Asymptotic Variance and Convergence Rates of Nearly-Periodic MCMC Algorithms

Asymptotic Variance and Convergence Rates of Nearly-Periodic MCMC Algorithms

On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, correspo...

Covariance Ordering for Discrete and Continuous Time Markov Chains

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

Permanence and Uniformly Asymptotic Stability of Almost Periodic Positive Solutions for a Dynamic Commensalism Model on Time Scales

In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.

A cautionary tale on the efficiency of some adaptive Monte Carlo Schemes

There is a growing interest in the literature for adaptive Markov Chain Monte Carlo methods based on sequences of random transition kernels {Pn} where the kernel Pn is allowed to have an invariant distribution πn not necessarily equal to the distribution of interest π (target distribution). These algorithms are designed such that as n → ∞, Pn converges to P , a kernel that has the correct invar...