Multi-dimensional parameter spaces are commonly encountered in astroparticle physics theories that attempt to capture novel phenomena. However, they often possess complicated posterior geometries that are expensive to traverse using techniques traditional to this community. Effectively sampling these spaces is crucial to bridge the gap between experiment and theory. Several recent innovations, which are only beginning to make their way into this field, have made navigating such complex posteriors possible. These include GPU acceleration, automatic differentiation, and neural-network-guided reparameterization. We apply these advancements to astroparticle physics experimental results in the context of novel neutrino physics and benchmark their performances against traditional nested sampling techniques. Compared to nested sampling alone, we find that these techniques increase performance for both nested sampling and Hamiltonian Monte Carlo, accelerating inference by factors of $\sim 100$ and $\sim 60$, respectively. As nested sampling also evaluates the Bayesian evidence, these advancements can be exploited to improve model comparison performance while retaining compatibility with existing implementations that are widely used in the natural sciences.

Learning energy-based model (EBM) requires MCMC sampling of the learned model as the inner loop of the learning algorithm. However, MCMC sampling of EBM in data space is generally not mixing, because the energy function, which is usually parametrized by deep network, is highly multi-modal in the data space. This is a serious handicap for both the theory and practice of EBM. In this paper, we propose to learn EBM with a flow-based model serving as a backbone, so that the EBM is a correction or an exponential tilting of the flow-based model. We show that the model has a particularly simple form in the space of the latent variables of the flow-based model, and MCMC sampling of the EBM in the latent space, which is a simple special case of neural transport MCMC, mixes well and traverses modes in the data space. This enables proper sampling and learning of EBM.