Related papers: Suppressing Random Walks in Markov Chain Monte Car…
To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…
Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans through graph partitioning. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…
We study the rate of convergence to equilibrium of the self-repellent random walk and its local time process on the discrete circle $\mathbb{Z}_n$. While the self-repellent random walk alone is non-Markovian since the jump rates depend on…
Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by…
We study decentralized learning over networks where data are distributed across nodes without a central coordinator. Random walk learning is a token-based approach in which a single model is propagated across the network and updated at each…
Markov chain Monte Carlo (MCMC) algorithms have played a significant role in statistics, physics, machine learning and others, and they are the only known general and efficient approach for some high-dimensional problems. The random walk…
Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…
The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…
The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…
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…
Preliminary mission design of low-thrust spacecraft trajectories in the Circular Restricted Three-Body Problem is a global search characterized by a complex objective landscape and numerous local minima. Formulating the problem as sampling…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We present a Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm for detecting hidden variables in a continuous time Bayesian network (CTBN), which uses reversible jumps in the sense defined by (Green 1995). In common with several…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…