Asymptotic variance for random walk Metropolis chains in high dimensions: logarithmic growth via the Poisson equation
نویسندگان
چکیده
منابع مشابه
On the Poisson Equation for Metropolis-hastings Chains
This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis-Hastings chain Φ. The scheme is based on the idea of weak approximation and gives rise to a natural sequence of control variates for the ergodic average Sk(F ) = (1/k) ∑k i=1 F (Φi), where F is the force function in the Poisson equation. The main results show that the sequence...
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The probability distribution of random walks on linear structures generated by random walks in d-dimensional space, Pd(r, t), is analytically studied for the case ξ ≡ r/t1/4 ≪ 1. It is shown to obey the scaling form Pd(r, t) = ρ(r)tξfd(ξ), where ρ(r) ∼ r 2−d is the density of the chain. Expanding fd(ξ) in powers of ξ, we find that there exists an infinite hierarchy of critical dimensions, dc = ...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2019
ISSN: 0001-8678,1475-6064
DOI: 10.1017/apr.2019.40