Research map / Probabilistic and scientific modeling / Variational and generative sampling

Contour Monte Carlo: Sampling via Energy Level Sets

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Stochastic gradient MCMC

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Proposes Contour Monte Carlo, a sampler that works on energy level sets of the target distribution, motivated by slow convergence of NUTS on ill-conditioned, heavy-tailed, or near-degenerate targets.

Problem

MCMC samplers such as the NUTS implementations in Stan and Turing.jl converge slowly on ill-conditioned, heavy-tailed, or near-degenerate target distributions.

Approach

Samples from the target by exploiting its energy level sets (contours), rather than standard gradient-based trajectories over the full state space; details beyond the abstract are not stated.

Experimental setup

Baselines: NUTS (Stan) NUTS (Turing.jl)

Builds on: NUTS

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