TransportMaps.Samplers¶

Classes

Class	Description
Sampler	Generic sampler of distribution `d`
ImportanceSampler	Importance sampler of distribution `d`, with biasing distribution `d_bias`
RejectionSampler	Rejection sampler of distribution `d`, with biasing distribution `d_bias`
MetropolisHastingsIndependentProposalsSampler	Metropolis-Hastings with independent proposal sampler of distribution `d`, with proposal distribution `d_prop`
MetropolisHastingsSampler	Metropolis-Hastings sampler of distribution `d`, with proposal `d_prop`
MetropolisHastingsWithinGibbsSampler	Metropolis-Hastings within Gibbs sampler of distribution `d`, with proposal `d_prop` and Gibbs block sampling `blocks`
HamiltonianMonteCarloSampler	Hamiltonian Monte Carlo sampler of distribution `d`, with proposal distribution `d_prop`

Functions

Function	Description
ess	Compute the Effective Sample Size (ESS) of a sample

Documentation

class TransportMaps.Samplers.Sampler(d)[source]¶

Generic sampler of distribution d

This main class just mirrors all the sampling methods provided by the distribution d.

Parameters:	d (Distributions.Distribution) – distribution to sample from.

rvs(m, *args, **kwargs)[source]¶

Generate \(m\) samples and weights from the distribution

Parameters:	m (int) – number of samples to generate
Returns:	(`tuple` (`ndarray` [\(m,d\)], `ndarray` [\(m\)])) – list of points and weights

class TransportMaps.Samplers.ImportanceSampler(d, d_bias)[source]¶

Importance sampler of distribution d, with biasing distribution d_bias

Parameters:	d (Distributions.Distribution) – distribution to sample from d_bias (Distributions.Distribution) – biasing distribution

rvs(m, mpi_pool_tuple=(None, None))[source]¶

Generate \(m\) samples and importance weights from the distribution

Parameters:	m (int) – number of samples to generate
Returns:	(`tuple` (`ndarray` [\(m,d\)], `ndarray` [\(m\)])) – list of points and weights

class TransportMaps.Samplers.RejectionSampler(d, d_bias)[source]¶

Rejection sampler of distribution d, with biasing distribution d_bias

Parameters:	d (Distributions.Distribution) – distribution to sample from d_bias (Distributions.Distribution) – biasing distribution

rvs(m, *args, **kwargs)[source]¶

Generate \(m\) samples and importance weights from the distribution

Parameters:	m (int) – number of samples to generate
Returns:	(`tuple` (`ndarray` [\(m,d\)], `ndarray` [\(m\)])) – list of points and weights

class TransportMaps.Samplers.MetropolisHastingsIndependentProposalsSampler(d, d_prop)[source]¶

Metropolis-Hastings with independent proposal sampler of distribution d, with proposal distribution d_prop

Parameters:	d (Distributions.Distribution) – distribution to sample from d_prop (Distributions.Distribution) – proposal distribution

rvs(m, x0=None, mpi_pool_tuple=(None, None))[source]¶

Generate a Markov Chain of \(m\) equally weighted samples from the distribution d

Parameters:	m (int) – number of samples to generate x0 (`ndarray` [\(1,d\)]) – initial chain value mpi_pool_tuple (`tuple` [2] of `mpi_map.MPI_Pool`) – pool of processes to be used for the evaluation of `d` and `prop_d`
Returns:	(`tuple` (`ndarray` [\(m,d\)], `ndarray` [\(m\)])) – list of points and weights

class TransportMaps.Samplers.MetropolisHastingsSampler(d, d_prop)[source]¶

Metropolis-Hastings sampler of distribution d, with proposal d_prop

Parameters:	d (Distributions.Distribution) – distribution \(\pi({\bf x})\) to sample from d_prop (Distributions.ConditionalDistribution) – conditional distribution \(\pi({\bf y}\vert{\bf x})\) to use as a proposal

rvs(m, x0=None, mpi_pool_tuple=(None, None))[source]¶

Generate a Markov Chain of \(m\) equally weighted samples from the distribution d

Parameters:	m (int) – number of samples to generate x0 (`ndarray` [\(1,d\)]) – initial chain value mpi_pool_tuple (`tuple` [2] of `mpi_map.MPI_Pool`) – pool of processes to be used for the evaluation of `d` and `prop_d`
Returns:	(`tuple` (`ndarray` [\(m,d\)], `ndarray` [\(m\)])) – list of points and weights

class TransportMaps.Samplers.MetropolisHastingsWithinGibbsSampler(d, d_prop_list, block_list=None)[source]¶

Metropolis-Hastings within Gibbs sampler of distribution d, with proposal d_prop and Gibbs block sampling blocks

Parameters:	d (Distributions.Distribution) – distribution \(\pi({\bf x})\) to sample from d_prop (`list` of `Distributions.ConditionalDistribution`) – conditional distribution \(\pi({\bf y}\vert{\bf x})\) to use as a proposal block_list (`list` of `list`) – list of blocks of variables

rvs(m, x0=None, mpi_pool_tuple=(None, None))[source]¶

Generate a Markov Chain of \(m\) equally weighted samples from the distribution d

Parameters:	m (int) – number of samples to generate x0 (`ndarray` [\(1,d\)]) – initial chain value mpi_pool_tuple (`tuple` [2] of `mpi_map.MPI_Pool`) – pool of processes to be used for the evaluation of `d` and `prop_d`
Returns:	(`tuple` (`ndarray` [\(m,d\)], `ndarray` [\(m\)])) – list of points and weights

class TransportMaps.Samplers.HamiltonianMonteCarloSampler(d)[source]¶

Hamiltonian Monte Carlo sampler of distribution d, with proposal distribution d_prop

This sampler requires the package pyhmc.

Parameters:	d (Distributions.Distribution) – distribution to sample from

rvs(m, x0=None, display=False, n_steps=1, persistence=False, decay=0.9, epsilon=0.2, window=1, return_logp=False, return_diagnostics=False, random_state=None)[source]¶: Generate a Markov Chain of \(m\) equally weighted samples from the distribution d

See also

pyhmc for arguments

TransportMaps.Samplers.ess(samps, quantile=0.99, do_xcorr=False, plotting=False, plot_lag=50, fig=None)[source]¶

Compute the Effective Sample Size (ESS) of a sample

The minimum ESS over all the dimension is returned. Cross-correlation can be optionally used as well in the determination of the ESS. Plotting of the correlation decay can be shown.

The ESS is computed as \(\lfloor m/\kappa \rfloor\), where

\[\kappa = 1 + \sum_{c_i>b_i} c_i \;,\]

\(c_i\) is the auto-correlation at lag \(i\) and \(b_i\) is the quantile-confidence interval for the \(i\)-th value of auto-correlation (i.e. only significant auto-correlation values are summed up).

Parameters:	samps (`ndarray` [\(m,d\)]) – \(d\)-dimensional sample on which to compute the ESS quantile (float) – condifence interval quantile do_xcorr (bool) – whether to compute and use the auto-correlation function plotting (bool) – whether to plot auto/cross-correlation decays plot_lag (int) – how many lags to plot fig (figure) – handle to a figure
Returns:	(`int`) – minimum ESS across the \(d\) dimensions