Bayesian information criterion
(1.2 hours to learn)
Summary
The Bayesian information criterion (BIC) is a rough approximation to the marginal likelihood, based on the asymptotic behavior of the Laplace approximation as more data is observed.
Context
This concept has the prerequisites:
- Bayesian model comparison (The BIC is an approximation to Bayesian model comparison.)
- the Laplace approximation (The Laplace approximation is a way of justifying the BIC.)
Goals
- Know the formula for the BIC
- Derive the formula in terms of the Laplace approximation
Core resources (read/watch one of the following)
-Free-
→ The Bayesian Information Criterion
Supplemental resources (the following are optional, but you may find them useful)
-Paid-
→ Pattern Recognition and Machine Learning
A textbook for a graduate machine learning course, with a focus on Bayesian methods.
Location:
Section 4.4.1, pages 216-217
→ Machine Learning: a Probabilistic Perspective
A very comprehensive graudate-level machine learning textbook.
Location:
Sections 5.3.2.4 (pages 161-162) and 8.4.2 (pages 255-256)
See also
- Akaike Information Criterion (AIC) is a different model selection criterion with different theoretical underpinnings, and practically, AIC does not penalize the number of parameters as severely as BIC
- Mathematical justification of the BIC.