Base class for Bayesian priors. More...
#include <Prior.h>
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 &litudes) const =0 |
| Evaluate the prior at the given point in nonlinear and amplitude space. More... | |
| virtual void | evaluateDerivatives (ndarray::Array< Scalar const, 1, 1 > const &nonlinear, ndarray::Array< Scalar const, 1, 1 > const &litudes, ndarray::Array< Scalar, 1, 1 > const &nonlinearGradient, ndarray::Array< Scalar, 1, 1 > const &litudeGradient, ndarray::Array< Scalar, 2, 1 > const &nonlinearHessian, ndarray::Array< Scalar, 2, 1 > const &litudeHessian, ndarray::Array< Scalar, 2, 1 > const &crossHessian) const =0 |
| Evaluate the derivatives of the prior at the given point in nonlinear and amplitude space. More... | |
| 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. More... | |
| virtual Scalar | maximize (Vector const &gradient, Matrix const &hessian, ndarray::Array< Scalar const, 1, 1 > const &nonlinear, ndarray::Array< Scalar, 1, 1 > const &litudes) const =0 |
| Compute the amplitude vector that maximizes the prior x likelihood product. More... | |
| 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 &litudes, ndarray::Array< Scalar, 1, 1 > const &weights, bool multiplyWeights=false) const =0 |
| Draw a set of Monte Carlo amplitude vectors. More... | |
| 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
Constructor & Destructor Documentation
◆ ~Prior()
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inlinevirtual |
◆ Prior() [1/3]
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delete |
◆ Prior() [2/3]
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delete |
◆ Prior() [3/3]
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inlineexplicitprotected |
Member Function Documentation
◆ drawAmplitudes()
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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::SoftenedLinearPrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::MixturePrior.
◆ evaluate()
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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::SoftenedLinearPrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::MixturePrior.
◆ evaluateDerivatives()
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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::SoftenedLinearPrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::MixturePrior.
◆ getTag()
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inline |
◆ marginalize()
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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::SoftenedLinearPrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::MixturePrior.
◆ maximize()
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pure virtual |
Compute the amplitude vector that maximizes the prior x likelihood product.
- Parameters
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[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::SoftenedLinearPrior, lsst::meas::modelfit::SemiEmpiricalPrior, and lsst::meas::modelfit::MixturePrior.
◆ operator=() [1/2]
◆ operator=() [2/2]
The documentation for this class was generated from the following file:
- /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/meas_modelfit/22.0.1-4-g44f2e3d+9e4ab0f4fa/include/lsst/meas/modelfit/Prior.h
