Bernoulli最新文献_第9页

Bayes-optimal prediction with frequentist coverage control 具有频率覆盖控制的贝叶斯最优预测

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-28 DOI: 10.3150/22-bej1484

P. Hoff

引用次数: 15

Diffusion means in geometric spaces 扩散指的是几何空间

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-25 DOI: 10.3150/22-bej1578

B. Eltzner, Pernille Hansen, S. Huckemann, S. Sommer

{"title":"Diffusion means in geometric spaces","authors":"B. Eltzner, Pernille Hansen, S. Huckemann, S. Sommer","doi":"10.3150/22-bej1578","DOIUrl":"https://doi.org/10.3150/22-bej1578","url":null,"abstract":"We introduce a location statistic for distributions on non-linear geometric spaces, the diffusion mean, serving as an extension and an alternative to the Fr'echet mean. The diffusion mean arises as the generalization of Gaussian maximum likelihood analysis to non-linear spaces by maximizing the likelihood of a Brownian motion. The diffusion mean depends on a time parameter $t$, which admits the interpretation of the allowed variance of the diffusion. The diffusion $t$-mean of a distribution $X$ is the most likely origin of a Brownian motion at time $t$, given the end-point distribution $X$. We give a detailed description of the asymptotic behavior of the diffusion estimator and provide sufficient conditions for the diffusion estimator to be strongly consistent. Particularly, we present a smeary central limit theorem for diffusion means and we show that joint estimation of the mean and diffusion variance rules out smeariness in all directions simultaneously in general situations. Furthermore, we investigate properties of the diffusion mean for distributions on the sphere $mathbb S^n$. Experimentally, we consider simulated data and data from magnetic pole reversals, all indicating similar or improved convergence rate compared to the Fr'echet mean. Here, we additionally estimate $t$ and consider its effects on smeariness and uniqueness of the diffusion mean for distributions on the sphere.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45207548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Hypothesis testing for equality of latent positions in random graphs 随机图中潜在位置相等性的假设检验

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-23 DOI: 10.3150/22-bej1581

Xinjie Du, M. Tang

{"title":"Hypothesis testing for equality of latent positions in random graphs","authors":"Xinjie Du, M. Tang","doi":"10.3150/22-bej1581","DOIUrl":"https://doi.org/10.3150/22-bej1581","url":null,"abstract":"We consider the hypothesis testing problem that two vertices $i$ and $j$ of a generalized random dot product graph have the same latent positions, possibly up to scaling. Special cases of this hypothesis test include testing whether two vertices in a stochastic block model or degree-corrected stochastic block model graph have the same block membership vectors, or testing whether two vertices in a popularity adjusted block model have the same community assignment. We propose several test statistics based on the empirical Mahalanobis distances between the $i$th and $j$th rows of either the adjacency or the normalized Laplacian spectral embedding of the graph. We show that, under mild conditions, these test statistics have limiting chi-square distributions under both the null and local alternative hypothesis, and we derived explicit expressions for the non-centrality parameters under the local alternative. Using these limit results, we address the model selection problems including choosing between the standard stochastic block model and its degree-corrected variant, and choosing between the ER model and stochastic block model. The effectiveness of our proposed tests are illustrated via both simulation studies and real data applications.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48847113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Is there an analog of Nesterov acceleration for gradient-based MCMC? 对于基于梯度的MCMC，是否有Nesterov加速度的类似物？

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-01 DOI: 10.3150/20-BEJ1297

Ma Yi-An, Niladri S. Chatterji, Xiang Cheng, Nicolas, Flammarion, P. Bartlett, Michael I. Jordan

引用次数: 44

Inference without compatibility: Using exponential weighting for inference on a parameter of a linear model 不兼容的推理:使用指数加权对线性模型的参数进行推理

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-01 DOI: 10.3150/20-BEJ1280

Michael Law, Y. Ritov

引用次数: 1

A convolution formula for the local time of an Itô diffusion reflecting at 0 and a generalized Stroock–Williams equation 反映在0的Itô扩散局部时间的卷积公式和广义Stroock–Williams方程

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-01 DOI: 10.3150/20-BEJ1295

J. Jakubowski, Maciej Wiśniewolski

引用次数: 3

Context-specific independencies in stratified chain regression graphical models 分层链回归图形模型中上下文特定的独立性

IF 1.5 2区数学

Bernoulli Pub Date : 2021-05-01 DOI: 10.3150/20-BEJ1302

F. Nicolussi, M. Cazzaro

{"title":"Context-specific independencies in stratified chain regression graphical models","authors":"F. Nicolussi, M. Cazzaro","doi":"10.3150/20-BEJ1302","DOIUrl":"https://doi.org/10.3150/20-BEJ1302","url":null,"abstract":"Graphical models are a useful tool with increasing diffusion. In the categorical variable framework, they provide important visual support to understand the relationships among the considered variables. Besides, particular chain graphical models are suitable to represent multivariate regression models. However, the associated parameterization, such as marginal log-linear models, is often difficult to interpret when the number of variables increases because of a large number of parameters involved. On the contrary, conditional and marginal independencies reduce the number of parameters needed to represent the joint probability distribution of the variables. In compliance with the parsimonious principle, it is worthwhile to consider also the so-called context-specific independencies, which are conditional independencies holding for particular values of the variables in the conditioning set. In this work, we propose a particular chain graphical model able to represent these context-specific independencies through labeled arcs. We provide also the Markov properties able to describe marginal, conditional, and context-specific independencies from this new chain graph. Finally, we show the results in an application to a real data set.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":"27 1","pages":"2091-2116"},"PeriodicalIF":1.5,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48491136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Testing and estimation for clustered signals 聚类信号的测试与估计

IF 1.5 2区数学

Bernoulli Pub Date : 2021-04-29 DOI: 10.3150/21-bej1355

Hongyuan Cao, W. Wu

引用次数: 2

Multilevel bootstrap particle filter 多级自举粒子滤波器

IF 1.5 2区数学

Bernoulli Pub Date : 2021-04-16 DOI: 10.3150/22-bej1468

K. Heine, D. Burrows

引用次数: 0

Asymptotics for densities of exponential functionals of subordinators 次子指数泛函密度的渐近性