DRAM

The DRAM class is imported using the following command:

>>> from UQpy.sampling.mcmc.DRAM import DRAM
class DRAM(pdf_target=None, log_pdf_target=None, args_target=None, burn_length=0, jump=1, dimension=None, seed=None, save_log_pdf=False, concatenate_chains=True, initial_covariance=None, covariance_update_rate=100, scale_parameter=None, delayed_rejection_scale=0.2, save_covariance=False, random_state=None, n_chains=None, nsamples=None, nsamples_per_chain=None)[source]

Delayed Rejection Adaptive Metropolis algorithm [28] [10]

In this algorithm, the proposal density is Gaussian and its covariance C is being updated from samples as C = scale_parameter * C_sample where C_sample is the sample covariance. Also, the delayed rejection scheme is applied, i.e, if a candidate is not accepted another one is generated from the proposal with covariance delayed_rejection_scale ** 2 * C.

Parameters:

  • pdf_target (Union[Callable, list[Callable], None]) –

    Target density function from which to draw random samples. Either pdf_target or log_pdf_target must be provided (the latter should be preferred for better numerical stability).

    If pdf_target is a callable, it refers to the joint pdf to sample from, it must take at least one input x, which are the point(s) at which to evaluate the pdf. Within MCMC the pdf_target is evaluated as: p(x) = pdf_target(x, *args_target)

    where x is a numpy.ndarray of shape :code:`(nsamples, dimension) and args_target are additional positional arguments that are provided to MCMC via its args_target input.

    If pdf_target is a list of callables, it refers to independent marginals to sample from. The marginal in dimension j is evaluated as: p_j(xj) = pdf_target[j](xj, *args_target[j]) where x is a numpy.ndarray of shape (nsamples, dimension)

  • log_pdf_target (Union[Callable, list[Callable], None]) –

    Logarithm of the target density function from which to draw random samples. Either pdf_target or log_pdf_target must be provided (the latter should be preferred for better numerical stability).

    Same comments as for input pdf_target.

  • args_target (Optional[tuple]) – Positional arguments of the pdf / log-pdf target function. See pdf_target

  • burn_length (int) – Length of burn-in - i.e., number of samples at the beginning of the chain to discard (note: no thinning during burn-in). Default is \(0\), no burn-in.

  • jump (int) – Thinning parameter, used to reduce correlation between samples. Setting jump=n corresponds to skipping n-1 states between accepted states of the chain. Default is \(1\) (no thinning).

  • dimension (Optional[int]) – A scalar value defining the dimension of target density function. Either dimension and n_chains or seed must be provided.

  • seed (Optional[list]) –

    Seed of the Markov chain(s), shape (n_chains, dimension). Default: zeros(n_chains x dimension).

    If seed is not provided, both n_chains and dimension must be provided.

  • save_log_pdf (bool) – Boolean that indicates whether to save log-pdf values along with the samples. Default: False

  • concatenate_chains (bool) – Boolean that indicates whether to concatenate the chains after a run, i.e., samples are stored as a numpy.ndarray of shape (nsamples * n_chains, dimension) if True, (nsamples, n_chains, dimension) if False. Default: True

  • n_chains (Optional[int]) – The number of Markov chains to generate. Either dimension and n_chains or seed must be provided.

  • initial_covariance (Optional[float]) – Initial covariance for the gaussian proposal distribution. Default: I(dim)

  • covariance_update_rate (float) – Rate at which covariance is being updated, i.e., every k0 iterations. Default: \(100\)

  • scale_parameter (Optional[float]) – Scale parameter for covariance updating. Default: \(2.38^2/dim\)

  • delayed_rejection_scale (float) – Scale parameter for delayed rejection. Default: \(1/5\)

  • save_covariance (bool) – If True, updated covariance is saved in attribute adaptive_covariance. Default: False

  • random_state (Union[None, int, RandomState]) – Random seed used to initialize the pseudo-random number generator. Default is None.

  • nsamples (Optional[int]) – Number of samples to generate.

  • nsamples_per_chain (Optional[int]) – Number of samples to generate per chain.

run_one_iteration(current_state, current_log_pdf)[source]

Run one iteration of the mcmc chain for DRAM algorithm, starting at current state - see MCMC class.