scholarly journals Convergence Rates of Attractive-Repulsive MCMC Algorithms

2021 ◽  
Author(s):  
Yu Hang Jiang ◽  
Tong Liu ◽  
Zhiya Lou ◽  
Jeffrey S. Rosenthal ◽  
Shanshan Shangguan ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Mcmc Algorithms

scholarly journals Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

2014 ◽  
Vol 46 (04) ◽  
pp. 1059-1083 ◽  
Author(s):  
Qifan Song ◽  
Mingqi Wu ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Weak Convergence ◽  
Stochastic Approximation ◽  
Convergence Rates ◽  
Gain Factor ◽  
Single Chain ◽  
Practical Applications ◽  
Mcmc Algorithms ◽  
Factor Sequence ◽  
Number Of Iterations

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

scholarly journals On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

2015 ◽  
Vol 52 (3) ◽  
pp. 811-825
Author(s):  
Yves Atchadé ◽  
Yizao Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Mixing Time ◽  
Regularity Conditions ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Variation Distance ◽  
Importance Resampling

In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, is O(n-1). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of order O(n-1/2).

scholarly journals Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

2014 ◽  
Vol 46 (4) ◽  
pp. 1059-1083 ◽  
Author(s):  
Qifan Song ◽  
Mingqi Wu ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Weak Convergence ◽  
Stochastic Approximation ◽  
Convergence Rates ◽  
Gain Factor ◽  
Single Chain ◽  
Practical Applications ◽  
Mcmc Algorithms ◽  
Factor Sequence ◽  
Number Of Iterations

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

scholarly journals On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

2015 ◽  
Vol 52 (03) ◽  
pp. 811-825
Author(s):  
Yves Atchadé ◽  
Yizao Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Mixing Time ◽  
Regularity Conditions ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Variation Distance ◽  
Importance Resampling

In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, isO(n-1). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of orderO(n-1/2).

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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