# minimize sampler¶

Synopsis: Posterior/likelihood maximization (i.e. -log(post) and chi^2 minimization). Jesus Torrado

This is a maximizator for posteriors or likelihoods, based on scipy.optimize.minimize and Py-BOBYQA (added in 2.0).

Note

BOBYQA tends to work better on Cosmological problems with the default settings.

It works more effectively when run on top of a Monte Carlo sample: just change the sampler for minimize with the desired options, and it will use as a starting point the maximum a posteriori (MAP) or best fit (maximum likelihood, o minimal $$\chi^2$$) found so far, as well as the covariance matrix of the sample for rescaling of the parameter jumps.

As text output, it produces two different files:

• [output prefix].minimum.txt, in the same format as Cobaya samples, but containing a single line.
• [output prefix].minimum, the equivalent GetDist-formatted file.

If ignore_prior: True, those files are named .bestfit[.txt] instead of minimum, and contain the best-fit (maximum of the likelihood) instead of the MAP (maximum of the posterior).

When called from a Python script, Cobaya’s run function returns the updated info and the products described below in the method products.

It is recommended to run a couple of parallel MPI processes: it will finally pick the best among the results.

Warning

Since Cobaya is often used on likelihoods featuring numerical noise (e.g. Cosmology), we have reduced the default accuracy criterion for the minimizers, so that they converge in a limited amount of time. If your posterior is fast to evaluate, you may want to refine the convergence parameters (see override options in the yaml below).

## Options and defaults¶

Simply copy this block in your input yaml file and modify whatever options you want (you can delete the rest).

# Default arguments for the -logposterior/chi^2 minimizer

sampler:
minimize:
# Method: bobyqa|scipy
method: bobyqa
# Minimizes the full posterior (False) or just the likelihood (True)
# Likelihood maximization is subject to prior bounds!
ignore_prior: False
# Maximum number of iterations (default: practically infinite)
max_evals: 1e6d
# Treatment of unbounded parameters: confidence level to use
# (Use with care if there are likelihood modes close to the edge of the prior)
confidence_for_unbounded: 0.9999995  # 5 sigmas of the prior
# Override keyword arguments for scipy.optimize.minimize() or pybobyqa.solve()
# scipy:
#  - https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html
#  - options for individual methods
override_scipy:
# option: value
# bobyqa:
#  - https://numericalalgorithmsgroup.github.io/pybobyqa/build/html/userguide.html
override_bobyqa:
# option: value
# Relaxed convergence criterion for numerically-noisiy likelihoods
rhoend: 0.05


## Minimize class¶

class samplers.minimize.minimize(info_sampler, model, output, resume=False, modules=None)
initialize()

Prepares the arguments for scipy.minimize.

run()

Runs scipy.minimize

close(*args)

Determines success (or not), chooses best (if MPI) and produces output (if requested).

products()

Returns a dictionary containing:

• minimum: OnePoint that maximizes the posterior or likelihood (depending on ignore_prior).
• result_object: instance of results class of scipy or pyBOBYQA.
• M: inverse of the affine transform matrix (see below). None if no transformation applied.
• X0: offset of the affine transform matrix (see below) None if no transformation applied.

If non-trivial M and X0 are returned, this means that the minimizer has been working on an affine-transformed parameter space $$x^\prime$$, from which the real space points can be obtained as $$x = M x^\prime + X_0$$. This inverse transformation needs to be applied to the coordinates appearing inside the result_object.