We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the Iwahori-Hecke algebra.

We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the Iwahori-Hecke algebra.

Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is sufficient but not necessary. We construct irreversible deformation of a given reversible algorithm capable of dramatic improvement of sampling from known dist...

We present a generalisation of the standard well known and widely used Metropolis-Hastings algorithm which, unlike the Metropolis-Hastings sampler, can mix well over a target distribution which has separated and possibly narrow modes. The idea arose via a consideration of a space augmented slice sampler where the uniform space required to be sampled for the slice sampler, say I , is augmented w...

In this paper we define and study new directional Metropolis–Hastings algorithms that propose states in hyperplanes. Each iteration in directional Metropolis–Hastings algorithms consist of three steps. First a direction is sampled by an auxiliary variable. Then a potential new state is proposed in the subspace defined by this direction and the current state. Lastly, the potential new state is a...

We describe a Metropolis-Hastings algorithm for sampling formal concepts, i.e., closed (item-) sets, according to any desired strictly positive distribution. Important applications are (a) estimating the number of all formal concepts as well as (b) discovering any number of interesting, non-redundant, and representative local patterns. Setting (a) can be used for estimating the runtime of algor...

We review recent work concerning optimal proposal scalings for Metropolis-Hastings MCMC algorithms, and adaptive MCMC algorithms for trying to improve the algorithm on the fly.

This paper presents a geometric approach to estimating subspaces as elements of complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices [elements of the unitary group U( )]. Subspace estimation or tracking then corresponds to inferences...