There's some [[statistics|data generating process]] $p_{*} \in \Delta(\mathcal{Y})$ that spits out observed data in some space $\mathcal{Y}$. How can we use that data to *infer* properties of $p_{*}$? A **statistical model class** is a subset $\mathcal{F} \subseteq \Delta(\mathcal{Y})$ of distributions that we [[hypothesis test|hypothesize]] contains $p_{*}$. Then the task is to find some $\hat p \in \mathcal{F}$ that gets as close to $p_{*}$ as possible (according to some [[loss function]]). ie an [[optimization]] problem. If $p_{*} \in \mathcal{F}$ then we call the problem [[interpolate|realizable]]. Statistical models are [[parameter|parametric]] or [[nonparametric]]. > [!NOTE] terminology > > We use the term [[prediction rule]] for [[supervised]] problems where we want to learn a mapping $x \mapsto y$. # sources [[STAT 111]] chap 2.1.1, chap 4.8 [[2013HastieEtAlElementsStatisticalLearning]] [ch::2.6]