Kernel Estimators of Asymptotic Variance for Adaptive Markov Chain Monte Carlo
نویسندگان
چکیده
We study the asymptotic behavior of kernel estimators of asymptotic variances (or long-run variances) for a class of adaptive Markov chains. The convergence is studied both in L and almost surely. The results apply to Markov chains as well and improve on the existing literature by imposing weaker conditions. We illustrate the results with applications to the GARCH(1, 1) Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.
منابع مشابه
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...
متن کاملTO ” KERNEL ESTIMATORS OF ASYMPTOTIC VARIANCE FOR ADAPTIVE MARKOV CHAIN MONTE CARLO ” By Yves
This is a supplement to the paper " Kernel estimators of asymp-totic variance for adaptive Markov Chain Monte Carlo " and contains the proofs to Theorems 4.1-4.3. For improved readability, we recall the theorems and their assumptions. 1. Statement of the theorems. A1 For each θ ∈ Θ, P θ is phi-irreducible, aperiodic with invariant distribution π. There exists a measurable function V : X → [1, ∞...
متن کاملAdaptive Markov Chain Monte Carlo Confidence Intervals
In Adaptive Markov Chain Monte Carlo (AMCMC) simulation, classical estimators of asymptotic variances are inconsistent in general. In this work we establish that despite this inconsistency, confidence interval procedures based on these estimators remain consistent. We study two classes of confidence intervals, one based on the standard Gaussian limit theory, and the class of so-called fixed-b c...
متن کاملStrong Consistency of Multivariate Spectral Variance Estimators in Markov Chain Monte Carlo
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and...
متن کاملCovariance 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010