Using Bayesian linear regression to predict

Bayesian Linear Regression \[P(\beta|y,X)=\frac{P(y,X|\beta)P(\beta)}{P(y,X)}\] where, \(P(y,X)=\int_{-\infty}^\infty P(y,X|\beta)P(\beta)d\beta\)

When predicting the output for a single data point using Bayesian Linear Model, we do not get a single value but a distribution. However, we can use mean regression line to produce a single outcome (i.e use mean values of posterior \(\boldsymbol{\beta}\) to predict).

Some useful links:

1.https://towardsdatascience.com/bayesian-linear-regression-with-bambi-a5e6570f167b

2.https://towardsdatascience.com/introduction-to-bayesian-linear-regression-e66e60791ea7

3.https://michaelpyrcz.com/my-resources