Metropolis - Hastings for diffusive deterministic dynamical systems
We provide the code that supports the results reported in the manuscript Monte Carlo sampling in diffusive dynamical systems. We implement here the Metropolis-Hastings algorithm for the estimation of a weighted distribution of the displacement.
In the folder Examples
we illustrate its basic use for two dynamical systems: Lorentz gas and Box map. For its use in other deterministic dynamical systems the dynamics should be introduced and the function rMCMC
. The steps to do it are always the same, namely:
-
The dynamical system is coded, taking care of defining it for both positive and negative times. You might use the package DynamicalSystems.jl .
-
The main parameters, i.e. the mean Lyapunov exponent and the diffusion coefficient are estimated or passed if they are previously known.
-
The two proposals are coded based on the dynamics. It would depend on the nature of the dynamical system (e.g. map or flow) and its dimension.
-
The observable
$r_{t_o}$ is defined and used insiderMCMC
. In our examples, it is thedistance
for the Lorentz gas andabs(evolution - 1/2)
for the box map.
Installation
From within Julia do
julia> Pkg.clone(https://github.com/dapias/MCMC-DIFFUSION.git")