spey.backends.default_pdf.EffectiveSigma

class spey.backends.default_pdf.EffectiveSigma(signal_yields: ndarray, background_yields: ndarray, data: ndarray, correlation_matrix: ndarray, absolute_uncertainty_envelops: List[Tuple[float, float]], signal_uncertainty_configuration: Dict[str, Any] | None = None)

Simplified likelihood interface with variable Gaussian. Variable Gaussian has been inspired by [arXiv:physics/0406120] sec. 3.6. This method modifies the effective \(B:=\sigma_{eff}\) term in the Poisson distribution of the simplified likelihood framework. Note that this approach does not modify the Gaussian of the likelihood, the naming of the approach is purely because it is originated from [arXiv:physics/0406120] sec. 3.6. The effective sigma term of the Poissonian can be modified using upper, \(\sigma^+\) and lower \(\sigma^-\) envelops of the absolute background uncertainties (see eqs 18-19 in [arXiv:physics/0406120]).

\[\sigma_{eff}(\theta) = \sqrt{\sigma^+\sigma^- + (\sigma^+ - \sigma^-)(\theta - n_{bkg})}\]

where the simplified likelihoo is modified as

\[\mathcal{L}(\mu,\theta) = \left[\prod_i^N{\rm Poiss}(n^i_{obs}|\mu n^i_s + n^i_{bkg} + \theta^i\sigma_{eff}^i(\theta)) \right]\cdot \mathcal{N}(\theta| 0, \rho)\]

Note

This likelihood is constrained by

\[n^i_{bkg} + \theta^i\sigma_{eff}^i(\theta) \geq 0\]

Parameters:

• signal_yields (np.ndarray) – signal yields

• background_yields (np.ndarray) – background yields

• data (np.ndarray) – observations

• correlation_matrix (np.ndarray) – correlations between regions

• absolute_uncertainty_envelops (List[Tuple[float, float]]) – upper and lower uncertainty envelops for each background yield.

• signal_uncertainty_configuration (Dict[Text, Any]], default None) –

  Configuration input for signal uncertainties

  • absolute_uncertainties (List[float]): Absolute uncertainties for the signal

  • absolute_uncertainty_envelops (List[Tuple[float, float]]): upper and lower

    uncertainty envelops

  • correlation_matrix (List[List[float]]): Correlation matrix

  • third_moments (List[float]): diagonal elemetns of the third moment

__init__(signal_yields: ndarray, background_yields: ndarray, data: ndarray, correlation_matrix: ndarray, absolute_uncertainty_envelops: List[Tuple[float, float]], signal_uncertainty_configuration: Dict[str, Any] | None = None)

Methods

__init__(signal_yields, background_yields, ...)
asimov_negative_loglikelihood([poi_test, ...])	Compute negative log-likelihood at fixed \(\mu\) for Asimov data.
combine(other, **kwargs)	A routine to combine to statistical models.
config([allow_negative_signal, poi_upper_bound])	Model configuration.
expected_data(pars[, include_auxiliary])	Compute the expected value of the statistical model
get_hessian_logpdf_func([expected, data])	Currently Hessian of \(\log\mathcal{L}(\mu, \theta)\) is only used to compute variance on \(\mu\).
get_logpdf_func([expected, data])	Generate function to compute \(\log\mathcal{L}(\mu, \theta)\) where \(\mu\) is the parameter of interest and \(\theta\) are nuisance parameters.
get_objective_function([expected, data, do_grad])	Objective function i.e. twice negative log-likelihood, \(-2\log\mathcal{L}(\mu, \theta)\).
get_sampler(pars)	Retreives the function to sample from.
minimize_asimov_negative_loglikelihood([...])	A backend specific method to minimize negative log-likelihood for Asimov data.
minimize_negative_loglikelihood([expected, ...])	A backend specific method to minimize negative log-likelihood.
negative_loglikelihood([poi_test, expected])	Backend specific method to compute negative log-likelihood for a parameter of interest \(\mu\).

Attributes

constraints	Constraints to be used during optimisation process
signal_uncertainty_configuration
arXiv	arXiv reference for the backend
author	Author of the backend
constraint_model	retreive constraint model distribution
doi	Citable DOI for the backend
is_alive	Returns True if at least one bin has non-zero signal yield.
main_model	retreive the main model distribution
name	Name of the backend
spey_requires	Spey version required for the backend
version	Version of the backend