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# The Pmc sampler

## Adaptive Importance Sampling

Name: **Pmc**

Version: **1.0**

Author(s): **CosmoSIS Team**

URL: **https://bitbucket.org/joezuntz/cosmosis**

Cite: ** MNRAS 405.4 2381-2390 (2010) **

Parallel: **embarrassing**

Population Monte-Carlo uses importance sampling with an initial distribution that is gradually adapted as more samples are taken and their likelihood found.

At each iteration some specified number of samples are drawn from a mixed Gaussian distribution. Their posteriors are then evaluated and importance weights calculated. This approximate distribution is then used to update the Gaussian mixture model so that it more closely mirrors the underlying distribution.

Components are dropped if they are found not to be necessary.

This is a python re-implementation of the CosmoPMC alogorithm in the cited paper.

##Installation

No special installation required; everything is packaged with CosmoSIS

##Parameters

These parameters can be set in the sampler's section in the ini parameter file.

If no default is specified then the parameter is required. A listing of "(empty)" means a blank string is the default.

Parameter | Type | Meaning | Default |
---|---|---|---|

iterations | integer | Number of iterations (importance updates) of PMC | 30 |

components | integer | Number of components in the Gaussian mixture | 5 |

samples_per_iteration | integer | Number of samples per iteration of PMC | 1000 |

final_samples | integer | Samples to take after the updating of the mixture is complete | 5000 |

student | boolean | Do not use this. It is a not yet functional attempt to use a Student t mixture. | F |

nu | float | Do not use this. It is the nu parameter for the non-function Student t mode. | 2.0 |

Updated