Abstract

The growing availability of large datasets has increased interest in stochastic processes that can capture stylized facts such as non-Gaussian tails, long memory, and even non-Markov dynamics. While such models are often easy to simulate, parameter estimation remains challenging. Simulation-based inference offers a promising way forward, but existing methods typically require large training datasets or complex architectures and frequently yield confidence (credible) regions that fail to attain their nominal values, raising questions on the reliability of estimates for the very features that motivate the use of these models. In this paper, we propose a two-stage, MCMC-free framework for amortized posterior inference for intractable stochastic processes. First, we sequentially learn the posterior density across parameter dimensions through telescoping density ratio estimation. Second, we use Chebyshev polynomial approximations to efficiently generate independent posterior samples, enabling accurate inference even when MCMC mixes poorly. We further extend amortization to improve estimator reusability and demonstrate the method’s effectiveness on trawl processes, an infinitely divisible generalization of univariate Gaussian processes.