Partition Modeling
In this tutorial, we apply BayesBay to a regression task involving observed data generated from a discontinuous piecewise function. Throughout, we consider the function
\[\begin{split}f(x) = \left\{
\begin{array}{ll}
1 & \quad x \leq 1 \\
20 & \quad 1 < x \leq 2.5 \\
0 & \quad 2.5 < x \leq 3 \\
-3 & \quad 3 < x \leq 4 \\
-10 & \quad 4 < x \leq 6 \\
-20 & \quad 6 < x \leq 6.5 \\
25 & \quad 6.5 < x \leq 8 \\
0 & \quad 8 < x \leq 9 \\
10 & \quad 9 < x \leq 10, \\
\end{array}
\right.\end{split}\]
Our goal is to infer \(f(x)\) from noisy observations \(\mathbf{d}_{obs} = f(x_i) + \mathcal{N}(0, \sigma)\) via Bayesian sampling.
This tutorial comprises: