Anton Thalmaier, James Thompson.

Source: Bernoulli, Volume 26, Number 3, 2202--2225.

Abstract:
In this article, we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions firstly on sub-Riemannian limits of Riemannian foliations and secondly in the nonsmooth setting of $operatorname{RCD}^{*}(K,N)$ spaces. In each case, the necessary ingredients are Itô’s formula and a comparison theorem for the Laplacian, for which we refer to the recent literature. As an application, we derive pointwise Carmona-type estimates on eigenfunctions of Schrödinger operators.

Sarat B. Moka, Dirk P. Kroese.

Source: Bernoulli, Volume 26, Number 3, 2082--2104.

Abstract:
We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC’17 – Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342–355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high and $Theta(1/r^{d})$ parallel processor units are available.

Arnak S. Dalalyan, Lionel Riou-Durand.

Source: Bernoulli, Volume 26, Number 3, 1956--1988.

Abstract:
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave densities defined on $mathbb{R}^{p}$. The present work focuses on this framework and studies the behavior of the Monte Carlo algorithm based on discretizations of the kinetic Langevin diffusion. We first prove the geometric mixing property of the kinetic Langevin diffusion with a mixing rate that is optimal in terms of its dependence on the condition number. We then use this result for obtaining improved guarantees of sampling using the kinetic Langevin Monte Carlo method, when the quality of sampling is measured by the Wasserstein distance. We also consider the situation where the Hessian of the log-density of the target distribution is Lipschitz-continuous. In this case, we introduce a new discretization of the kinetic Langevin diffusion and prove that this leads to a substantial improvement of the upper bound on the sampling error measured in Wasserstein distance.

Tom Alberts, Firas Rassoul-Agha, Mackenzie Simper.

Source: Bernoulli, Volume 26, Number 3, 1927--1955.

Abstract:
We prove that given any fixed asymptotic velocity, the finite length O’Connell–Yor polymer has an infinite length limit satisfying the law of large numbers with this velocity. By a Markovian property of the quenched polymer this reduces to showing the existence of Busemann functions : almost sure limits of ratios of random point-to-point partition functions. The key ingredients are the Burke property of the O’Connell–Yor polymer and a comparison lemma for the ratios of partition functions. We also show the existence of infinite length limits in the Brownian last passage percolation model.

Pavel Chigansky, Marina Kleptsyna, Dmytro Marushkevych.

Source: Bernoulli, Volume 26, Number 3, 1706--1726.

Abstract:
Spectral decomposition of the covariance operator is one of the main building blocks in the theory and applications of Gaussian processes. Unfortunately, it is notoriously hard to derive in a closed form. In this paper, we consider the eigenproblem for Gaussian bridges. Given a base process, its bridge is obtained by conditioning the trajectories to start and terminate at the given points. What can be said about the spectrum of a bridge, given the spectrum of its base process? We show how this question can be answered asymptotically for a family of processes, including the fractional Brownian motion.

Amir Najafi, Seyed Abolfazl Motahari, Hamid R. Rabiee.

Source: Bernoulli, Volume 26, Number 2, 1535--1559.

Abstract:
A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from a theoretical perspective, when the number of clusters is unknown. In particular, we stipulate a set of conditions on the sample complexity and dimension of the model in order to guarantee the Probably Approximately Correct (PAC)-clusterability of a dataset. To the best of our knowledge, these findings are the first non-asymptotic bounds on the sample complexity of learning or clustering BMMs.

Kamran Kalbasi, Thomas Mountford.

Source: Bernoulli, Volume 26, Number 2, 1504--1534.

Abstract:
In this paper, we study the local times of vector-valued Gaussian fields that are ‘diagonally operator-self-similar’ and whose increments are stationary. Denoting the local time of such a Gaussian field around the spatial origin and over the temporal unit hypercube by $Z$, we show that there exists $lambdain(0,1)$ such that under some quite weak conditions, $lim_{n ightarrow+infty}frac{sqrt[n]{mathbb{E}(Z^{n})}}{n^{lambda}}$ and $lim_{x ightarrow+infty}frac{-logmathbb{P}(Z>x)}{x^{frac{1}{lambda}}}$ both exist and are strictly positive (possibly $+infty$). Moreover, we show that if the underlying Gaussian field is ‘strongly locally nondeterministic’, the above limits will be finite as well. These results are then applied to establish similar statements for the intersection local times of diagonally operator-self-similar Gaussian fields with stationary increments.

Wensheng Wang, Zhonggen Su, Yimin Xiao.

Source: Bernoulli, Volume 26, Number 2, 1410--1430.

Abstract:
We establish the exact moduli of non-differentiability of Gaussian random fields with stationary increments. As an application of the result, we prove that the uniform Hölder condition for the maximum local times of Gaussian random fields with stationary increments obtained in Xiao (1997) is optimal. These results are applicable to fractional Riesz–Bessel processes and stationary Gaussian random fields in the Matérn and Cauchy classes.

Emanuele Dolera, Stefano Favaro.

Source: Bernoulli, Volume 26, Number 2, 1294--1322.

Abstract:
Given a sequence ${X_{n}}_{ngeq 1}$ of exchangeable Bernoulli random variables, the celebrated de Finetti representation theorem states that $frac{1}{n}sum_{i=1}^{n}X_{i}stackrel{a.s.}{longrightarrow }Y$ for a suitable random variable $Y:Omega ightarrow [0,1]$ satisfying $mathsf{P}[X_{1}=x_{1},dots ,X_{n}=x_{n}|Y]=Y^{sum_{i=1}^{n}x_{i}}(1-Y)^{n-sum_{i=1}^{n}x_{i}}$. In this paper, we study the rate of convergence in law of $frac{1}{n}sum_{i=1}^{n}X_{i}$ to $Y$ under the Kolmogorov distance. After showing that a rate of the type of $1/n^{alpha }$ can be obtained for any index $alpha in (0,1]$, we find a sufficient condition on the distribution of $Y$ for the achievement of the optimal rate of convergence, that is $1/n$. Besides extending and strengthening recent results under the weaker Wasserstein distance, our main result weakens the regularity hypotheses on $Y$ in the context of the Hausdorff moment problem.

Nina Gantert, Markus Heydenreich, Timo Hirscher.

Source: Bernoulli, Volume 26, Number 2, 1269--1293.

Abstract:
We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a realignment of opinions closer towards each other. This mechanism triggers formation of consensus among the individuals. Our main focus is on strong consensus (i.e., global agreement of all individuals) versus weak consensus (i.e., local agreement among neighbors). By extending a known model to a more general opinion space, which lacks a “central” opinion acting as a contraction point, we provide an example of an opinion formation process on the one-dimensional lattice $mathbb{Z}$ with weak consensus but no strong consensus.

Chao Gao.

Source: Bernoulli, Volume 26, Number 2, 1139--1170.

Abstract:
This paper studies robust regression in the settings of Huber’s $epsilon$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $epsilon$-contamination models for various regression problems including nonparametric regression, sparse linear regression, reduced rank regression, etc. We also discuss a general notion of depth function for linear operators that has potential applications in robust functional linear regression.

Leif Döring, Philip Weissmann.

Source: Bernoulli, Volume 26, Number 2, 980--1015.

Abstract:
Conditioning stable Lévy processes on zero probability events recently became a tractable subject since several explicit formulas emerged from a deep analysis using the Lamperti transformations for self-similar Markov processes. In this article, we derive new harmonic functions and use them to explain how to condition stable processes to hit continuously a compact interval from the outside.

Nhat Ho, XuanLong Nguyen, Ya’acov Ritov.

Source: Bernoulli, Volume 26, Number 2, 828--857.

Abstract:
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we empirically believe our data are generated from and use these kernels to fit our models. Nevertheless, as long as the chosen kernel and the true kernel are different, statistical inference of mixing measure under this setting will be highly unstable. To overcome this challenge, we propose flexible and efficient robust estimators of the mixing measure in these models, which are inspired by the idea of minimum Hellinger distance estimator, model selection criteria, and superefficiency phenomenon. We demonstrate that our estimators consistently recover the true number of components and achieve the optimal convergence rates of parameter estimation under both the well- and misspecified kernel settings for any fixed bandwidth. These desirable asymptotic properties are illustrated via careful simulation studies with both synthetic and real data.

Stanislav Minsker, Xiaohan Wei.

Source: Bernoulli, Volume 26, Number 1, 694--727.

Abstract:
Let $Y$ be a $d$-dimensional random vector with unknown mean $mu $ and covariance matrix $Sigma $. This paper is motivated by the problem of designing an estimator of $Sigma $ that admits exponential deviation bounds in the operator norm under minimal assumptions on the underlying distribution, such as existence of only 4th moments of the coordinates of $Y$. To address this problem, we propose robust modifications of the operator-valued U-statistics, obtain non-asymptotic guarantees for their performance, and demonstrate the implications of these results to the covariance estimation problem under various structural assumptions.

Yi Shen, Yizao Wang.

Source: Bernoulli, Volume 26, Number 1, 500--530.

Abstract:
We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In this model, each copy in the aggregation is a $pm 1$-valued random field built from two correlated one-dimensional random walks, the law of each determined by a random persistence parameter. A flexible joint distribution of the two parameters is introduced, and given the parameters the two correlated random walks are conditionally independent. For the aggregated random field, when the persistence parameters are independent, the scaling limit is a fractional Brownian sheet. When the persistence parameters are tail-dependent, characterized in the framework of multivariate regular variation, the scaling limit is more delicate, and in particular depends on the growth rates of the underlying rectangular region along two directions: at different rates different operator-scaling Gaussian random fields appear as the region area tends to infinity. In particular, at the so-called critical speed, a large family of Gaussian random fields with long-range dependence arise in the limit. We also identify four different regimes at non-critical speed where fractional Brownian sheets arise in the limit.

Eduard Belitser, Nurzhan Nurushev.

Source: Bernoulli, Volume 26, Number 1, 191--225.

Abstract:
In the general signal$+$noise (allowing non-normal, non-independent observations) model, we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which gives rise to a new slicing of the entire space that is suitable for uncertainty quantification. Under EBR and some mild exchangeable exponential moment condition on the noise, we establish the local (oracle) optimality of the proposed confidence ball. Without EBR, we propose another confidence ball of full coverage, but its radius contains an additional $sigma n^{1/4}$-term. In passing, we also get the local optimal results for estimation , posterior contraction problems, and the problem of weak recovery of sparsity structure . Adaptive minimax results (also for the estimation and posterior contraction problems) over various sparsity classes follow from our local results.

Fuhlbohm (Family)

Siekmann, Francis Heinrich Ernst, 1830-1917.

Hicks (Family)

South Australia -- Genealogy.

South Australia -- History -- Sources.

Traeger, Ernst Wilhelm, 1805-1874.

Fuhlbohm (Family)

Kraus, Peter -- Biography.

Sherwell (Family)

Scott Marion, who consults states on testing, talks about why it's important for vendors and public officials to work cooperatively in renegotiating contracts amid assessment cancellations caused by COVID-19.

The post How States, Assessment Companies Can Work Together Amid Coronavirus Testing Cancellations appeared first on Market Brief.

The Round Rock Independent School District in Texas is looking for a digital curriculum and blended learning program. Baltimore is looking for a comprehensive high school literacy program.

The post Austin-Area District Looks for Digital/Blended Learning Program; Baltimore Seeks High School Literacy Program appeared first on Market Brief.

EdWeek Market Brief asked district officials in a nationwide survey about their most urgent assessment needs, as they cope with COVID-19 and tentatively plan for reopening schools.

The post What Districts Want From Assessments, as They Grapple With the Coronavirus appeared first on Market Brief.

Reaction and analysis from Fox News contributor Byron York and former Florida Attorney General Pam Bondi.

Vice President Pence’s trip to Iowa shows how the Trump administration’s aims to move past coronavirus are sometimes complicated by the virus itself.

The Office of Special Counsel is recommending that ousted vaccine official Dr. Rick Bright be reinstated while it investigates his case, his lawyers announced Friday.Bright while leading coronavirus vaccine development was recently removed from his position as the director of the Department of Health and Human Services' Biomedical Advanced Research and Development Authority, and he alleges it was because he insisted congressional funding not go toward "drugs, vaccines, and other technologies that lack scientific merit" and limited the "broad use" of hydroxychloroquine after it was touted by President Trump. In a whistleblower complaint, he alleged "cronyism" at HHS. He has also alleged he was "pressured to ignore or dismiss expert scientific recommendations and instead to award lucrative contracts based on political connections."On Friday, Bright's lawyers said that the Office of Special Counsel has determined there are "reasonable grounds to believe" his firing was retaliation, The New York Times reports. The federal watchdog also recommended he be reinstated for 45 days to give the office "sufficient time to complete its investigation of Bright's allegations," CNN reports. The decision on whether to do so falls on Secretary of Health and Human Services Alex Azar, and Office of Special Counsel recommendations are "not binding," the Times notes. More stories from theweek.com Outed CIA agent Valerie Plame is running for Congress, and her launch video looks like a spy movie trailer 7 scathing cartoons about America's rush to reopen Trump says he couldn't have exposed WWII vets to COVID-19 because the wind was blowing the wrong way

Indian authorities used drones and fire engines to disinfect the pandemic-hit city of Ahmedabad on Saturday, as virus cases surged and police clashed with migrant workers protesting against a reinforced lockdown. The western city of 5.5 million people in Prime Minister Narendra Modi's home state has become a major concern for authorities as they battle an uptick in coronavirus deaths and cases across India.

U.S. Chief Justice John Roberts on Friday put a temporary hold on the disclosure to a Democratic-led House of Representatives committee of grand jury material redacted from former Special Counsel Robert Mueller's report on Russian interference in the 2016 election. The U.S. Court of Appeals for the District of Columbia Circuit ruled in March that the materials had to be disclosed to the House Judiciary Committee and refused to put that decision on hold. The appeals court said the materials had to be handed over by May 11 if the Supreme Court did not intervene.

Boeing CEO Dave Calhoun said the company was aiming to resume production this month, despite the ongoing grounding and coronavirus pandemic.

For millions of Americans, working at home isn't an option. NBC News identified seven occupations in which employees are at especially high risk of COVID-19.

Delta said it is making the move to protect employees amid the coronavirus pandemic, but planes have been flying near empty

While President Donald Trump traveled to the battleground state of Arizona this week, his Democratic opponent for the White House, Joe Biden, campaigned from his basement as he has done throughout the coronavirus pandemic. The freeze on in-person campaigning during the outbreak has had an upside for Biden, giving the former vice president more time to court donors and shielding him from on-the-trail gaffes. "I personally would like to see him out more because he's in his element when he's meeting people," said Tom Sacks-Wilner, a fundraiser for Biden who is on the campaign's finance committee.

Austin-Bergstrom International Airport said it was "aware of an individual that was struck and killed on runway 17-R by a landing aircraft."

The bombastic military parade through Moscow's Red Square on Saturday was slated to be the spectacle of the year on the Kremlin's calendar. Standing with Chinese leader Xi Jinping and French President Emmanuel Macron, President Vladimir Putin would have overseen a 90-minute procession of Russia's military might, showcasing 15,000 troops and the latest hardware. Now, military jets will roar over an eerily quiet Moscow, spurting red, white and blue smoke to mark 75 years since the defeat of Nazi Germany.

The staffer of Vice President Mike Pence who tested positive for coronavirus is apparently his press secretary and the wife of White House senior adviser Stephen Miller.Reports emerged on Friday that a member of Pence's staff had tested positive for COVID-19, creating a delay in his flight to Iowa amid concern over who may have been exposed. Later in the day, Trump said the staffer is a "press person" named Katie.Politico reported he was referring to Katie Miller, Pence's press secretary and the wife of Stephen Miller. This report noted this raises the risk that "a large swath of the West Wing's senior aides may also have been exposed." She confirmed her positive diagnosis to NBC News, saying she does not have symptoms.Trump spilled the beans to reporters, saying Katie Miller "hasn't come into contact with me" but has "spent some time with the vice president." This news comes one day after a personal valet to Trump tested positive for COVID-19, which reportedly made the president "lava level mad." Pence and Trump are being tested for COVID-19 every day.Asked Friday if he's concerned about the potential spread of coronavirus in the White House, Trump said "I'm not worried, no," adding that "we've taken very strong precautions."More stories from theweek.com Outed CIA agent Valerie Plame is running for Congress, and her launch video looks like a spy movie trailer 7 scathing cartoons about America's rush to reopen Trump says he couldn't have exposed WWII vets to COVID-19 because the wind was blowing the wrong way