Bernoulli最新文献_第3页

Characterization of the second order random fields subject to linear distributional PDE constraints 线性分布PDE约束下二阶随机场的特征

IF 1.5 2区数学

Bernoulli Pub Date : 2023-01-17 DOI: 10.3150/23-bej1588

Iain Henderson, P. Noble, O. Roustant

{"title":"Characterization of the second order random fields subject to linear distributional PDE constraints","authors":"Iain Henderson, P. Noble, O. Roustant","doi":"10.3150/23-bej1588","DOIUrl":"https://doi.org/10.3150/23-bej1588","url":null,"abstract":"Let $L$ be a linear differential operator acting on functions defined over an open set $mathcal{D}subset mathbb{R}^d$. In this article, we characterize the measurable second order random fields $U = (U(x))_{xinmathcal{D}}$ whose sample paths all verify the partial differential equation (PDE) $L(u) = 0$, solely in terms of their first two moments. When compared to previous similar results, the novelty lies in that the equality $L(u) = 0$ is understood in the sense of distributions, which is a powerful functional analysis framework mostly designed to study linear PDEs. This framework enables to reduce to the minimum the required differentiability assumptions over the first two moments of $(U(x))_{xinmathcal{D}}$ as well as over its sample paths in order to make sense of the PDE $L(U_{omega})=0$. In view of Gaussian process regression (GPR) applications, we show that when $(U(x))_{xinmathcal{D}}$ is a Gaussian process (GP), the sample paths of $(U(x))_{xinmathcal{D}}$ conditioned on pointwise observations still verify the constraint $L(u)=0$ in the distributional sense. We finish by deriving a simple but instructive example, a GP model for the 3D linear wave equation, for which our theorem is applicable and where the previous results from the literature do not apply in general.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48871886","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: 3

Exponential concentration for geometric-median-of-means in non-positive curvature spaces 非正曲率空间中几何均值的指数集中

IF 1.5 2区数学

Bernoulli Pub Date : 2022-11-30 DOI: 10.3150/22-BEJ1569

H. Yun, B. Park

{"title":"Exponential concentration for geometric-median-of-means in non-positive curvature spaces","authors":"H. Yun, B. Park","doi":"10.3150/22-BEJ1569","DOIUrl":"https://doi.org/10.3150/22-BEJ1569","url":null,"abstract":"In Euclidean spaces, the empirical mean vector as an estimator of the population mean is known to have polynomial concentration unless a strong tail assumption is imposed on the underlying probability measure. The idea of median-of-means tournament has been considered as a way of overcoming the sub-optimality of the empirical mean vector. In this paper, to address the sub-optimal performance of the empirical mean in a more general setting, we consider general Polish spaces with a general metric, which are allowed to be non-compact and of infinite-dimension. We discuss the estimation of the associated population Frechet mean, and for this we extend the existing notion of median-of-means to this general setting. We devise several new notions and inequalities associated with the geometry of the underlying metric, and using them we study the concentration properties of the extended notions of median-of-means as the estimators of the population Frechet mean. We show that the new estimators achieve exponential concentration under only a second moment condition on the underlying distribution, while the empirical Frechet mean has polynomial concentration. We focus our study on spaces with non-positive Alexandrov curvature since they afford slower rates of convergence than spaces with positive curvature. We note that this is the first work that derives non-asymptotic concentration inequalities for extended notions of the median-of-means in non-vector spaces with a general metric.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41551240","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: 3

On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold 紧黎曼流形上固定路径空间上布朗桥测度的表征

IF 1.5 2区数学

Bernoulli Pub Date : 2022-11-01 DOI: 10.3150/21-bej1420

Fuzhou Gong, Xiaoxia Sun

引用次数: 0

Asymptotics of AIC, BIC and Cp model selection rules in high-dimensional regression 高维回归中AIC、BIC和Cp模型选择规则的渐近性

IF 1.5 2区数学

Bernoulli Pub Date : 2022-11-01 DOI: 10.3150/21-bej1422

Z. Bai, K. P. Choi, Y. Fujikoshi, Jiang Hu

引用次数: 5

A pseudo-marginal sequential Monte Carlo online smoothing algorithm 一种伪边缘序列蒙特卡罗在线平滑算法

IF 1.5 2区数学

Bernoulli Pub Date : 2022-11-01 DOI: 10.3150/21-bej1431

P. Gloaguen, Sylvain Le Corff, J. Olsson

{"title":"A pseudo-marginal sequential Monte Carlo online smoothing algorithm","authors":"P. Gloaguen, Sylvain Le Corff, J. Olsson","doi":"10.3150/21-bej1431","DOIUrl":"https://doi.org/10.3150/21-bej1431","url":null,"abstract":": We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but possible to estimate, with or without bias. Using pseudo-marginalisation techniques we are able to extend the particle- based, rapid incremental smoother (PaRIS) algorithm proposed in [J. Olsson and J. Westerborn. Eﬃcient particle-based online smoothing in general hidden Markov models: The PaRIS algorithm. Bernoulli , 23(3):1951–1996, 2017] to this setting. The resulting algorithm, which has a linear complex- ity in the number of particles and constant memory requirements, applies to a wide range of challenging path-space Monte Carlo problems, includ- ing smoothing in partially observed diﬀusion processes and models with intractable likelihood. The algorithm is furnished with several theoretical results, including a central limit theorem, establishing its convergence and numerical stability. Moreover, under strong mixing assumptions we estab- lish a novel O ( nε ) bound on the asymptotic bias of the algorithm, where n is the path length and ε controls the bias of the density estimators.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48369375","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: 8

Upper functions for sample paths of Lévy(-type) processes Lévy（-型）过程样本路径的上函数

IF 1.5 2区数学

Bernoulli Pub Date : 2022-11-01 DOI: 10.3150/21-bej1441

F. Kühn

引用次数: 2

Deviation inequalities and Cramér-type moderate deviations for the explosive autoregressive process 爆炸自回归过程的偏差不等式和Cramér型中偏差

IF 1.5 2区数学

Bernoulli Pub Date : 2022-11-01 DOI: 10.3150/21-bej1432

Hui Jiang, Yilong Wan, Guangyu Yang

引用次数: 4

Nonparametric inference for reversed mean models with panel count data 具有面板计数数据的反向均值模型的非参数推理