Simple or Composite Hypothesis

Definition (Ost20 pp.116, Simple or Composite Hypothesis). Let $p_{\theta }(y)$ be a Parametric Probabilistic Model. A simple hypothesis refers to a subset of parameter space which contains a single element, for example ${\Theta }_0:={\theta }_0$. A composite hypothesis refers to a subset of parameter space which contains more than one element, for example ${\Theta }_0:={\mathbb{R}}_{\le 0}$.

The commonly encountered null hypothesis ${\Theta }_0=0$, also referred to as nil hypothesis, is an example for a simple hypothesis.