Regression using Bayes’ Theorem

What is Bayesian regression?

Bayesian regression is a statistical method that uses Bayes’ theorem to estimate the probability distribution of model parameters given the observed data. The process involves defining a prior distribution for the parameters, updating this distribution using the observed data through Bayes’ theorem, and obtaining the posterior distribution of the parameters.

The following steps outline the process of developing a Bayesian linear regression model:

1. Defining the model: We define the linear regression model, where the dependent variable is a linear combination of the independent variables with Gaussian noise.

2. Specifying prior distributions: We assign prior distributions for the model parameters. This can be done using a conjugate prior if available; otherwise, a noninformative prior can be used.

3. Calculating the posterior distribution: We use Bayes’ theorem to calculate the posterior distribution of the parameters given ...