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  "body": "\n## Summary\n\nThe Jeffreys prior is a [[prior distribution|00NBBSXRQS]] whose density is proportional to the square root of the determinant of the [[Fisher information|G1Z3WSTE8Q]].\nIts defining property is invariance: it gives the same prior no matter how the parameter is written.\nIt is a standard choice of a non-informative prior in [[Bayesian inference|0JWRJX2RMP]], and it is often improper.\n\n## Explanations\n\n### L1 human\n\nA flat prior on a parameter is not flat on a transformed parameter, such as its square or its logarithm.\nSo \"flat\" depends on how the parameter is written down.\nThe Jeffreys prior avoids this by measuring distances with the Fisher information, which measures how well data can tell nearby parameter values apart.\nFor a coin with chance $p$ of heads, it gives the density proportional to $1/\\sqrt{p(1 - p)}$, which puts a little more weight near $0$ and $1$.\n",
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