spey.backends.default_pdf.simple_pdf.Gaussian

class spey.backends.default_pdf.simple_pdf.Gaussian(signal_yields: List[float], background_yields: List[float], data: List[int], absolute_uncertainties: List[float])

Gaussian distribution for uncorrelated likelihoods.

\[\mathcal{L}(\mu) = \prod_{i\in{\rm bins}} \frac{1}{\sigma^i \sqrt{2\pi}} \exp\left[-\frac{1}{2} \left(\frac{\mu n_s^i + n_b^i - n^i}{\sigma^i} \right)^2 \right]\]

where \(n_{s,b}\) are signal and background yields and \(n\) are the observations.

Added in version 0.1.9.

Parameters:

• signal_yields (List[float]) – signal yields

• background_yields (List[float]) – background yields

• data (List[int]) – data

• absolute_uncertainties (List[float]) – absolute uncertainties on the background

__init__(signal_yields: List[float], background_yields: List[float], data: List[int], absolute_uncertainties: List[float])

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, **kwargs)	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. negative log-likelihood, \(-\log\mathcal{L}(\mu, \theta)\).
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

absolute_uncertainties	absolute uncertainties on the background
author	Author of the backend
background_yields
data
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
signal_yields
spey_requires	Spey version required for the backend
version	Version of the backend