Related papers: Geodesic Slice Sampler for Multimodal Distribution…
We propose a theoretically justified and practically applicable slice sampling based Markov chain Monte Carlo (MCMC) method for approximate sampling from probability measures on Riemannian manifolds. The latter naturally arise as posterior…
Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling…
Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…
Elliptical slice sampling is a widely used gradient-free Markov chain Monte Carlo algorithm that is tuning-free and capable of adapting to local characteristics of the target distribution. However, its primary limitation is that sampling…
Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…
In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic on a suitable Riemannian manifold. We then combine the notion…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension.…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family…
We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the…
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing…
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…
Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from polytopes in R^n specified by m inequalities. The walk is a discrete-time simulation of a stochastic…