Related papers: The Boomerang Sampler
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
Markov chain 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 availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
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…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…
Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an…
Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Medical and social sciences demand sampling techniques which are robust, reliable, replicable and have the least dissimilarity between the samples obtained. Majority of the applications of sampling use randomized sampling, albeit with…
In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…
Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance…
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…
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…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact…
The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can…
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires…