The Maxlike sampler

Find the maximum likelihood using various methods in scipy

Name	maxlike
Version	1.0
Author(s)	SciPy developers
URL	http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.optimize.minimize.html
Citation(s)
Parallelism	serial

This sampler attempts to find the single point in parameter space with the highest likelihood. It wraps a variety of samplers from the scipy.minimize package.

These methods are all iterative and local, not global, so they can only find the nearest local maximum likelihood point from the parameter starting position.

Maximum likelihood using these kinds of methods can be something of a dark art. Results can be quite sensitive to the starting position and exact parameters used, so if you need precision ML then you should carefully explore the robustness of your results.

These samplers are wrapped in the current version of scipy:

• Nelder-Mead

• Powell

• CG

• BFGS

• Newton-CG

• Anneal (deprecated by scipy)

• L-BFGS-B

• TNC

• COBYLA

• SLSQP

• dogleg

• trust-ncg

• bobyqa (requires pybobyqa)

Each has different (dis)advantages, and which works best will depend on your particular application. The default in CosmoSIS is Nelder-Mead. See the references on the scipy URL above for more details.

Some methods can also output an estimated covariance matrix at the likelihood peak.

Installation

Requires SciPy 0.14 or above. This is installed by the CosmoSIS bootstrap, but if you are installing manually you can get it with the command:

pip install scipy #to install centrally, may require sudo

pip install scipy –user #to install just for you

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.

Name	Type	Default	Description
method	string	Nelder-Mead	The minimization method to use.
tolerance	real	1e-3	The tolerance parameter for termination. Meaning depends on the sampler - see scipy docs.
maxiter	integer	1000	Maximum number of iterations of the sampler
output_ini	string	(empty)	if present, save the resulting parameters to a new ini file with this name
output_covmat	string	(empty)	if present and the sampler supports it, save the estimated covariance to this file
output_block	string	(empty)	if present, save the complete datablock output to this directory
max_posterior	bool	False	find the max a posteriori point instead of max like (includes the priors as well)
repeats	integer	1	number of times to repeat the minimization from different starting points
reiterations	integer	1	number of times to continue the minimization from the end of the previous run
start_method	string	(empty)	method to use to generate starting points. Options are ‘prior’ and ‘chain’, ‘cov’, or blank for default start’
start_input	string	(empty)	input file to use for starting points if start_method is ‘chain’ or ‘cov’
nsteps	integer	varies	number of steps to output at once