Bayesian Information Criterion (BIC)
The Bayesian Information Criterion (BIC) is a measure used[Tex]k[/Tex] to compare different statistical models. It helps us choose the best model from a set of candidates by considering both how well a model fits the data and how complex it is.
Formula:
[Tex] BIC = -2 \times \log(L) + k \times \log(n) [/Tex]
Where,
- [Tex]L[/Tex] represents the likelihood of the data given the model. In simple terms, it measures how probable the observed data is under a specific model.
- is the number of parameters in the model. Parameters are like knobs that the model can adjust to fit the data better.
- [Tex]n[/Tex] is the number of data points we have.
The BIC has two terms: one based on the likelihood of the data [Tex]2 \times \log(L)[/Tex] and another based on the number of parameters [Tex]k \times \log(n)[/Tex].
The first term rewards models that fit the data well, while the second term penalizes models with more parameters, which tend to be more complex. By combining these two terms, the BIC helps us find the model that strikes the best balance between fitting the data and simplicity. It favors simpler models that still explain the data well, making it a valuable tool in model selection.
Bayesian Model Selection
Bayesian Model Selection is an essential statistical method used in the selection of models for data analysis. Rooted in Bayesian statistics, this approach evaluates a set of statistical models to identify the one that best fits the data according to Bayesian principles. The approach is characterized by its use of probability distributions rather than point estimates, providing a robust framework for dealing with uncertainty in model selection.
Table of Content
- What is the Bayesian Model Selection?
- Bayesian Inference
- Key Components of Bayesian Statistics
- Prior and Posterior Probability
- Prior Probability
- Posterior Probability
- Model Comparison Techniques
- Bayesian Factor (BF)
- Bayesian Information Criterion (BIC)
- Advantages of Bayesian Model Selection
- Conclusion