On Markov Chain Monte Carlo Acceleration

Abstract

Markov chain Monte Carlo (MCMC) methods are currently enjoying a surge of interest within the statistical community. The goal of this work is to formalize and support two distinct adaptive strategies that typically accelerate the convergence of an MCMC algorithm. One approach is through resampling; the other incorporates adaptive switching of the transition kernel. Support is both by analytic arguments and simulation study. Application is envisioned in low-dimensional but nontrivial problems. Two pathological illustrations are presented. Connections with reparameterization are discussed as well as possible difficulties with infinitely often adaptation.     

Generalized Evolutionary Point Processes: Model Specifications and Model Comparison

Methodology and Computing in Applied Probability - Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the...     

Integrability of linear and nonlinear evolution equations and the associated nonlinear fourier transforms

The inverse spectral method is a nonlinear Fourier transform method for solving certain equations. Here, we emphasize that such transforms should be considered in their own right. We also elucidate further the connection between the Fourier transform and inverse spectral methods by establishing that linear equations can also be solved through the inverse spectral method.     

Smoothness Properties and Gradient Analysis Under Spatial Dirichlet Process Models

When analyzing point-referenced spatial data, interest will be in the first order or global behavior of associated surfaces. However, in order to better understand these surfaces, we may also be interested in second order or local behavior, e.g., in the rate of change of a spatial surface at a given location in a given direction. In a Bayesian parametric setting, such smoothness analysis has been pursued by Banerjee and Gelfand (2003) and Banerjee et al. (2003). We study continuity and differentiability of random surfaces in the Bayesian nonparametric setting proposed by Gelfand et al. (2005), which is based on the formulation of a spatial Dirichlet process (SDP). We provide conditions under which the random surfaces sampled from a SDP are smooth. We also obtain complete distributional theory for the directional finite difference and derivative processes associated with those random surfaces. We present inference under a Bayesian framework and illustrate our methodology with a simulated dataset.     

The lattice of flats and its underlying flag matroid polytope

LetM be a matroid andF the collection of all linear orderings of bases ofM, orflags ofM. We define the flag matroid polytope Δ(F). We determine when two vertices of Δ(F) are adjacent, and provide a bijection between maximal chains in the lattice of flats ofM and certain maximal faces of Δ(F). Supported in part by NSA grant MDA904-95-1-1056.     

The algebra of Weyl symmetrised polynomials and its quantum extension

The Algebra of Weyl symmetrised polynomials in powers of Hamiltonian operatorsP andQ which satisfy canonical commutation relations is constructed. This algebra is shown to encompass all recent infinite dimensional algebras acting on two-dimensional phase space. In particular the Moyal bracket algebra and the Poisson bracket algebra, of which the Moyal is the unique one parameter deformation are shown to be different aspects of this infinite algebra. We propose the introduction of a second deformation, by the replacement of the Heisenberg algebra forP, Q with aq-deformed commutator, and construct algebras ofq-symmetrised Polynomials.Research supported in part by the Department of Energy under Grant DE/FG02/88/ER25065, and by a grant from the Alfred P. Sloan Foundation and the Fulbright Commission     

Mediating Order and Modulating Porosity by Controlled Hydrolysis in a Phosphonate Monoester Metal–Organic Framework

A crystalline and permanently porous copper phosphonate monoester framework has been synthesized from a tetraaryl trigonal phosphonate monoester linker. This material has a surface area over 1000 m² g^?1, as measured by N₂ sorption, the highest reported for a phosphonate‐based metal–organic framework (MOF). The monoesters result in hydrophobic pore surfaces that give a low heat of adsorption for CO₂ and low calculated selectivity for CO₂ over N₂ and CH₄ in binary mixtures. By careful manipulation of synthetic conditions, it is possible to selectively remove some of the monoesters lining the pore to form a hydrogen phosphonate while giving an isomorphous structure. This increases the affinity of the framework for CO₂ giving higher ambient uptake, higher heat of adsorption, and much higher calculated selectivity for CO₂ over both N₂ and CH₄. Formation of the acid groups is noteworthy as complexation with the parent acid gives a different structure.     

On the efficiency of semi-closed blast inhibitors

Numerical efficiency analysis of those blast inhibitors (BI) consisting of a vertical cylinder open at the top is presented and compared with the existing data from other authors. It was proven computationally that such low-height “semi-closed” BI do not provide blast wave suppression according to the minimum practical requirements (overpressure and pressure impulse reduction at several times) and, if one wishes to compare, other existing criteria (Bowen injury diagrams and similar guidelines adopted in different countries).