Assessment of gradient-based samplers in standard cosmological likelihoods.

We assess the usefulness of gradient-based samplers, such as the no-U-turn sampler (NUTS), by comparison with traditional Metropolis–Hastings (MH) algorithms, in tomographic |$3\times 2$| point analyses. Specifically, we use the Dark Energy Survey (DES) Year 1 data and a simulated dataset for the Large Synoptic Survey Telescope (LSST) survey as representative examples of these studies, containing a significant number of nuisance parameters (20 and 32, respectively) that affect the performance of rejection-based samplers. To do so, we implement a differentiable forward model using jax-cosmo , and we use it to derive parameter constraints from both data sets using the nuts algorithm implemented in numpyro , and the Metropolis–Hastings algorithm as implemented in cobaya. When quantified in terms of the number of effective number of samples taken per likelihood evaluation, we find a relative efficiency gain of |$\mathcal {O}(10)$| in favour of NUTS. However, this efficiency is reduced to a factor |$\sim 2$| when quantified in terms of computational time, since we find the cost of the gradient computation (needed by nuts) relative to the likelihood to be |$\sim 4.5$| times larger for both experiments. We validate these results making use of analytical multivariate distributions (a multivariate Gaussian and a Rosenbrock distribution) with increasing dimensionality. Based on these results, we conclude that gradient-based samplers such as NUTS can be leveraged to sample high-dimensional parameter spaces in Cosmology, although the efficiency improvement is relatively mild for moderate (⁠|$\mathcal {O}(50)$|⁠) dimension numbers, typical of tomographic large-scale structure analyses. [ABSTRACT FROM AUTHOR]