spey.backends.default_pdf.simple_pdf.MultivariateNormal

spey.backends.default_pdf.simple_pdf.MultivariateNormal#

class spey.backends.default_pdf.simple_pdf.MultivariateNormal(signal_yields: List[float], background_yields: List[float], data: List[int], covariance_matrix: List[List[float]] | callable)[source]#

Multivariate Gaussian distribution.

\[\mathcal{L}(\mu) = \frac{1}{\sqrt{(2\pi)^k {\rm det}[\Sigma] }} \exp\left[-\frac{1}{2} (\mu n_s + n_b - n)\Sigma^{-1} (\mu n_s + n_b - n)^T \right]\]

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

Added in version 0.1.9.

covariance_matrix can also take callable function as an input where function takes nuisance parameters as inputs and return a new covariance matrix as output.

Example:

>>> import spey
>>> import numpy as np

>>> signal_yields = np.array([12.0, 15.0])
>>> background_yields = np.array([50.0, 48.0])
>>> data = np.array([36., 33.])
>>> covariance_matrix = np.array([[144.0, 13.0], [25.0, 256.0]])
>>> covariance_signal = np.array([[5.0, 1.0], [2.0, 3.0]])

>>> def cov_matrix(pars: np.ndarray) -> np.ndarray:
>>>     return covariance_matrix + covariance_signal * pars[0]**2

>>> pdf_wrapper = spey.get_backend('default.multivariate_normal')
>>> model = pdf_wrapper(
...     signal_yields=signal_yields,
...     background_yields=background_yields,
...     data=data,
...     covariance_matrix=cov_matrix,
... )

Changed in version 0.2.6: The ability to input a callable covariance matrix has been added.

Parameters:

  • signal_yields (List[float]) – signal yields

  • background_yields (List[float]) – background yields

  • data (List[int]) – data

  • covariance_matrix (List[List[float]] | callable) –

    covariance matrix (square matrix)

__init__(signal_yields: List[float], background_yields: List[float], data: List[int], covariance_matrix: List[List[float]] | callable)[source]#

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

covariance_matrix

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

constraints

Constraints to be used during optimisation process
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