Bayesian information criterion
Bayesian Information Criterion (BIC), also known as Schwarz Information Criterion (SIC), is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. It is based on the likelihood function and is closely related to the Akaike Information Criterion (AIC). However, BIC introduces a penalty term for the number of parameters in the model to prevent overfitting, which is more stringent than that of AIC.
Overview[edit | edit source]
The BIC is an asymptotic result derived under the assumption that the data distribution is in the exponential family. It is defined as:
\[ \text{BIC} = -2 \cdot \ln(\hat{L}) + k \cdot \ln(n) \]
where:
- \( \hat{L} \) is the maximum value of the likelihood function for the model,
- \( k \) is the number of parameters to be estimated in the model,
- \( n \) is the number of observations or sample size.
The term \( -2 \cdot \ln(\hat{L}) \) penalizes lack of fit, while the term \( k \cdot \ln(n) \) penalizes complexity. The BIC is particularly useful in model selection where the goal is to select the model that balances a good fit with simplicity.
Comparison with AIC[edit | edit source]
Both AIC and BIC aim to resolve the trade-off between model fit and complexity but do so in slightly different ways. The key difference lies in the penalty term for the number of parameters: BIC's penalty term is larger, especially as the sample size \( n \) increases. This means BIC tends to select simpler models than AIC, particularly as the sample size grows.
Applications[edit | edit source]
BIC is widely used in many areas of statistical analysis, including:
- Regression analysis
- Structural equation modeling
- Machine learning for model selection
- Factor analysis
It is particularly popular in the fields of econometrics, sociology, and psychology, where complex models are common, and the risk of overfitting is a concern.
Limitations[edit | edit source]
While BIC is a powerful tool for model selection, it has limitations:
- It assumes that the true model is among the set of candidate models, which may not always be the case.
- BIC can be overly simplistic in situations where model complexity does not linearly relate to the number of parameters.
- It relies on the assumption of the data being identically and independently distributed, which may not hold in all scenarios.
See Also[edit | edit source]
References[edit | edit source]
Navigation: Wellness - Encyclopedia - Health topics - Disease Index - Drugs - World Directory - Gray's Anatomy - Keto diet - Recipes
Search WikiMD
Ad.Tired of being Overweight? Try W8MD's physician weight loss program.
Semaglutide (Ozempic / Wegovy and Tirzepatide (Mounjaro) available.
Advertise on WikiMD
WikiMD is not a substitute for professional medical advice. See full disclaimer.
Credits:Most images are courtesy of Wikimedia commons, and templates Wikipedia, licensed under CC BY SA or similar.Contributors: Prab R. Tumpati, MD