hypothesis testing

We have a null hypothesis $H_0$ and (usually, though see Fisher’s paradigm) an alternative hypothesis $H_1$, both of which are collections (possibly singletons) of distributions on some measurable space $(\Omega ,\mathcal{F})$. We obtain a sample $X\sim R\in H_0\cup H_1$ and want to determine if there is sufficient evidence to reject the null (that $R\in H_0$).

There are many subtopics in hypothesis testing. Eg:

• game-theoretic hypothesis testing
• duality between hypothesis tests and CIs
• two-sample testing
• conditional independence testing
• multiple testing