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  "body": "\n## Summary\n\nThe Bayesian information criterion (BIC), also called the Schwarz criterion, scores a fitted model by its maximized [[likelihood|0VW9E4QXR6]] with a penalty of $\\ln n$ per parameter.\nAmong candidate models, one prefers the model with the smallest BIC.\nIt comes from a large-sample approximation of the marginal likelihood of a model in [[Bayesian inference|0JWRJX2RMP]].\nIts penalty is heavier than that of the [[Akaike information criterion|CMAX3KF9H0]] once $n \\ge 8$.\n\n## Explanations\n\n### L1 human\n\nLike the AIC, the BIC trades the fit of a model against its number of parameters.\nIts price for each parameter grows slowly with the sample size $n$, as $\\ln n$.\nSo with much data, the BIC prefers simpler models than the AIC does.\nFor $n = 100$ observations, each parameter costs about $4.6$ units instead of $2$.\n",
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