(sec:details-of-mcmc)=
# Details of MCMC

Here we provide formal and detailed discussions on stochastic processes in general, including random walk and Gaussian process examples, and then on Markov Chain Monte Carlo and the Metropolis Hasting algorithm.


* {ref}`sec:StochasticProcesses` introduces the concept of a stochastic process, with code examples and several exercises.

* {ref}`sec:ExampleRandomWalk` provides a basic example.

* {ref}`sec:StochasticGP` introduces the Gaussian process, which we will revisit in detail in {ref}`sec:RootGP`.

* {ref}`sec:MarkovChains` has a detailed introduction to Markov chains, with examples.

* {ref}`sec:MetropolisHastings` provides a complete definition and some exercises.