance Relationships

Derived Types

Class Documentation

class Likelihood

Base class for optimizer/sampler likelihood functions that compute likelihood at a point.

Likelihood abstracts the problem of computing the likelihood over different kinds of data. It is responsible for creating a “model matrix” that maps amplitudes to data values, and maintaining a vector of scaled, weighted data values that corresponds to it. Its components can be represented best in the mathematical formula for a -log likelihood assuming Gaussian data and a model with both nonlinear parameters \(\theta\) and linear (“amplitude”) parameters \(\alpha\):

\[ L(\alpha,\theta) = \frac{1}{2}\left(y - A(\theta)\alpha\right)^T\, \Sigma^{-1}\,\left(y - A(\theta)\alpha\right) \]
where \(y\) is the data vector, \(\Sigma\) is the data covariance matrix (assumed to be diagonal), and \(A(\theta)\) is the “true” model matrix (parametrized on the nonlinear parameters).

When fitting or sampling from the likelihood, however, we don’t want to use these quantities directly, and they aren’t what the Likelihood class provides. Instead, we reparametrize with:

\[ w_i \equiv \Sigma_{i,i}^{-1/2} \]
\[ z_i = w_i y_i \]
\[ B_{i,j} = w_i A_{i,j} \]
resulting in the equivalent formula:
\[ L(\alpha,\theta) = \frac{1}{2}\left(z-B(\theta)\alpha\right)^T\,\left(z-B(\theta)\alpha\right) \]
The \(w_i\) are the weights, which are applied to both the data vector and the model matrix to account for the noise in the data. In some cases, we may choose to use a constant weight rather than per-pixel weights, but will will still use a vector to represent it.

Subclassed by lsst::meas::modelfit::MultiShapeletPsfLikelihood, lsst::meas::modelfit::UnitTransformedLikelihood

Public Functions

int getDataDim() const

Return the number of data points.

int getAmplitudeDim() const

Return the number of linear parameters (columns of the model matrix)

int getNonlinearDim() const

Return the number of nonlinear parameters (which parameterize the model matrix)

int getFixedDim() const

Return the number of fixed nonlinear parameters (set on Likelihood construction)

ndarray::Array<Scalar const, 1, 1> getFixed() const

Return the vector of fixed nonlinear parameters.

ndarray::Array<Pixel const, 1, 1> getData() const

Return the vector of weighted, scaled data points \(z\).

ndarray::Array<Pixel const, 1, 1> getUnweightedData() const

Return the vector of unweighted data points \(y\).

ndarray::Array<Pixel const, 1, 1> getWeights() const

Return the vector of weights \(w\) applied to data points and model matrix rows

Will be an empty array if no weights are applied.

ndarray::Array<Pixel const, 1, 1> getVariance() const

Return the vector of per-data-point variances.

PTR(Model) const

Return an object that defines the model and its parameters.

virtual void computeModelMatrix(ndarray::Array<Pixel, 2, -1> const &modelMatrix, ndarray::Array<Scalar const, 1, 1> const &nonlinear, bool doApplyWeights = true) const = 0

Evaluate the model for the given vector of nonlinear parameters.

Parameters

  • [out] modelMatrix: The dataDim x amplitudeDim matrix \(B\) that expresses the model projected in such a way that it can be compared to the data when multiplied by an amplitude vector \(\alpha\). It should be weighted if the data vector is. The caller is responsible for guaranteeing that the shape of the matrix correct, but implementations should not assume anything about the initial values of the matrix elements.

  • [in] nonlinear: Vector of nonlinear parameters at which to evaluate the model.

  • [in] doApplyWeights: If False, do not apply the weights to the modelMatrix.

virtual ~Likelihood()
Likelihood(const Likelihood&)
Likelihood &operator=(const Likelihood&)
Likelihood(Likelihood&&)
Likelihood &operator=(Likelihood&&)

Protected Functions

lsst::meas::modelfit::Likelihood::Likelihood(PTR ( Model ) model, ndarray::Array< Scalar const, 1, 1 > const & fixed)
PTR(Model)

Protected Attributes

ndarray::Array<Scalar const, 1, 1> _fixed
ndarray::Array<Pixel, 1, 1> _data
ndarray::Array<Pixel, 1, 1> _unweightedData
ndarray::Array<Pixel, 1, 1> _variance
ndarray::Array<Pixel, 1, 1> _weights