In this paper, we study the asymptotic efficiency of the delayed rejection strategy. In particular, the efficiency of the delayed rejection Metropolis-Hastings algorithm is compared to that of the regular Metropolis algorithm. To allow for a fair comparison, the study is carried under optimal mixing conditions for each of these algorithms. After introducing optimal scaling results for the delay...

that is, the sample covariance matrix of the history of the chain plus a (small) constant ǫ > 0 multiple of the identity matrix I. The lower bound on the eigenvalues of Sn induced by the factor ǫI is theoretically convenient, but practically cumbersome, as a good value for the parameter ǫ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitl...

This paper investigates the use of linear representations of trees (i.e. mappings from the set of trees into a finite dimensional vector space which are induced by rational series on trees) in the context of structured data learning. We argue that this representation space can be more appealing than the space of trees to handle machine learning problems involving trees. Focusing on a tree serie...

The Metropolis-Hastings algorithm transforms a given stochastic matrix into a reversible stochastic matrix with a prescribed stationary distribution. We show that this transformation gives the minimum distance solution in an L1 metric.

Abstract Under a compactness assumption, we show that a φ-irreducible and aperiodic MetropolisHastings chain is geometrically ergodic if and only if its rejection probability is bounded away from unity. In the particular case of the Independence Metropolis-Hastings algorithm, we obtain that the whole spectrum of the induced operator is contained in (and in many cases equal to) the essential ran...

This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman, and Tamminen [8], for target distributions with a non-compact support. The conditions ensuring a strong law of large numbers and a central limit theorem require that the tails of the target density decay super-exponentially, and have regular enough convex con...

This paper considers high-dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well-understood and it is now well-known how to scale their proposal distribution variances. For the random walk Metropolis algorithm, convergence during the transient phase is extremely regular to the extent that the algorithm’s sample path actually r...

We propose a probabilistic interpretation of a class of reversible communicating processes. The rate of forward and backward computing steps, instead of being given explicitly, is derived from a set of formal energy parameters. This is similar to the Metropolis-Hastings algorithm. We find a lower bound on energy costs which guarantees that a process converges to a probabilistic equilibrium stat...

The square-root principle is known to achieve low search time for peer-to-peer search techniques that do not utilize query routing indices (e.g., query flooding or random walk searches). Under this principle, each object is probed with probability proportional to the square root of its query popularity. Existing search methods realize the square-root principle by using either object replication...

The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete patterns for the Finite Element Method (FEM). Appropriate meshes together with the FEM approach constitute an effective tool to deal with differential problems...