The Multinest sampler
Author(s): Farhan Feroz,Mike Hobson
Cite: arXiv:0809.3437, arXiv:0704.3704, arXiv:1306.2144
Nested sampling is a method designed to calculate the Bayesian Evidence of a distribution, for use in comparing multiple models to see which fit the data better.
The evidence is the integral of the likelihood over the prior; it is equivalent to the probability of the model given the data (marginalizing over the specific parameter values): B = P(D|M) = \int P(D|Mp) P(p|M) dp
Nested sampling is an efficient method for evaluating this integral using members of an ensemble of live points and steadily replacing the lowest likelihood point with a new one from a gradually shrinking proposal so and evaluating the integral in horizontal slices.
Multinest is a particularly sophisticated implementation of this which can cope with multi-modal distributions using a k-means clustering algorithm and a proposal made from a collection of ellipsoids.
The output from multinest is not a set of posterior samples, but rather a set of weighted samples - when making histograms or parameter estimates these must be included.
The primary mulitnest parameter is the number of live points in the ensemble. If this number is too small you will get too few posterior samples in the result, and if it is too large the sampling will take a long time. A few hundred seems to be reasonable for typical cosmology problems.
One odd feature of the multinest output is that it doesn't save any results until it has done a complete run through the parameter space. It then starts again on a second run, and sometimes a third depending on the parameters. So don't worry if you don't see any lines in the output file for a while.
No special installation required; everything is packaged with CosmoSIS
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.
|max_iterations||integer||Maximum number of samples to take|
|live_points||integer||Number of live points in the ensemble|
|feedback||bool||Print out progression information from multinest||T|
|multinest_outfile_root||str||In addition to CosmoSIS output, save a collection of multinest output files||(empty)|
|resume||bool||If you previously set multinest_outfile_root you can restart an interrupted chain with this setting||F|
|update_interval||integer||Frequency of printed output from inside multinest||200|
|random_seed||integer||Seed to use for random proposal; -1 to generate from current time. Allows re-running chains exactly||-1|
|ins||boolean||Use Importance Nested Sampling (INS) mode - see papers for more info||True|
|constant_efficiency||bool||Constant efficiency mode - see papers||N|
|efficiency||float||Target efficiency for INS - see papers||0.1|
|log_zero||float||Log-probabilities lower than this value are considered to be -infinity||-1e5|
|tolerance||float||Target error on evidence||0.1|
|mode_separation||bool||Optimize for multi-modal or other odd likelihoods - split into different proposal modes||N|
|max_modes||integer||If multi-modal, maximum number of allowed modes||100|
|cluster_dimensions||integer||Look for multiple modes only on the first dimensions||-1|
|mode_ztolerance||float||If multi-modal, get separate stats for modes with this evidence difference||0.5|
|wrapped_params||str||Space separated list of parameters (section--name) that should be given periodic boundary conditions. Can help sample params that hit edge of prior.||(empty)|