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Assessment of Gradient-Based Samplers in Standard Cosmological Likelihoods
Arrykrishna Mootoovaloo, Jaime Ruiz-Zapatero, Carlos García-García, David Alonso
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We assess the usefulness of gradient-based samplers, such as the No-U-Turn Sampler (NUTS), by comparison with traditional Metropolis-Hastings algorithms, in tomographic 3 ×2 point analyses. Specifically, we use the DES Year 1 data and a simulated future LSST-like 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 (Campagne et al. 2023), and we use it to derive parameter constraints from both datasets using the NUTS algorithm as implemented in {\S}4, and the Metropolis-Hastings algorithm as implemented in Cobaya (Lewis 2013). When quantified in terms of the number of effective number of samples taken per likelihood evaluation, we find a relative efficiency gain of 𝒪(10) in favour of NUTS. However, this efficiency is reduced to a factor ∼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 ∼4.5 times larger for both experiments. We validate these results making use of analytical multi-variate 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 (𝒪(50)) dimension numbers, typical of tomographic large-scale structure analyses.
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