一类具有消失加性噪声的自动回归模型的截止点

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Scandinavian Journal of Statistics Pub Date : 2024-08-22 DOI:10.1111/sjos.12748

Balázs Gerencsér, Andrea Ottolini

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引用次数: 0

摘要

我们分析了欧几里得空间上的自动回归马尔可夫链的收敛率，该链取决于一个参数，其中每一步随机选择的坐标都由其他坐标的噪声阻尼加权平均值代替。该模型与德菲内蒂（de Finetti）在分析部分可交换数据时引入的某种贝叶斯方案有关，因而引起了人们的兴趣。我们的主要结果表明，当 n 变大时（对应于噪声消失），就会出现截断现象。

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Cutoff for a class of auto‐regressive models with vanishing additive noise

We analyze the convergence rates for a family of auto‐regressive Markov chains on Euclidean space depending on a parameter , where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The interest in the model comes from the connection with a certain Bayesian scheme introduced by de Finetti in the analysis of partially exchangeable data. Our main result shows that, when n gets large (corresponding to a vanishing noise), a cutoff phenomenon occurs.

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来源期刊

Scandinavian Journal of Statistics 数学-统计学与概率论

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia. It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications. The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems. The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.