The tutorial begins by providing a background on Bayesian inference and the key probability distributions used in MCMC sampling. It then presents a simple MCMC sampler implementation using the Metropolis-Hastings algorithm.
The core of the tutorial focuses on Bayesian linear models and Bayesian neural networks. For the linear models, the tutorial covers the definition of the likelihood function, prior distributions, and the MCMC sampling implementation. It then extends the approach to Bayesian neural networks, discussing the structure of neural networks and the challenges in sampling the multi-modal posterior distributions that arise.
The tutorial provides detailed Python code implementations for all the models, along with instructions for running the code and interpreting the results. It highlights the strengths and weaknesses of the MCMC approach for Bayesian neural networks, and the need for further improvements in convergence diagnosis methods.
Overall, this tutorial serves as a comprehensive guide for researchers and practitioners interested in implementing Bayesian neural networks using MCMC sampling techniques.
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