Bayesian Functions¶

The Bayes and Parameter estimation classes¶

Likelihood marginalisation and helper functions¶

These C and Cython functions provide tools, and wrappers, to perform the likelihood ratio evaluation. There are also helper functions for use in numerical integration of functions.

`C`-functions¶

These C-functions are used performing likelihood ratio evaluation when analytically marginalising over a set of model component amplitudes. For further documentation of these functions see [1] and [2].

LOG2PI¶: The natural logarithm of \(2\pi\) defined using the GSL macros (M_LN2 + M_LNPI)

LOGPI_2¶: The natural logarithm of \(\pi/2\) defined using the GSL macros (M_LNPI - M_LN2)

double log_marg_amp_full_C(int Nmodels, double modelModel[], double dataModel[], double sigma, unsigned int lastHalfRange)¶

This function calculates the log-likelihood ratio for a signal model (consisting of a number Nmodels components, each with an amplitude that is marginalised over) compared to a pure Gaussian noise model. For all bar the last model component the amplitudes are analytically marginalised between \(-\infty\) and \(\infty\), whilst if lastHalfRange is true the final amplitude will be marginalised between 0 and infinity (i.e. it must be positive).

For a more complete description of this function see [1] or Algorithm 1 in [2].

Parameters:

Nmodels : int

The number of model components.

modelModel : double array

A flattened 1D array consisting of the summed cross terms for each model component [size: Nmodels -by- Nmodels].

dataModel : double array

A 1D array of the summed data crossed with each model component [size: Nmodels]

sigma : double

The underlying Gaussian noise standard deviation

lastHalfRange : bool

A boolean saying whether the final model component amplitudes should be marginalised over the full \(-\infty\) to \(\infty\) range (False), or between 0 and \(\infty\) (True).

Returns:

logL : double

The log-likelihood ratio marginalised over the model component amplitudes.

double log_marg_amp_except_final_C(int Nmodels, double modelModel[], double dataModel[], double sigma)¶

This function calculates the log-likelihood ratio for a signal model (consisting of a number Nmodels components) compared to a pure Gaussian noise model. For all bar the last model component the amplitudes are analytically marginalised between \(-\infty\) and \(\infty\).

For a more complete description of this function see [1] or Algorithm 2 in [2].