John R. Tipton, Mevin B. Hooten, Connor Nolan, Robert K. Booth, Jason McLachlan.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2363--2388.

Abstract:
Multivariate compositional count data arise in many applications including ecology, microbiology, genetics and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what underlying values of a covariate(s) give rise to the observed composition. Learning the relationship between covariates and the compositional count allows for inverse prediction of unobserved covariates given compositional count observations. Gaussian processes provide a flexible framework for modeling functional responses with respect to a covariate without assuming a functional form. Many scientific disciplines use Gaussian process approximations to improve prediction and make inference on latent processes and parameters. When prediction is desired on unobserved covariates given realizations of the response variable, this is called inverse prediction. Because inverse prediction is often mathematically and computationally challenging, predicting unobserved covariates often requires fitting models that are different from the hypothesized generative model. We present a novel computational framework that allows for efficient inverse prediction using a Gaussian process approximation to generative models. Our framework enables scientific learning about how the latent processes co-vary with respect to covariates while simultaneously providing predictions of missing covariates. The proposed framework is capable of efficiently exploring the high dimensional, multi-modal latent spaces that arise in the inverse problem. To demonstrate flexibility, we apply our method in a generalized linear model framework to predict latent climate states given multivariate count data. Based on cross-validation, our model has predictive skill competitive with current methods while simultaneously providing formal, statistical inference on the underlying community dynamics of the biological system previously not available.

Carolyn M. Rutter, Jonathan Ozik, Maria DeYoreo, Nicholson Collier.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2189--2212.

Abstract:
Microsimulation models (MSMs) are used to inform policy by predicting population-level outcomes under different scenarios. MSMs simulate individual-level event histories that mark the disease process (such as the development of cancer) and the effect of policy actions (such as screening) on these events. MSMs often have many unknown parameters; calibration is the process of searching the parameter space to select parameters that result in accurate MSM prediction of a wide range of targets. We develop Incremental Mixture Approximate Bayesian Computation (IMABC) for MSM calibration which results in a simulated sample from the posterior distribution of model parameters given calibration targets. IMABC begins with a rejection-based ABC step, drawing a sample of points from the prior distribution of model parameters and accepting points that result in simulated targets that are near observed targets. Next, the sample is iteratively updated by drawing additional points from a mixture of multivariate normal distributions and accepting points that result in accurate predictions. Posterior estimates are obtained by weighting the final set of accepted points to account for the adaptive sampling scheme. We demonstrate IMABC by calibrating CRC-SPIN 2.0, an updated version of a MSM for colorectal cancer (CRC) that has been used to inform national CRC screening guidelines.

Hannah Worthington, Rachel McCrea, Ruth King, Richard Griffiths.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2043--2064.

Abstract:
Capture-recapture studies often involve collecting data on numerous capture occasions over a relatively short period of time. For many study species this process is repeated, for example, annually, resulting in capture information spanning multiple sampling periods. To account for the different temporal scales, the robust design class of models have traditionally been applied providing a framework in which to analyse all of the available capture data in a single likelihood expression. However, these models typically require strong constraints, either the assumption of closure within a sampling period (the closed robust design) or conditioning on the number of individuals captured within a sampling period (the open robust design). For real datasets these assumptions may not be appropriate. We develop a general modelling structure that requires neither assumption by explicitly modelling the movement of individuals into the population both within and between the sampling periods, which in turn permits the estimation of abundance within a single consistent framework. The flexibility of the novel model structure is further demonstrated by including the computationally challenging case of multi-state data where there is individual time-varying discrete covariate information. We derive an efficient likelihood expression for the new multi-state multi-period stopover model using the hidden Markov model framework. We demonstrate the significant improvement in parameter estimation using our new modelling approach in terms of both the multi-period and multi-state components through both a simulation study and a real dataset relating to the protected species of great crested newts, Triturus cristatus .

Seong-Hwan Jun, Samuel W. K. Wong, James V. Zidek, Alexandre Bouchard-Côté.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1678--1707.

Abstract:
In this paper, we consider the knot-matching problem arising in computational forestry. The knot-matching problem is an important problem that needs to be solved to advance the state of the art in automatic strength prediction of lumber. We show that this problem can be formulated as a quadripartite matching problem and develop a sequential decision model that admits efficient parameter estimation along with a sequential Monte Carlo sampler on graph matching that can be utilized for rapid sampling of graph matching. We demonstrate the effectiveness of our methods on 30 manually annotated boards and present findings from various simulation studies to provide further evidence supporting the efficacy of our methods.

Lisa Schlosser, Torsten Hothorn, Reto Stauffer, Achim Zeileis.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1564--1589.

Abstract:
To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this only captures the location of the distribution but over the last decade there has been increasing interest in distributional regression approaches modeling all parameters including location, scale and shape. Notably, so-called nonhomogeneous Gaussian regression (NGR) models both mean and variance of a Gaussian response and is particularly popular in weather forecasting. Moreover, generalized additive models for location, scale and shape (GAMLSS) provide a framework where each distribution parameter is modeled separately capturing smooth linear or nonlinear effects. However, when variable selection is required and/or there are nonsmooth dependencies or interactions (especially unknown or of high-order), it is challenging to establish a good GAMLSS. A natural alternative in these situations would be the application of regression trees or random forests but, so far, no general distributional framework is available for these. Therefore, a framework for distributional regression trees and forests is proposed that blends regression trees and random forests with classical distributions from the GAMLSS framework as well as their censored or truncated counterparts. To illustrate these novel approaches in practice, they are employed to obtain probabilistic precipitation forecasts at numerous sites in a mountainous region (Tyrol, Austria) based on a large number of numerical weather prediction quantities. It is shown that the novel distributional regression forests automatically select variables and interactions, performing on par or often even better than GAMLSS specified either through prior meteorological knowledge or a computationally more demanding boosting approach.

Ahmed Aziz Ezzat, Mikyoung Jun, Yu Ding.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1484--1510.

Abstract:
Accurate short-term forecasts are indispensable for the integration of wind energy in power grids. On a wind farm, local wind conditions exhibit sizeable variations at a fine temporal resolution. Existing statistical models may capture the in-sample variations in wind behavior, but are often shortsighted to those occurring in the near future, that is, in the forecast horizon. The calibrated regime-switching method proposed in this paper introduces an action of regime dependent calibration on the predictand (here the wind speed variable), which helps correct the bias resulting from out-of-sample variations in wind behavior. This is achieved by modeling the calibration as a function of two elements: the wind regime at the time of the forecast (and the calibration is therefore regime dependent), and the runlength, which is the time elapsed since the last observed regime change. In addition to regime-switching dynamics, the proposed model also accounts for other features of wind fields: spatio-temporal dependencies, transport effect of wind and nonstationarity. Using one year of turbine-specific wind data, we show that the calibrated regime-switching method can offer a wide margin of improvement over existing forecasting methods in terms of both wind speed and power.

Lin Liu, Yuqi Qiu, Loki Natarajan, Karen Messer.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1370--1396.

Abstract:
It is common to encounter missing data among the potential predictor variables in the setting of model selection. For example, in a recent study we attempted to improve the US guidelines for risk stratification after screening colonoscopy ( Cancer Causes Control 27 (2016) 1175–1185), with the aim to help reduce both overuse and underuse of follow-on surveillance colonoscopy. The goal was to incorporate selected additional informative variables into a neoplasia risk-prediction model, going beyond the three currently established risk factors, using a large dataset pooled from seven different prospective studies in North America. Unfortunately, not all candidate variables were collected in all studies, so that one or more important potential predictors were missing on over half of the subjects. Thus, while variable selection was a main focus of the study, it was necessary to address the substantial amount of missing data. Multiple imputation can effectively address missing data, and there are also good approaches to incorporate the variable selection process into model-based confidence intervals. However, there is not consensus on appropriate methods of inference which address both issues simultaneously. Our goal here is to study the properties of model-based confidence intervals in the setting of imputation for missing data followed by variable selection. We use both simulation and theory to compare three approaches to such post-imputation-selection inference: a multiple-imputation approach based on Rubin’s Rules for variance estimation ( Comput. Statist. Data Anal. 71 (2014) 758–770); a single imputation-selection followed by bootstrap percentile confidence intervals; and a new bootstrap model-averaging approach presented here, following Efron ( J. Amer. Statist. Assoc. 109 (2014) 991–1007). We investigate relative strengths and weaknesses of each method. The “Rubin’s Rules” multiple imputation estimator can have severe undercoverage, and is not recommended. The imputation-selection estimator with bootstrap percentile confidence intervals works well. The bootstrap-model-averaged estimator, with the “Efron’s Rules” estimated variance, may be preferred if the true effect sizes are moderate. We apply these results to the colorectal neoplasia risk-prediction problem which motivated the present work.

Jorge A. León.

Source: Bernoulli, Volume 26, Number 3, 2436--2462.

Abstract:
Let $B^{H}$ be a fractional Brownian motion with Hurst parameter $Hin (0,1/2)$ and $p:mathbb{R} ightarrow mathbb{R}$ a polynomial function. The main purpose of this paper is to introduce a Stratonovich type stochastic integral with respect to $B^{H}$, whose domain includes the process $p(B^{H})$. That is, an integral that allows us to integrate $p(B^{H})$ with respect to $B^{H}$, which does not happen with the symmetric integral given by Russo and Vallois ( Probab. Theory Related Fields 97 (1993) 403–421) in general. Towards this end, we combine the approaches utilized by León and Nualart ( Stochastic Process. Appl. 115 (2005) 481–492), and Russo and Vallois ( Probab. Theory Related Fields 97 (1993) 403–421), whose aims are to extend the domain of the divergence operator for Gaussian processes and to define some stochastic integrals, respectively. Then, we study the relation between this Stratonovich integral and the extension of the divergence operator (see León and Nualart ( Stochastic Process. Appl. 115 (2005) 481–492)), an Itô formula and the existence of a unique solution of some Stratonovich stochastic differential equations. These last results have been analyzed by Alòs, León and Nualart ( Taiwanese J. Math. 5 (2001) 609–632), where the Hurst paramert $H$ belongs to the interval $(1/4,1/2)$.

Piotr Kokoszka, Neda Mohammadi Jouzdani.

Source: Bernoulli, Volume 26, Number 3, 2383--2399.

Abstract:
This paper is concerned with frequency domain theory for functional time series, which are temporally dependent sequences of functions in a Hilbert space. We consider a variance decomposition, which is more suitable for such a data structure than the variance decomposition based on the Karhunen–Loéve expansion. The decomposition we study uses eigenvalues of spectral density operators, which are functional analogs of the spectral density of a stationary scalar time series. We propose estimators of the variance components and derive convergence rates for their mean square error as well as their asymptotic normality. The latter is derived from a frequency domain invariance principle for the estimators of the spectral density operators. This principle is established for a broad class of linear time series models. It is a main contribution of the paper.

Peter Bank, Yan Dolinsky.

Source: Bernoulli, Volume 26, Number 3, 2176--2201.

Abstract:
We prove a scaling limit theorem for the super-replication cost of options in a Cox–Ross–Rubinstein binomial model with transient price impact. The correct scaling turns out to keep the market depth parameter constant while resilience over fixed periods of time grows in inverse proportion with the duration between trading times. For vanilla options, the scaling limit is found to coincide with the one obtained by PDE-methods in ( Math. Finance 22 (2012) 250–276) for models with purely temporary price impact. These models are a special case of our framework and so our probabilistic scaling limit argument allows one to expand the scope of the scaling limit result to path-dependent options.

Akio Fujiwara, Koichi Yamagata.

Source: Bernoulli, Volume 26, Number 3, 2105--2142.

Abstract:
We herein develop a theory of contiguity in the quantum domain based upon a novel quantum analogue of the Lebesgue decomposition. The theory thus formulated is pertinent to the weak quantum local asymptotic normality introduced in the previous paper [Yamagata, Fujiwara, and Gill, Ann. Statist. 41 (2013) 2197–2217], yielding substantial enlargement of the scope of quantum statistics.

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.

Ulrike Mayer, Henryk Zähle, Zhou Zhou.

Source: Bernoulli, Volume 26, Number 3, 1891--1911.

Abstract:
We derive a functional weak limit theorem for a local empirical process of a wide class of piece-wise locally stationary (PLS) time series. The latter result is applied to derive the asymptotics of weighted empirical quantiles and weighted V-statistics of non-stationary time series. The class of admissible underlying time series is illustrated by means of PLS linear processes and PLS ARCH processes.

Jason M. Klusowski, Yihong Wu.

Source: Bernoulli, Volume 26, Number 3, 1635--1664.

Abstract:
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman ( Ann. Math. Stat. 20 (1949) 572–579) and Frank ( Scand. J. Stat. 5 (1978) 177–188). We revisit a problem formulated by Frank ( Scand. J. Stat. 5 (1978) 177–188) of estimating the number of connected components in a large graph based on the subgraph sampling model, in which we randomly sample a subset of the vertices and observe the induced subgraph. The key question is whether accurate estimation is achievable in the sublinear regime where only a vanishing fraction of the vertices are sampled. We show that it is impossible if the parent graph is allowed to contain high-degree vertices or long induced cycles. For the class of chordal graphs, where induced cycles of length four or above are forbidden, we characterize the optimal sample complexity within constant factors and construct linear-time estimators that provably achieve these bounds. This significantly expands the scope of previous results which have focused on unbiased estimators and special classes of graphs such as forests or cliques. Both the construction and the analysis of the proposed methodology rely on combinatorial properties of chordal graphs and identities of induced subgraph counts. They, in turn, also play a key role in proving minimax lower bounds based on construction of random instances of graphs with matching structures of small subgraphs.

Ilya Pavlyukevich, Georgiy Shevchenko.

Source: Bernoulli, Volume 26, Number 2, 1381--1409.

Abstract:
In this paper, we study the Stratonovich stochastic differential equation $mathrm{d}X=|X|^{alpha }circ mathrm{d}B$, $alpha in (-1,1)$, which has been introduced by Cherstvy et al. ( New J. Phys. 15 (2013) 083039) in the context of analysis of anomalous diffusions in heterogeneous media. We determine its weak and strong solutions, which are homogeneous strong Markov processes spending zero time at $0$: for $alpha in (0,1)$, these solutions have the form egin{equation*}X_{t}^{ heta }=((1-alpha)B_{t}^{ heta })^{1/(1-alpha )},end{equation*} where $B^{ heta }$ is the $ heta $-skew Brownian motion driven by $B$ and starting at $frac{1}{1-alpha }(X_{0})^{1-alpha }$, $ heta in [-1,1]$, and $(x)^{gamma }=|x|^{gamma }operatorname{sign}x$; for $alpha in (-1,0]$, only the case $ heta =0$ is possible. The central part of the paper consists in the proof of the existence of a quadratic covariation $[f(B^{ heta }),B]$ for a locally square integrable function $f$ and is based on the time-reversion technique for Markovian diffusions.

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.

Yating Liu, Gilles Pagès.

Source: Bernoulli, Volume 26, Number 2, 1171--1204.

Abstract:
We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic (convergence for the $L^{p}$-Wasserstein distance). We first propose a criterion on the quantization level $N$, valid for any norm on $mathbb{R}^{d}$ and any order $p$ based on a geometrical approach involving the Voronoï diagram. Then, we prove that in the $L^{2}$-case on a (separable) Hilbert space, the condition on the level $N$ can be reduced to $N=2$, which is optimal. More quantization based characterization cases in dimension 1 and a discussion of the completeness of a distance defined by the quantization error function can be found at the end of this paper.

Giacomo Aletti, Irene Crimaldi, Andrea Ghiglietti.

Source: Bernoulli, Volume 26, Number 2, 1098--1138.

Abstract:
This work deals with a system of interacting reinforced stochastic processes , where each process $X^{j}=(X_{n,j})_{n}$ is located at a vertex $j$ of a finite weighted directed graph, and it can be interpreted as the sequence of “actions” adopted by an agent $j$ of the network. The interaction among the dynamics of these processes depends on the weighted adjacency matrix $W$ associated to the underlying graph: indeed, the probability that an agent $j$ chooses a certain action depends on its personal “inclination” $Z_{n,j}$ and on the inclinations $Z_{n,h}$, with $h eq j$, of the other agents according to the entries of $W$. The best known example of reinforced stochastic process is the Pólya urn. The present paper focuses on the weighted empirical means $N_{n,j}=sum_{k=1}^{n}q_{n,k}X_{k,j}$, since, for example, the current experience is more important than the past one in reinforced learning. Their almost sure synchronization and some central limit theorems in the sense of stable convergence are proven. The new approach with weighted means highlights the key points in proving some recent results for the personal inclinations $Z^{j}=(Z_{n,j})_{n}$ and for the empirical means $overline{X}^{j}=(sum_{k=1}^{n}X_{k,j}/n)_{n}$ given in recent papers (e.g. Aletti, Crimaldi and Ghiglietti (2019), Ann. Appl. Probab. 27 (2017) 3787–3844, Crimaldi et al. Stochastic Process. Appl. 129 (2019) 70–101). In fact, with a more sophisticated decomposition of the considered processes, we can understand how the different convergence rates of the involved stochastic processes combine. From an application point of view, we provide confidence intervals for the common limit inclination of the agents and a test statistics to make inference on the matrix $W$, based on the weighted empirical means. In particular, we answer a research question posed in Aletti, Crimaldi and Ghiglietti (2019).

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.

Jing Lei.

Source: Bernoulli, Volume 26, Number 1, 767--798.

Abstract:
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization can cover Euclidean spaces with large dimensionality, with the optimal dependence on the dimensionality. Our method also covers the important case of Gaussian processes in separable Hilbert spaces, with rate-optimal upper bounds for functional data distributions whose coordinates decay geometrically or polynomially. Moreover, our bounds of the expected value can be combined with mean-concentration results to yield improved exponential tail probability bounds for the Wasserstein error of empirical measures under Bernstein-type or log Sobolev-type conditions.

Nicolas Privault, Grzegorz Serafin.

Source: Bernoulli, Volume 26, Number 1, 587--615.

Abstract:
We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and weighted $U$-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraph counts in the Erdős–Rényi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering recent results obtained for triangles and improving other bounds in the Wasserstein distance.

Tobias Zwingmann, Hajo Holzmann.

Source: Bernoulli, Volume 26, Number 1, 323--351.

Abstract:
We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo- convergence as introduced in A. Bücher, J. Segers and S. Volgushev (2014), ‘ When Uniform Weak Convergence Fails: Empirical Processes for Dependence Functions and Residuals via Epi- and Hypographs ’, Annals of Statistics 42 . We impose assumptions for which it is known that weak convergence with respect to the supremum norm generally fails to hold. For quantiles, we consider stationary observations, where the marginal distribution function is assumed to be strictly increasing and continuous except for finitely many points and to admit strictly positive – possibly infinite – left- and right-sided derivatives. For expectiles, we focus on independent and identically distributed (i.i.d.) observations. Only a finite second moment and continuity at the boundary points but no further smoothness properties of the distribution function are required. We also show consistency of the bootstrap for this mode of convergence in the i.i.d. case for quantiles and expectiles.

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.

Thomson (Family)

St. Philip and St. James Church (Noarlunga, S.A.)

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King's Orphan Schools (New Town, Tas.)

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Cheesman, John -- Family.

Huppatz (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.

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.

Three weeks before he was shot dead, Miguel Calderon, an inmate in the lawless Los Llanos jail on Venezuela's central plains, sent a voice message to his father. Like many of the prisoners in Venezuela's overcrowded and violent penitentiaries, Los Llanos's 4,000 inmates normally subsist on food relatives bring them. The guards, desperate themselves amid national shortages, began stealing the little food getting behind bars, inmates said, forcing some prisoners to turn to eating stray animals.

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

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

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.

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 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

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

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.

The military is preparing to deploy to the region to try to stop illegal logging and mining.

Georgia is one of four states that doesn't have a hate crime law. Arbery's killing has reignited calls for legislation.

The Justice Department announced Thursday that it is dropping its criminal case against President Trump's first national security adviser Michael Flynn. Flynn twice admitted in court he lied to the FBI about his conversations with Russia's U.S. ambassador, and then cooperated in Special Counsel Robert Mueller's investigation. It was an unusual move by the Justice Department, and CNN's legal and political analysts smelled a rat."Attorney General [William] Barr is already being accused of creating a special justice system just for President Trump's friends," and this will only feed that perception, CNN's Jake Tapper suggested. Political correspondent Sara Murray agreed, noting that the prosecutor in the case, Brandon Van Grack, withdrew right before the Justice Department submitted its filing, just like when Barr intervened to request a reduced sentence for Roger Stone.National security correspondent Jim Sciutto laid out several reason why the substance of Flynn's admitted lie was a big deal, and chief legal analyst Jeffrey Toobin was appalled. "It is one of the most incredible legal documents I have read, and certainly something that I never expected to see from the United States Department of Justice," Toobin said. "The idea that the Justice Department would invent an argument -- an argument that the judge in this case has already rejected -- and say that's a basis for dropping a case where a defendant admitted his guilt shows that this is a case where the fix was in."Barr told CBS News' Cathrine Herridge on Thursday that dropping Flynn's case actually "sends the message that there is one standard of justice in this country." Herridge told Barr he would take flak for this, asking: "When history looks back on this decision, how do you think it will be written?" Barr laughed: "Well, history's written by the winners. So it largely depends on who's writing the history." Watch below. 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

Matthew R. Williams, Terrance D. Savitsky.

Source: Bayesian Analysis, Volume 15, Number 1, 57--77.

Abstract:
An informative sampling design leads to unit inclusion probabilities that are correlated with the response variable of interest. However, multistage sampling designs may also induce higher order dependencies, which are ignored in the literature when establishing consistency of estimators for survey data under a condition requiring asymptotic independence among the unit inclusion probabilities. This paper constructs new theoretical conditions that guarantee that the pseudo-posterior, which uses sampling weights based on first order inclusion probabilities to exponentiate the likelihood, is consistent not only for survey designs which have asymptotic factorization, but also for survey designs that induce residual or unattenuated dependence among sampled units. The use of the survey-weighted pseudo-posterior, together with our relaxed requirements for the survey design, establish a wide variety of analysis models that can be applied to a broad class of survey data sets. Using the complex sampling design of the National Survey on Drug Use and Health, we demonstrate our new theoretical result on multistage designs characterized by a cluster sampling step that expresses within-cluster dependence. We explore the impact of multistage designs and order based sampling.

Matthew Moores, Geoff Nicholls, Anthony Pettitt, Kerrie Mengersen.

Source: Bayesian Analysis, Volume 15, Number 1, 1--27.

Abstract:
The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There is a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open-source implementation of our algorithm is available in the R package bayesImageS .

Andrea Cremaschi, Raffaele Argiento, Katherine Shoemaker, Christine Peterson, Marina Vannucci.

Source: Bayesian Analysis, Volume 14, Number 4, 1271--1301.

Abstract:
Gaussian graphical models are useful tools for exploring network structures in multivariate normal data. In this paper we are interested in situations where data show departures from Gaussianity, therefore requiring alternative modeling distributions. The multivariate $t$ -distribution, obtained by dividing each component of the data vector by a gamma random variable, is a straightforward generalization to accommodate deviations from normality such as heavy tails. Since different groups of variables may be contaminated to a different extent, Finegold and Drton (2014) introduced the Dirichlet $t$ -distribution, where the divisors are clustered using a Dirichlet process. In this work, we consider a more general class of nonparametric distributions as the prior on the divisor terms, namely the class of normalized completely random measures (NormCRMs). To improve the effectiveness of the clustering, we propose modeling the dependence among the divisors through a nonparametric hierarchical structure, which allows for the sharing of parameters across the samples in the data set. This desirable feature enables us to cluster together different components of multivariate data in a parsimonious way. We demonstrate through simulations that this approach provides accurate graphical model inference, and apply it to a case study examining the dependence structure in radiomics data derived from The Cancer Imaging Atlas.

Nadja Klein, Michael Stanley Smith.

Source: Bayesian Analysis, Volume 14, Number 4, 1143--1171.

Abstract:
We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors—a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection—and both univariate and multivariate function bases. The implicit copulas are high-dimensional, have flexible dependence structures that are far from that of a Gaussian copula, and are unavailable in closed form. However, we show how they can be evaluated by first constructing a Gaussian copula conditional on the regularization parameters, and then integrating over these. Combined with non-parametric margins the regularized smoothers can be used to model the distribution of non-Gaussian univariate responses conditional on the covariates. Efficient Markov chain Monte Carlo schemes for evaluating the copula are given for this case. Using both simulated and real data, we show how such copula smoothing models can improve the quality of resulting function estimates and predictive distributions.