Bayesian vs OLS

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I found this question online. Can someone explain in details please, why using OLS is better? Is it only because the number of samples is not enough? Also, why not use all the 1000 samples to estimate the prior distribution?

We have 1000 randomly sampled data points. The goal is to try to build a regression model with one response variable from k regressor variables. Which is better? 1. (Bayesian Regression) Using the first 500 samples to estimate the parameters of an assumed prior distribution and then use the last 500 samples to update the prior to a posterior distribution with posterior estimates to be used in the final regression model. 2. (OLS Regression) Use a simple ordinary least squares regression model with all 1000 regressor variables

bayesian linear-regression machine-learning
2 Answers

In my opinion is not a matter of better but a matter of which inference approach you're comfortable with.

You must remember that OLS comes from the frequentist school of inference and estimation is donde ML process which for this particular problem coincides with a geometric argument of distance minimization (in my personal opinion it is very odd, as supposedly we aare dealing with a rondom phenomena).

On the other hand, in the bayesian approach, inference is done through posterior distribution which is the multiplication of the prior (that represents the decision maker's previous information about the phenom) and the likelihood.

Again, the question is a matter of what inference approach you're comfortable with.

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