Scipy

Download this notebook This notebook shows the advantage of Bayesian Linear Regression vs. regular Least-Squares-Estimation-based Linear Regression with respect to outliers. The Bayesian part of the approach shown here is that the error’s/noise’s standard deviation $\sigma$ is now not necessarily constant, but a random variable, too, bounded by a lower bound $\sigma_0$ and an upper bound $\infty$. Standard Linear Regression Assumption: f(x) = a + bx with measurement $y_i = f(x_i) + \epsilon_i$ with $\epsilon_i \sim \mathcal{N}\left(0,\sigma_0^2\right)$.