Profile Sampler for Cobaya

This package provides a sampler for the Cobaya framework that allows obtaining the profile likelihood of a given parameter of interest.

Overview

The Profiler sampler inherits from the standard Minimize to loop various minimization processes on a selected parameter. In the end, the output will be a SampleCollection of minimized points, storing the selected points and their corresponding $\chi^2_{min}$ (or maximum likelihood through exponentiation). It is also possible to obtain the posterior equivalent of that by setting ignore_prior=False.

This sampler works best if an MCMC run is already present on the same parameter space. Indeed, this allows the optimization of the initial point for minimizations and the covariance matrix of parameters.

Also, through the Profiler.products method, it is possible to recover the full set of minima among the parallel runs (bets_of parameter). This allows us to ensure that the minimum recovered is the absolute minimum. Furthermore, the dispersion of these points gives a rough idea of the accuracy of the minimization process.

Parameters

• profiled_param: string identifying the profiled parameter. It must be part of the sampled parameters!
• profiled_values: list of profiled values at which to perform the minimization.
• start: as an alternative to explicitly providing a list of values, one can set a range by passing a starting and ending point with a number of steps in between those. Note that profiled_values takes precedence w.r.t. this method!
• stop: ending point of the range.
• steps: number of steps between start and stop. Note that the range is obtained using numpy.linspace and setting endpoint=True!

The rest of the parameters are the same as the Minimize sampler, thus refer to its documentation.

Usage

Here, you can find a straightforward example to run the Profiler on a Gaussian likelihood.

A similar implementation of this code was used in 2405.04455 to profile the tensor-to-scalar ratio and the tensor spectral tilt (code under development at the time of paper writing). There you can also find more details on the theory of profile likelihoods.

Bibliography

Please cite the following associated paper if you use this code in your work:

@article{Galloni:2024lre,
    author = "Galloni, Giacomo and Henrot-Versill\'e, Sophie and Tristram, Matthieu",
    title = "{Robust constraints on tensor perturbations from cosmological data: A comparative analysis from Bayesian and frequentist perspectives}",
    eprint = "2405.04455",
    archivePrefix = "arXiv",
    primaryClass = "astro-ph.CO",
    doi = "10.1103/PhysRevD.110.063511",
    journal = "Phys. Rev. D",
    volume = "110",
    number = "6",
    pages = "063511",
    year = "2024"
}