Geometric analysis for the metropolis algorithm on Lipschitz domains

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

On the Ergodicity of the Adaptive Metropolis Algorithm on Unbounded Domains

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...

Variable Transformation to Obtain Geometric Ergodicity in the Random-walk Metropolis Algorithm

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition (Jarner and Hansen, 2000). Many applications, including Bayesian analysis with conjugate priors of logistic and Poisson regression and of log-linear models for categorical data result in posterior distributions that are not super-exponentially lig...

Some Geometric Properties for a Class of Non-Lipschitz Domains

In this paper, we introduce a class C, of domains of RN , N ≥ 2, which satisfy a geometric property of the inward normal (such domains are not Lipschitz, in general). We begin by giving various results concerning this property, and we show the stability of the solution of the Dirichlet problem when the domain varies in C.

Efficient Numerical Solution of Neumann Problems on Complicated Domains

In this paper, we will consider elliptic PDEs with Neumann boundary conditions on complicated domains. The discretization is performed by composite finite elements. The a-priori error analysis typically is based on the precise knowledge of the regularity of the solution. However, the constants in the regularity estimates, possibly, depend critically on the geometric details of the domain and th...