Transformed-space sampling
--------------------------

The distribution of the corrupted speech does not have a closed form.
This is because of the non-linearity in the mismatch function (which relates the signals of the speech, noise, and corrupted speech).
The compensation methods in :ref:`parametrised` therefore approximate the corrupted speech distribution.
The papers in the :ref:`bibliography` introduce an alternative approximation that uses sampling.
In the limit, it finds the exact likelihood of one observation.
The classes and functions below implement this method.

:class:`SampleObservationDensity <noise.sample_observation_density.SampleObservationDensity>`
uses sequential importance resampling (see :func:`sequentialImportanceResample <sequential_importance_resample.sequentialImportanceResample>`\ )
to evaluate the integral in the likelihood expression.
This integral is most naturally written over the speech, noise and the phase factor, but, as the papers in the :ref:`bibliography` detail, can be transformed into an integral over the phase factor and a substitute variable.
In this domain, the integrand is factorised (see :class:`QuasiConditionalFactorGenerator <noise.factor_integrand.QuasiConditionalFactorGenerator>`\ ) and a proposal distribution (see :class:`proposalForFactor <factor_integrand.proposalForFactor>`\ ) is defined.
It then becomes feasible to apply sequential importance re-sampling.

..  autoclass:: noise.sample_observation_density.SampleObservationDensity
    :members:
    :undoc-members:

..  autoclass:: noise.factor_integrand.QuasiConditionalFactorGenerator
    :members: given

..  autoclass:: noise.factor_integrand.PostponedFactorGenerator
    :members:

Target density
^^^^^^^^^^^^^^

..  autoclass:: noise.factor_integrand.SubstituteFactor
    :members:
    :undoc-members:

..  autoclass:: noise.factor_integrand.SubstituteFactorOneSource
    :members:
    :undoc-members:


Proposal distribution
^^^^^^^^^^^^^^^^^^^^^

..  autofunction:: noise.factor_integrand.proposalForFactor

..  autoclass:: noise.sample_observation_density.PhaseProposer
    :members:
    :undoc-members:

..  autoclass:: noise.sample_observation_density.AlwaysProposer
    :members:
    :undoc-members:

..  autoclass:: noise.sample_observation_density.DummyFactor
    :members:
    :undoc-members:

..  autofunction:: noise.sample_observation_density.oneWeighter


Partial samples
^^^^^^^^^^^^^^^

..  autoclass:: noise.factor_integrand.PartialSample(channelPhase = numpy.empty ((0, 1)), substitute = numpy.empty ((0, 1)))
    :members:
    :undoc-members:

..  autofunction:: noise.factor_integrand.appendChannelPhase

..  autofunction:: noise.factor_integrand.appendSubstitute