Review for NeurIPS paper: Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation: Bayesian inference for latent Gaussian models and beyond

Weaknesses: My main questions regarding the paper: 1) When computing the Laplace approximation, this still requires calculation of the Hessian, which I believe is with respect to the latent (theta). This is referred to as W in Algorithm 1. Would it be possible to comment further on the kind of trade-off between implementing full-HMC, versus the overhead of calculating the Hessian. I think this is the issue you are referring to in the second paragraph of the discussion section, whereby you mention higher-order automatic differentiation. I assume you stick to analytical Hessians (e.g. For example "Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models" by Zhang and Sutton jointly sample over hyperparameters and parameters to overcome similar funnel-like behaviours to that of the Gaussian latent variable models that you explore.