摘要翻译:
本文结合两个平均场自旋系统,即所谓的平均场Ising模型和Blume-Emery-Griffiths模型,研究了Metropolis算法。在这两个例子中,对于某些参数,建议链的幼稚选择引起了一个缓慢混合的大都市链,即一个谱隙指数快速减小的链(在问题的维数$N$内)。在这里,我们展示了如何在建议链中的一个微小的变化可以避免这个问题,保持平均计算成本与通常的大都市成本相似。更准确地说,我们证明了,在适当的变体中,大都市链有一个以1/n为单位的多项式递减的谱间隙。该方法利用能量的某种对称结构,在起始状态的能级内允许适当的跳跃。
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英文标题:
《Metropolis algorithm and equienergy sampling for two mean field spin
systems》
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作者:
Bassetti Federico, Leisen Fabrizio
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Computation 计算
分类描述:Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
In this paper we study the Metropolis algorithm in connection with two mean--field spin systems, the so called mean--field Ising model and the Blume--Emery--Griffiths model. In both this examples the naive choice of proposal chain gives rise, for some parameters, to a slowly mixing Metropolis chain, that is a chain whose spectral gap decreases exponentially fast (in the dimension $N$ of the problem). Here we show how a slight variant in the proposal chain can avoid this problem, keeping the mean computational cost similar to the cost of the usual Metropolis. More precisely we prove that, with a suitable variant in the proposal, the Metropolis chain has a spectral gap which decreases polynomially in 1/N. Using some symmetry structure of the energy, the method rests on allowing appropriate jumps within the energy level of the starting state.
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PDF链接:
https://arxiv.org/pdf/704.0906