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  "body": "\n## Summary\n\nContiguity is an asymptotic form of absolute continuity for sequences of probability measures.\nA sequence $(Q_n)$ is contiguous with respect to $(P_n)$ if every sequence of events whose $P_n$-probability tends to zero also has $Q_n$-probability tending to zero.\nIt was introduced by Lucien Le Cam.\nIt lets one transfer convergence in probability from a null hypothesis to nearby alternatives.\nThis is the basis of asymptotic power calculations and of local asymptotic theory.\n\n## Explanations\n\n### L1 human\n\nTwo sequences of probability models are contiguous if, as the sample grows, events that become impossible under one also become impossible under the other.\nThe models may differ, but never so much that the data could tell them apart with certainty.\nFor $n$ normal observations, a mean of $0$ and a mean of $1/\\sqrt{n}$ stay contiguous, because the shift is of the size of the statistical noise.\nA mean of $0$ and a mean of $1$ are not contiguous: with many observations one can tell them apart almost surely.\n",
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