Likelihood ratio - frequentist

$\Lambda =\frac{{\max }_{\theta \in {\Theta }_0}\mathcal{L}(\theta )}{{\max }_{\theta \in {\Theta }_A}\mathcal{L}(\theta )}$

Or put another way using the MLE for each model: $\Lambda =\frac{p(y|{\hat{\theta }}_0)}{p(y|{\hat{\theta }}_A)}$

---

References

@rice2007 - Chapter 8