  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 $3 \times 2$ 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 $\mathcal{O}(10)$ 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
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 $(\mathcal{O}(50))$ dimension
numbers, typical of tomographic large-scale structure analyses.
