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A ratio comparing the evidence of two competing hypotheses in Bayesian analysis.
DESCRIPTION
The Bayes factor quantifies relative support for one model versus another by comparing their marginal likelihoods. It integrates out parameters under prior distributions, yielding evidence that balances fit and complexity. Interpreting Bayes factors often uses qualitative scales (e.g., Kass and Raftery). Unlike p-values, Bayes factors compare models rather than testing against a null alone. They are sensitive to prior choice and can be computationally demanding. Bayes factors support principled model selection in scientific and applied contexts. Approximations like BIC offer practical alternatives.
ALTERNATIVE DEFINITIONS
Stanford Encyclopedia of Philosophy
The Bayes factor is the ratio of the marginal likelihoods of two competing models, measuring the strength of evidence provided by the data.
Philosophical and formal emphasis on marginal likelihoods.
Kass and Raftery (1995) via NCBI
The Bayes factor provides a summary of the evidence provided by the data in favor of one scientific theory against another.
Classic reference framing Bayes factors as evidence summaries.
Nature
Bayes factors compare how well two models predict the observed data, quantifying relative support.
Practical, predictive framing for scientific modeling.
RELATED TERMS
Bayesian Inference Likelihood Posterior Probability Model Evidence Hypothesis Testing Prior Distribution Bayesian Model Comparison
COMPETING TERMS
p-value Akaike Information Criterion Bayesian Information Criterion
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer Analytics Engineer Chief Data Officer
EXTERNAL SOURCES
- Wikipedia - Bayes factor
- NCBI - Kass & Raftery classic paper
- Stanford Encyclopedia of Philosophy - Bayesian foundations and Bayes factor
TOP QUESTIONS
How is Bayes Factor computed?
It is the ratio of model evidences (marginal likelihoods), integrating likelihood over parameter priors for each model.
Category: Definition
How do Bayes Factors differ from p-values?
Bayes factors compare models directly and incorporate priors, while p-values test against a null without prior information.
Category: Difference
What is a common interpretive scale for Bayes Factors?
Kass and Raftery’s qualitative scale ranks evidence from weak to very strong based on thresholds of the Bayes factor.
Category: Overview
What are risks of using Bayes Factors?
Results can be sensitive to priors and are computationally intensive; poor prior choices may mislead inference.
Category: Risk
What alternatives to Bayes Factors exist?
Information criteria like AIC and BIC, and cross-validation approaches provide practical model selection alternatives.
Category: Alternatives
Where are Bayes Factors applied?
They are used in genetics, psychology, economics, and any domain requiring principled model comparison.
Category: Application
How to handle priors when computing Bayes Factors?
Choose well-justified priors, test sensitivity, and consider objective priors where appropriate.
Category: Best practices
Can Bayes Factors be approximated?
Yes, BIC approximates the log Bayes factor under certain regularity conditions in large samples.
Category: Opinion
What is a big misunderstanding about Bayes Factors?
That they always favor complex models; they penalize complexity through integration over priors.
Category: Misunderstanding