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We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…
In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…
We establish conditions under which Metropolis-Hastings (MH) algorithms with a position-dependent proposal covariance matrix will or will not have the geometric rate of convergence. Some of the diffusions based MH algorithms like the…
Global search and optimization of long-duration, low-thrust spacecraft trajectories with the indirect method is challenging due to a complex solution space and the difficulty of generating good initial guesses for the costate variables.…
Markov chain Monte Carlo (MCMC) samplers are numerical methods for drawing samples from a given target probability distribution. We discuss one particular MCMC sampler, the MALA-within-Gibbs sampler, from the theoretical and practical…
Antithetic coupling is a general stratification strategy for reducing Monte Carlo variance without increasing the simulation size. The use of the antithetic principle in the Monte Carlo literature typically employs two strata via antithetic…
Several recent publications investigated Markov-chain modelling of linear optimization by a $(1,\lambda)$-ES, considering both unconstrained and linearly constrained optimization, and both constant and varying step size. All of them assume…
We present an approach to interface branching random walks with Markov chain Monte Carlo sampling, and to switch seamlessly between the two. The approach is discussed in the context of auxiliary-field quantum Monte Carlo (AFQMC) but is…
The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis-Hastings (MH)…
Monte Carlo algorithms simulate some prescribed number of samples, taking some random real time to complete the computations necessary. This work considers the converse: to impose a real-time budget on the computation, which results in the…
We study the split Conformal Prediction method when applied to Markovian data. We quantify the gap in terms of coverage induced by the correlations in the data (compared to exchangeable data). This gap strongly depends on the mixing…
Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
Sampling from high-dimensional distributions has wide applications in data science and machine learning but poses significant computational challenges. We introduce Subspace Langevin Monte Carlo (SLMC), a novel and efficient sampling method…
Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…
Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…