Monte Carlo
-----------

*Sequential importance sampling* is an instantiation of *importance sampling*, which approximates integrals by sampling.
The instantiation merely specifies that sampling takes place per dimension.
The technique becomes useful with :ref:`re-sampling <resampling>`\ , which between dimensions redistributes the probability mass to the most likely regions of space.

..  autofunction:: probability.sequential_importance_resample.sequentialImportanceResample(targetFactors, proposers, number, weighters=…, combiners=…, combiners=…, emptySample=…)

The following are small helper functions.

..  autofunction:: probability.sequential_importance_resample.densityWeighter

..  autofunction:: probability.sequential_importance_resample.unnormalisedDensityWeighter

..  autofunction:: probability.sequential_importance_resample.massWeighter

..  autofunction:: probability.sequential_importance_resample.appendToVector

..  autofunction:: probability.sequential_importance_resample.appendToTuple

.. _resampling:

Re-sampling
^^^^^^^^^^^

The element that makes sequential importance re-sampling useful is re-sampling.
It approximates a categorical distribution by a distribution with integer weights.
It can be seen as a way of re-focusing the probability mass on high-probability areas of the space.

..  autofunction:: probability.categorical.resample(source, number, strategy=systematicResampling)

..  autofunction:: probability.categorical.multinomialResampling

..  autofunction:: probability.categorical.residualResampling

..  autofunction:: probability.categorical.systematicResampling