This set of mainly C++ files allow one to do probabilistic inversion of (Linear) models. What this means is that it takes a function, or an algorithm, accompanied by (synthetic) data and tries to invert for the input parameters.

It does so in a probabilistic sense; there's is not one solution, only the solution. This solution contains the probabilities for all possible combinations of parameters. This allows for heavily underdetermined problems to still have a meaningful solution without the need for stabilization.

Typically (which might have been some decades ago, as methods have advanced), one would sample our so-called posterior distrubtion by randomly proposing models (based on some prior information) and calculate the misfit. This process is done many times, and each time a model satisfies some criterion, it increases the likelihood of a solution in that 'neighborhood' (since one can not infenitessimally explore the model space, we avarage over cells). A typical algorithm for this is Metropolis-Hastings.

However, if one has a very poor idea of where the parameters would be, the proposals will mostly be rejeceted. This is where Hamiltonian Monte Carlo comes in. It not only uses the prior information, but also the local curvature of the misfit functional (typically a scalar function on many dimensions, \( \chi = f(x_1,x_2,x_3, \ldots , x_n) \)) to direct the new proposal towards a likeli model. This propagation takes no history of proposals, so it is called a Markov Chain Monte Carlo (MCMC) method.

For a more detailed explanation, I do strongly recommend taking a look at larsgeb.github.io where a full technical document is present, with more mathematical rigour. The purpose of this site is merely the documentation and clarification of code in a nice online format.

I recommend taking a first look at the classes in montecarlo.hpp and auxiliary.hpp, which define all the constructs for the theoretical parts. The rest is mostly tools for linear algebra or random number generators. Interesting, but not essential.