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  "body": "\n## Summary\n\nA Dirichlet process is a random [[probability measure|059TJN0NZ1]] whose values on every finite partition of the space follow a [[Dirichlet distribution|RX4CVSSRRJ]].\nIt depends on a concentration parameter $\\alpha \u003e 0$ and a base probability measure $H$.\nIt is the basic prior distribution on probability measures in nonparametric [[Bayesian inference|0JWRJX2RMP]].\nIts samples are discrete measures almost surely, and the posterior after observing data is again a Dirichlet process.\n\n## Explanations\n\n### L1 human\n\nA Dirichlet process draws a whole probability distribution at random.\nOn average the drawn distribution equals the base measure $H$, and a large $\\alpha$ keeps it close to $H$.\nThe drawn distribution puts all its mass on countably many points, like a random histogram with infinitely many thin bars.\nFor example, with $H$ uniform on $[0, 1]$, the mass that a draw gives to $[0, 1/2]$ is a random number with mean $1/2$.\nDrawing values from such a random distribution again and again produces ties, and the pattern of ties is the [[Chinese restaurant process|2SEF8QTYQF]].\n",
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