Hamiltonian Monte Carlo Algorithm

Module containing Markov Chains Monte Carlo sampler utilizing Hamiltonian Monte Carlo (HMC) algorithm. HMC uses Hamiltonian dynamics to sample by moving a particle through the posterior to perform numerical integration that is then corrected by Metropolis acceptance criterion.

class monte.hamiltonian_mc.HamiltonianMC(log_posterior, log_posterior_gradient)

Bases: BaseSampler

__init__(log_posterior, log_posterior_gradient) → None

Initializes the problem sampler object

Parameters:

• log_posterior (callable) – Log-probability of the target distribution to be sampled from

• log_posterior_gradient (callable) – Log-probability of the gradient of the target distribution to be sampled from

sample(iter, warmup, theta, epsilon, l, metric=None, lag=1, **kwargs)

Samples from the log_posterior distribution

Parameters:

• iter (int) – Number of iterations of the algorithm

• warmup (int) – Number of warmup steps of the algorithm. These are discarded so that the only samples recorded are the ones obtained after the Markov chain has reached the stationary distribution

• theta (ndarray) – Vector of initial values of parameter(s)

• epsilon (float) – Discretization time or timestep

• l (int) – Number of leapfrog steps taken

• metric (ndarray) – Covariance matrix of the momentum vector sampling distribution

• lag (int, optional) – Sampler lag. Parameter specifying every how many iterations will the sample be recorded. Used to limit autocorrelation of the samples. If lag=1, every sample is recorded, if lag=3 each third sample is recorded, etc. , defaults to 1

Returns:

Numpy arrays of samples and acceptance information for every algorithm iteration.

Return type:

ndarray, ndarray