Exercise: Bayesian Approaches

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

1. Apply Bayesian linear regression with gaussian basis functions to a data sampled from a nonlionear function of your interest and see how \(\alpha\), \(\beta\), \(M\) and \(N\) affect the performance.

2. Compute the log evidence for the above models and see how that is related to the predictin errors.

3. Try forward-backward algorithm with different chains and inputs.

4. In the dynamic Bayesian inference example, we assumed that only one or no sensor raises a signal at each time. Consider a case where each sensor responds independently with others, possibly with different degree of reliabilites, i.e., setting of the observation models.