Bayesian Inference
Bayesian inference is a statistical method for updating beliefs about unknown parameters using observed data and prior knowledge. It’s based on Bayes’ theorem:
[Tex]P(\theta|D) = \frac{P(D|\theta) \times P(\theta)}{P(D)} [/Tex]
Here,
- [Tex]P(\theta|D)[/Tex] is the posterior probability of the parameter [Tex]\theta[/Tex] given data D.
- [Tex]P(D|\theta)[/Tex] is the likelihood of data D given[Tex]\theta [/Tex].
- [Tex]P(\theta)[/Tex] is the prior probability of [Tex]\theta [/Tex].
- [Tex]P(D) [/Tex]is the marginal likelihood of data.
So basically , we update our belief [Tex]\theta [/Tex] based on new evidence [Tex]data ( D )[/Tex]. The likelihood[Tex]P(D|\theta)[/Tex] measures how probable the data is under certain parameter values. The prior[Tex] P(\theta)[/Tex] represents our initial belief about [Tex]\theta[/Tex] before seeing the data. We then combine this with the likelihood to get the posterior[Tex]P(\theta|D) [/Tex], our updated belief after observing the data.
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
Contact Us