spey.hypothesis_testing.test_statistics.q0

spey.hypothesis_testing.test_statistics.q0(mu: float, muhat: float, max_logpdf: float, logpdf: Callable[[float], float]) → float

Discovery test statistics, \(q_{0}\) see eq. (47) of [arXiv:1007.1727].

\[\begin{split}q_0 = \begin{cases} 0 & \text{if}\ \hat{\mu} < 0\ ,\\ -2\log\left( \frac{\mathcal{L}(0, \theta_0)}{\mathcal{L}(\hat{\mu}, \hat{\theta})} \right) & \text{otherwise} \end{cases}\end{split}\]

Parameters:

• mu (float) –

  parameter of interest, \(\mu\).

  Note

  mu argument is overwritten by zero. This input is only for consistency with other test statistic functions.

• muhat (float) – \(\hat\mu\) value that maximizes the likelihood.

• max_logpdf (float) – maximum value of \(\log\mathcal{L}\).

• logpdf (Callable[[float], float]) – \(\log\mathcal{L}(\mu, \theta_\mu)\).

Returns:

the value of \(q_{0}\).

Return type:

float