Compare Bayesian linear regression VS linear regression

Question

I recently studied the Bayesian linear regression model, but what I got confused about is that in this situation we should use linear regression and when to use the Bayesian version. How about the performance of the two? And the same Bayesian logistic regression and logistic regression? I read an article about using Bayesian probit regression to predict CTR ads, I'm just wondering why using a Bayesian version?

Answer 1

In your two cases of linear regression and logistic regression, the Bayesian version uses statistical analysis in the context of Bayesian inference, for example Bayesian linear regression .

On Wikipedia,

This (ordinary linear regression) is a frequency approach, and it assumes that there are enough measurements to say something meaningful. In the Bayesian approach, the data is supplemented by additional information in the form of a preliminary probability distribution. The previous opinion about the parameters is combined with the likelihood function of the data by the Bayesian theorem in order to get a back view of the parameters.

The usual way of Bayesian analysis (adding Bayesian taste):

• Define the likelihood function of the data.
• Select a preliminary distribution for all unknown parameters.
• Use Bayes' theorem to determine the back distribution for all parameters.

Why is the Bayesian version? ^[1]

• Bayesian models are more flexible, handle more complex models.
• The choice of the Bayesian model is probably superior (BIC / AIC).
• Bayesian hierarchical models are easier to extend to many levels.
• Philosophical differences (compared to frequent analysis).
• Bayesian analysis is more accurate in small samples (but then it may depend on the priors).
• Bayesian models may include preliminary information

This contains good lecture slides for Bayesian analysis.