Getting Started

Copy the include folder to your project.

Example Usage (Random Walk a Normal distribution)

#include <mcmc/samplers/random_walk_metropolis_hastings_sampler.hpp>
#include <mcmc/markov_chain.hpp>

void main()
{
  Eigen::VectorXf initial_state(1);
  initial_state[0] = 450.0f;
  
  Eigen::MatrixXf covariance_matrix(1, 1);
  covariance_matrix.setIdentity();

  mcmc::random_walk_metropolis_hastings_sampler<Eigen::VectorXf, Eigen::MatrixXf> sampler(
    [ ] (const Eigen::VectorXf& state)
    {
      return normal_distribution_density(500.0f, 1.0f, state[0]);
    },
    covariance_matrix, 
    100.0f);

  mcmc::markov_chain<Eigen::VectorXf> markov_chain(initial_state);
  for(auto i = 0; i < 100000; ++i)
  {
    markov_chain.update(sampler);
    std::cout << markov_chain.state().format(Eigen::IOFormat()) << "\n";
  }
}

See the tests for the details and usage of individual samplers.

Notes

• All kernel functions should return logarithmic scale values unless explicitly stated otherwise.
• Boost/Math provides probability density functions for common distributions.

Coverage

The following list is based on Michael Clark's MCMC algorithms directory with a few extensions. Please feel free to add any missing samplers.

• Adaptive Directional Metropolis-within-Gibbs
• Adaptive Equi-Energy Sampler
• Adaptive Griddy-Gibbs
• Adaptive Hamiltonian Monte Carlo
• Adaptive Metropolis
• Adaptive Metropolis-within-Gibbs
• Adaptive-Mixture Metropolis
• Affine-Invariant Ensemble Sampler
• Automated Factor Slice Sampler
• Componentwise Hit-And-Run Metropolis
• Delayed Rejection Adaptive Metropolis
• Delayed Rejection Metropolis
• Differential Evolution Markov Chain
• Elliptical Slice Sampler
• Equi-Energy Sampler
• Gibbs Sampler
• Griddy-Gibbs
• Hamiltonian Monte Carlo
• Hamiltonian Monte Carlo with Dual-Averaging
• Hessian-Hamiltonian Monte Carlo
• Hit-And-Run Metropolis
• Independence Metropolis
• Interchain Adaptation
• Metropolis-Adjusted Langevin Algorithm
• Metropolis-Coupled Markov Chain Monte Carlo
• Metropolis-Hastings 1953
• Metropolis-within-Gibbs
• Multiple-Try Metropolis
• No-U-Turn Sampler
• Oblique Hyperrectangle Slice Sampler
• Preconditioned Crank-Nicolson
• Random Dive Metropolis-Hastings
• Random-Walk Metropolis
• Reflective Slice Sampler
• Refractive Sampler
• Reversible-Jump
• Riemannian Manifold Hamiltonian Monte Carlo
• Riemannian Manifold Metropolis Adjusted Langevin Algorithm
• Robust Adaptive Metropolis
• Sequential Adaptive Metropolis-within-Gibbs
• Sequential Metropois-within-Gibbs
• Slice Sampler
• Stochastic Gradient Fisher Scoring
• Stochastic Gradient Langevin Dynamics
• Stochastic Gradient Nose-Hoover Thermostat
• T-Walk
• Tempered Hamiltonian Monte Carlo
• Univariate Eigenvector Slice Sampler
• Updating Sequential Adaptive Metropolis-within-Gibbs
• Updating Sequential Metropolis-within-Gibbs

The following list contains stochastic Variational Inference (VI) samplers.

• Black Box Sampler
• Doubly Stochastic Sampler
• Nonparametric Sampler
• Particle Mirror Descent Sampler
• Stein Variational Gradient Descent

Future Work

• More samplers.
• Quasi-random number generators (van der Corput-Halton sequence, Faure-Niederreiter sequence, Hammersley set, Poisson disk sampling, Sobol low-discrepancy sequence, ...).

Acknowledgements

Several samplers in this library are inspired by Keith O'Hara's library with the same name.