🤖 AI Summary
This work proposes a novel small-sample approximation method for Markov chain Monte Carlo (MCMC) simulation that dramatically improves sampling efficiency while preserving the target stationary distribution. Conventional MCMC approaches require millions of sample paths to adequately approximate the stationary distribution, incurring substantial computational costs. In contrast, the proposed technique leverages eigenvalue decomposition to reduce the number of required simulation paths to as few as ten, without compromising distributional fidelity. By integrating Wasserstein distance–based evaluation with explicit modeling of the stationary distribution, the method achieves accuracy comparable to traditional MCMC while significantly reducing estimator variance. This advancement enhances both the stability and computational tractability of MCMC-based inference, offering a scalable alternative for applications where large-scale path simulation is prohibitive.
📝 Abstract
This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed eigenvalue-based methodology reduces the number of paths required for Monte Carlo from as many as 1,000,000 to as few as 10 (depending on the simulation time horizon $T$), and delivers comparable, distributionally robust results, as measured by the Wasserstein distance. The proposed methodology also produces a significant variance reduction in the steady-state distribution.