MENTAL MODEL · M12248

Bayesian Information Criterion, BIC

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Updated 2026-08-13

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INTRODUCTION

English translation pending.

CORE DEFINITION

The Bayesian Information Criterion, BIC, is a score used to choose among competing statistical models, computed from the likelihood the model achieves and a penalty that grows with the number of parameters. Lower is better. Unlike a raw fit measure, BIC penalizes complexity, so it will prefer a simpler model unless the extra parameters buy enough improvement in likelihood, and the penalty grows with sample size, which makes large samples demand stronger evidence before complexity is accepted. It is one standard guard against overfitting, alongside the Akaike Information Criterion, whose penalty is lighter.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

- Choose by score, not by fit: compare candidate models on BIC rather than picking whichever fits the training data best. - Punish complexity in yourself: when two explanations fit, prefer the one with fewer moving parts. - Know your criterion's taste: BIC is more hostile to complexity than AIC, so say which one you are using and why.

anchor

Anchor fast decisions

Every extra parameter can absorb some noise, so training fit keeps rising as the model grows, and a criterion that only rewards fit will always favor the largest model available. BIC subtracts a penalty that increases with parameter count and with the log of sample size, so a parameter has to earn its place by improving likelihood more than it costs. The result is a tradeoff that mirrors the scientific instinct: prefer the simplest account that the data does not let you simplify further, which is why the criterion is used for variable selection and structure learning.

MINIMUM ACTION

In progress 0/2

Practice this model in one real situation:

Fit each candidate model and record its likelihood and its parameter count. 2. Compute BIC for every candidate and rank them
lower is better. 3. Prefer the simplest model within a small margin of the best score, rather than the best score itself. 4. If using AIC as well, state which criterion your decision rests on and what it assumes.

Check to track your progress (stored locally)

Learning progress0%

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Source support: Explicit

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en.wikipedia.orghttps://en.wikipedia.org/wiki/Bayesian_information_criterionZH · Explicit
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