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  "body": "\n## Definition\n\nLet $\\mathcal{P} = \\set{P_\\theta : \\theta \\in \\Theta}$ be a [[statistical model|JZ6R7J36K5]] on a measurable space $(S, \\mathcal{S})$.\nThe model is a *parametric model* if its parameter space $\\Theta$ is a subset of $\\R^k$ for some finite $k \\ge 1$.\nThe number $k$ is the dimension of the parameter.\n\n## Remarks\n\nExample: the normal model on $S = \\R$ with $P_{(\\mu, \\sigma^2)} = \\mathcal{N}(\\mu, \\sigma^2)$ and $\\Theta = \\R \\times (0, \\infty) \\subseteq \\R^2$ is parametric with $k = 2$.\nNon-example: the model of all probability measures on $\\R$ with finite variance is not given by a natural finite-dimensional parameter, and it is called nonparametric.\nIn practice one also asks that the map $\\theta \\mapsto P_\\theta$ is regular, for example that the densities depend smoothly on $\\theta$.\nWithout such a condition the definition is weak, since any set of at most continuum many laws can be indexed by a subset of $\\R$.\n",
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