Martin Kolb, Mladen Savov.

Source: Bernoulli, Volume 26, Number 2, 1453--1472.

Abstract:
We derive a criterium for the almost sure finiteness of perpetual integrals of Lévy processes for a class of real functions including all continuous functions and for general one-dimensional Lévy processes that drifts to plus infinity. This generalizes previous work of Döring and Kyprianou, who considered Lévy processes having a local time, leaving the general case as an open problem. It turns out, that the criterium in the general situation simplifies significantly in the situation, where the process has a local time, but we also demonstrate that in general our criterium can not be reduced. This answers an open problem posed in ( J. Theoret. Probab. 29 (2016) 1192–1198).

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.

Pier Luigi Conti, Daniela Marella, Fulvia Mecatti, Federico Andreis.

Source: Bernoulli, Volume 26, Number 2, 1044--1069.

Abstract:
In this paper, a class of resampling techniques for finite populations under $pi $ps sampling design is introduced. The basic idea on which they rest is a two-step procedure consisting in: (i) constructing a “pseudo-population” on the basis of sample data; (ii) drawing a sample from the predicted population according to an appropriate resampling design. From a logical point of view, this approach is essentially based on the plug-in principle by Efron, at the “sampling design level”. Theoretical justifications based on large sample theory are provided. New approaches to construct pseudo populations based on various forms of calibrations are proposed. Finally, a simulation study is performed.

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.

Mingjie Liang, René L. Schilling, Jian Wang.

Source: Bernoulli, Volume 26, Number 1, 664--693.

Abstract:
We present a general method to construct couplings of stochastic differential equations driven by Lévy noise in terms of coupling operators. This approach covers both coupling by reflection and refined basic coupling which are often discussed in the literature. As applications, we prove regularity results for the transition semigroups and obtain successful couplings for the solutions to stochastic differential equations driven by additive Lévy noise.

Zhuang Ma, Xiaodong Li.

Source: Bernoulli, Volume 26, Number 1, 432--470.

Abstract:
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by the recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose two losses based on the principal angles between the model spaces spanned by the sample canonical variates and their population correspondents, respectively. We further characterize the non-asymptotic error bounds for the estimation risks under the proposed error metrics, which reveal how the performance of sample CCA depends adaptively on key quantities including the dimensions, the sample size, the condition number of the covariance matrices and particularly the population canonical correlation coefficients. The optimality of our uniform upper bounds is also justified by lower-bound analysis based on stringent and localized parameter spaces. To the best of our knowledge, for the first time our paper separates $p_{1}$ and $p_{2}$ for the first order term in the upper bounds without assuming the residual correlations are zeros. More significantly, our paper derives $(1-lambda_{k}^{2})(1-lambda_{k+1}^{2})/(lambda_{k}-lambda_{k+1})^{2}$ for the first time in the non-asymptotic CCA estimation convergence rates, which is essential to understand the behavior of CCA when the leading canonical correlation coefficients are close to $1$.

Michael V. Boutsikas, Eutichia Vaggelatou

Source: Bernoulli, Volume 16, Number 2, 301--330.

Abstract:
Let X 1 , X 2 , …, X n be a sequence of independent or locally dependent random variables taking values in ℤ + . In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the distribution of the sum ∑ i =1 n X i and an appropriate Poisson or compound Poisson distribution. These bounds include a factor which depends on the smoothness of the approximating Poisson or compound Poisson distribution. This “smoothness factor” is of order O( σ −2 ), according to a heuristic argument, where σ 2 denotes the variance of the approximating distribution. In this way, we offer sharp error estimates for a large range of values of the parameters. Finally, specific examples concerning appearances of rare runs in sequences of Bernoulli trials are presented by way of illustration.

Klemm (Family)

Our Lady of Grace School (Glengowrie, S.A.)

Gambling (Family)

Nixon, Geoffrey Owen, 1921-2011.

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.

Members of the future American workforce could see losses of earnings that add up to trillions of dollars, depending on how long coronavirus-related school closures persist.

The post Economists Expect Huge Future Earnings Loss for Students Missing School Due to COVID-19 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.

ACT and the American Federation of Teachers are partnering to provide free resources as educators increasingly switch to distance learning amid the COVID-19 pandemic.

The post ACT and Teachers’ Union Partner to Provide Remote Learning Resources Amid Pandemic appeared first on Market Brief.

Savvas Learning Company will continue to provide its K-12 products and services, and is working to support districts with their remote learning needs during school closures.

The post Pearson K12 Spinoff Rebranded as ‘Savvas Learning Company’ appeared first on Market Brief.

The CEO of Move This World isn't big on screen time, but in the midst of the coronavirus pandemic, technology--when used with care--can help strengthen relationships.

The post 4 Ways to Help Students Cultivate Meaningful Connections Through Tech appeared first on Market Brief.

The New York City police department (NYPD) is conducting an internal investigation into a May 2 incident involving the violent arrests of multiple people, allegedly members of a group who were not social distancing

Barack Obama said the “rule of law is at risk” following the justice department’s decision to drop charges against former Trump advisor Mike Flynn, as he issued a stark warning about the long-term impact on the American way of life by his successor.

Zhi-Qiang Wang, Nian-Sheng Tang.

Source: Bayesian Analysis, Volume 15, Number 2, 579--604.

Abstract:
Bayesian inference on quantile regression (QR) model with mixed discrete and non-ignorable missing covariates is conducted by reformulating QR model as a hierarchical structure model. A probit regression model is adopted to specify missing covariate mechanism. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm is developed to simultaneously produce Bayesian estimates of unknown parameters and latent variables as well as their corresponding standard errors. Bayesian variable selection method is proposed to recognize significant covariates. A Bayesian local influence procedure is presented to assess the effect of minor perturbations to the data, priors and sampling distributions on posterior quantities of interest. Several simulation studies and an example are presented to illustrate the proposed methodologies.

Abhishek Bishoyi, Xiaojing Wang, Dipak K. Dey.

Source: Bayesian Analysis, Volume 15, Number 1, 215--239.

Abstract:
Missing data often appear as a practical problem while applying classical models in the statistical analysis. In this paper, we consider a semiparametric regression model in the presence of missing covariates for nonparametric components under a Bayesian framework. As it is known that Gaussian processes are a popular tool in nonparametric regression because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. However, in the absence of covariates, the most frequently used covariance functions of a Gaussian process will not be well defined. We propose an imputation method to solve this issue and perform our analysis using Bayesian inference, where we specify the objective priors on the parameters of Gaussian process models. Several simulations are conducted to illustrate effectiveness of our proposed method and further, our method is exemplified via two real datasets, one through Langmuir equation, commonly used in pharmacokinetic models, and another through Auto-mpg data taken from the StatLib library.

Lizhen Lin, Niu Mu, Pokman Cheung, David Dunson.

Source: Bayesian Analysis, Volume 14, Number 3, 907--926.

Abstract:
Gaussian processes (GPs) are very widely used for modeling of unknown functions or surfaces in applications ranging from regression to classification to spatial processes. Although there is an increasingly vast literature on applications, methods, theory and algorithms related to GPs, the overwhelming majority of this literature focuses on the case in which the input domain corresponds to a Euclidean space. However, particularly in recent years with the increasing collection of complex data, it is commonly the case that the input domain does not have such a simple form. For example, it is common for the inputs to be restricted to a non-Euclidean manifold, a case which forms the motivation for this article. In particular, we propose a general extrinsic framework for GP modeling on manifolds, which relies on embedding of the manifold into a Euclidean space and then constructing extrinsic kernels for GPs on their images. These extrinsic Gaussian processes (eGPs) are used as prior distributions for unknown functions in Bayesian inferences. Our approach is simple and general, and we show that the eGPs inherit fine theoretical properties from GP models in Euclidean spaces. We consider applications of our models to regression and classification problems with predictors lying in a large class of manifolds, including spheres, planar shape spaces, a space of positive definite matrices, and Grassmannians. Our models can be readily used by practitioners in biological sciences for various regression and classification problems, such as disease diagnosis or detection. Our work is also likely to have impact in spatial statistics when spatial locations are on the sphere or other geometric spaces.

Ioannis Ntzoufras, Claudia Tarantola, Monia Lupparelli.

Source: Bayesian Analysis, Volume 14, Number 3, 797--823.

Abstract:
We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.

Yushu Shi, Michael Martens, Anjishnu Banerjee, Purushottam Laud.

Source: Bayesian Analysis, Volume 14, Number 3, 677--702.

Abstract:
Dirichlet process mixture (DPM) models provide flexible modeling for distributions of data as an infinite mixture of distributions from a chosen collection. Specifying priors for these models in individual data contexts can be challenging. In this paper, we introduce a scheme which requires the investigator to specify only simple scaling information. This is used to transform the data to a fixed scale on which a low information prior is constructed. Samples from the posterior with the rescaled data are transformed back for inference on the original scale. The low information prior is selected to provide a wide variety of components for the DPM to generate flexible distributions for the data on the fixed scale. The method can be applied to all DPM models with kernel functions closed under a suitable scaling transformation. Construction of the low information prior, however, is kernel dependent. Using DPM-of-Gaussians and DPM-of-Weibulls models as examples, we show that the method provides accurate estimates of a diverse collection of distributions that includes skewed, multimodal, and highly dispersed members. With the recommended priors, repeated data simulations show performance comparable to that of standard empirical estimates. Finally, we show weak convergence of posteriors with the proposed priors for both kernels considered.

T. Tony Cai.

Source: Statistical Science, Volume 34, Number 4, 635--656.

Abstract:
A wide range of nonparametric function estimation models have been studied individually in the literature. Among them the homoscedastic nonparametric Gaussian regression is arguably the best known and understood. Inspired by the asymptotic equivalence theory, Brown, Cai and Zhou ( Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046) and Brown et al. ( Probab. Theory Related Fields 146 (2010) 401–433) developed a unified approach to turn a collection of non-Gaussian function estimation models into a standard Gaussian regression and any good Gaussian nonparametric regression method can then be used. These Gaussianization Machines have two key components, binning and transformation. When combined with BlockJS, a wavelet thresholding procedure for Gaussian regression, the procedures are computationally efficient with strong theoretical guarantees. Technical analysis given in Brown, Cai and Zhou ( Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046) and Brown et al. ( Probab. Theory Related Fields 146 (2010) 401–433) shows that the estimators attain the optimal rate of convergence adaptively over a large set of Besov spaces and across a collection of non-Gaussian function estimation models, including robust nonparametric regression, density estimation, and nonparametric regression in exponential families. The estimators are also spatially adaptive. The Gaussianization Machines significantly extend the flexibility and scope of the theories and methodologies originally developed for the conventional nonparametric Gaussian regression. This article aims to provide a concise account of the Gaussianization Machines developed in Brown, Cai and Zhou ( Ann. Statist. 36 (2008) 2055–2084; Ann. Statist. 38 (2010) 2005–2046), Brown et al. ( Probab. Theory Related Fields 146 (2010) 401–433).

Pantelis Samartsidis, Shaun R. Seaman, Anne M. Presanis, Matthew Hickman, Daniela De Angelis.

Source: Statistical Science, Volume 34, Number 3, 486--503.

Abstract:
Researchers are often challenged with assessing the impact of an intervention on an outcome of interest in situations where the intervention is nonrandomised, the intervention is only applied to one or few units, the intervention is binary, and outcome measurements are available at multiple time points. In this paper, we review existing methods for causal inference in these situations. We detail the assumptions underlying each method, emphasize connections between the different approaches and provide guidelines regarding their practical implementation. Several open problems are identified thus highlighting the need for future research.

Sijia Xiang, Weixin Yao, Guangren Yang.

Source: Statistical Science, Volume 34, Number 3, 391--404.

Abstract:
Finite mixture models have offered a very important tool for exploring complex data structures in many scientific areas, such as economics, epidemiology and finance. Semiparametric mixture models, which were introduced into traditional finite mixture models in the past decade, have brought forth exciting developments in their methodologies, theories, and applications. In this article, we not only provide a selective overview of the newly-developed semiparametric mixture models, but also discuss their estimation methodologies, theoretical properties if applicable, and some open questions. Recent developments are also discussed.

Nathan B. Cruze, Andreea L. Erciulescu, Balgobin Nandram, Wendy J. Barboza, Linda J. Young.

Source: Statistical Science, Volume 34, Number 2, 301--316.

Abstract:
In the United States, county-level estimates of crop yield, production, and acreage published by the United States Department of Agriculture’s National Agricultural Statistics Service (USDA NASS) play an important role in determining the value of payments allotted to farmers and ranchers enrolled in several federal programs. Given the importance of these official county-level crop estimates, NASS continually strives to improve its crops county estimates program in terms of accuracy, reliability and coverage. In 2015, NASS engaged a panel of experts convened under the auspices of the National Academies of Sciences, Engineering, and Medicine Committee on National Statistics (CNSTAT) for guidance on implementing models that may synthesize multiple sources of information into a single estimate, provide defensible measures of uncertainty, and potentially increase the number of publishable county estimates. The final report titled Improving Crop Estimates by Integrating Multiple Data Sources was released in 2017. This paper discusses several needs and requirements for NASS county-level crop estimates that were illuminated during the activities of the CNSTAT panel. A motivating example of planted acreage estimation in Illinois illustrates several challenges that NASS faces as it considers adopting any explicit model for official crops county estimates.

Roger Koenker, Jiaying Gu.

Source: Statistical Science, Volume 34, Number 2, 209--213.

Abstract:
Efron’s elegant approach to $g$-modeling for empirical Bayes problems is contrasted with an implementation of the Kiefer–Wolfowitz nonparametric maximum likelihood estimator for mixture models for several examples. The latter approach has the advantage that it is free of tuning parameters and consequently provides a relatively simple complementary method.

The capacity to process information in conceptual form is a fundamental aspect of human cognition, yet little is known about how this type of information is encoded in the brain. Although the role of sensory and motor cortical areas has been a focus of recent debate, neuroimaging studies of concept representation consistently implicate a network of heteromodal areas that seem to support concept retrieval in general rather than knowledge related to any particular sensory-motor content. We used predictive machine learning on fMRI data to investigate the hypothesis that cortical areas in this "general semantic network" (GSN) encode multimodal information derived from basic sensory-motor processes, possibly functioning as convergence–divergence zones for distributed concept representation. An encoding model based on five conceptual attributes directly related to sensory-motor experience (sound, color, shape, manipulability, and visual motion) was used to predict brain activation patterns associated with individual lexical concepts in a semantic decision task. When the analysis was restricted to voxels in the GSN, the model was able to identify the activation patterns corresponding to individual concrete concepts significantly above chance. In contrast, a model based on five perceptual attributes of the word form performed at chance level. This pattern was reversed when the analysis was restricted to areas involved in the perceptual analysis of written word forms. These results indicate that heteromodal areas involved in semantic processing encode information about the relative importance of different sensory-motor attributes of concepts, possibly by storing particular combinations of sensory and motor features.

SIGNIFICANCE STATEMENT The present study used a predictive encoding model of word semantics to decode conceptual information from neural activity in heteromodal cortical areas. The model is based on five sensory-motor attributes of word meaning (color, shape, sound, visual motion, and manipulability) and encodes the relative importance of each attribute to the meaning of a word. This is the first demonstration that heteromodal areas involved in semantic processing can discriminate between different concepts based on sensory-motor information alone. This finding indicates that the brain represents concepts as multimodal combinations of sensory and motor representations.

London : Cleanair, Smoke-free Environment (33 Stillness Rd, London, SE23 1NG), [198-?]

London : Cleanair, Smoke-free Environment (33 Stillness Rd, London, SE23 1NG), [198-?]

The rainbow sports bra and leggings set from Splits59 is a must-have for anyone craving a pop of color in their workout wardrobe.

The chic sneaks are part of Zappos' massive Cyber Monday sale.

This retro style is making a comeback for a reason.

They’re already going out of stock.

The new style is available to shop today.

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