Diffusion limits of the random walk Metropolis algorithm in high dimensions

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring high-dimensional measures found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.Comment: Published in at http://dx.doi.org/10.1214/10-AAP754 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Geometric erogdicity of a bead-spring pair with stochastic Stokes forcing

We consider a simple model for the uctuating hydrodynamics of a exible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes uid velocity field. This is a generalization of previous models which have used linear spring forces as well as white-in-time uid velocity fields. We follow previous work combining control theoretic arguments, Lyapunov functions, and hypo-elliptic diffusion theory to prove exponential convergence via a Harris chain argument. To this, we add the possibility of excluding certain "bad" sets in phase space in which the assumptions are violated but from which the systems leaves with a controllable probability. This allows for the treatment of singular drifts, such as those derived from the Lennard-Jones potential, which is an novel feature of this work

Fish and shellfish diseases in culture systems IX Screening of bacteria for identification

Taxonomy is a significant aspect -of study, for a microbiologist, in any application. But, the problems are greater for an aquatic microbiologist as compared to those of a medical microbiologist, because studies have been made in depth in medical microbiology

Fish and shellfish diseases in culture systems V. Prophylaxis and Disease check up

As the nature of the culture ecosystem differs, the applicability of the undermen tioned guidelines may also vary. In the enclosed water culture ecosystem, disease prevent ion is relatively easier than that of the open sea culture ecosystems in cages and pens wherein control over the ecosystem can be only minimal or precticallynil

Fish and shelfish diseases in culture systems XI. Furunculosis

Furunculosis is an important systemic bacterial disease found among finfishes both in culture systems and in the wild. This disease was originally described by Emmerich and Weibel in 1894 isolating the causative bacterium from hatchery trout from Germany

Fish and shellfish diseases in culture systems I. Concept of disease and pathogen

Just as in land animals or in agricultural crops fishes and shellfishes living in the aquatic environment are susceptible to diseases whenever certain abnormal biological, physological or environmental changes occur

Fish and shellfish diseases in culture systems III. Defenses against infection

When a pathogen infects a host, there may be some initial abnormalities, in the host because of infection, multiplication of .the pathogen, release of microbial toxin and due to the efforts made by the host to defend itself from the pathoge