Applies a bijector to the MCMC's state space

The transformed transition kernel enables fitting a bijector which serves to decorrelate the Markov chain Monte Carlo (MCMC) event dimensions thus making the chain mix faster. This is particularly useful when the geometry of the target distribution is unfavorable. In such cases it may take many evaluations of the target_log_prob_fn for the chain to mix between faraway states.

mcmc_transformed_transition_kernel(inner_kernel, bijector, name = NULL)

Arguments

inner_kernel	TransitionKernel-like object which has a target_log_prob_fn argument.
bijector	bijector or list of bijectors. These bijectors use forward to map the inner_kernel state space to the state expected by inner_kernel$target_log_prob_fn.
name	string prefixed to Ops created by this function. Default value: NULL (i.e., "transformed_kernel").

Value

a Monte Carlo sampling kernel

Details

The idea of training an affine function to decorrelate chain event dims was presented in Parno and Marzouk (2014). Used in conjunction with the Hamiltonian Monte Carlo transition kernel, the Parno and Marzouk (2014) idea is an instance of Riemannian manifold HMC (Girolami and Calderhead, 2011).

The transformed transition kernel enables arbitrary bijective transformations of arbitrary transition kernels, e.g., one could use bijectors tfb_affine, tfb_real_nvp, etc. with transition kernels mcmc_hamiltonian_monte_carlo, mcmc_random_walk_metropolis, etc.

References

• Matthew Parno and Youssef Marzouk. Transport map accelerated Markov chain Monte Carlo. arXiv preprint arXiv:1412.5492, 2014.

• Mark Girolami and Ben Calderhead. Riemann manifold langevin and hamiltonian monte carlo methods. In Journal of the Royal Statistical Society, 2011.

See also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()