3.3.1 Bayesian Linear Regression: Parameter Distribution (with Code!) - PRML

In this section we begin our discussion of Bayesian linear regression. We study the setting of a Gaussian likelihood combined with a conjugate Gaussian prior and leverage our previous results to compute the mean and covariance of the posterior distribution. We then use a toy example of estimating the slope and intercept of linear data to demonstrate sequential Bayesian estimation of the parameters, where the posterior computed after incorporating a data point serves as the prior when incorporating the next. We emphasize throughout how the Bayesian approach doesn't just report a point estimate of the parameters but preserves a distribution over the parameters, quantifying our uncertainty over their values. Code discussion starts at 23:53. Code is available here: https://github.com/stootoon/prml-bayesian-linreg-param-dist