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

Moore, Amy, 1908-2005.

Hewish Henry -- Family.

Grant (Family)

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

Klemm (Family)

Names, Personal -- Welsh.

Names, Personal -- Scottish.

Genetic genealogy -- Handbooks, manuals, etc.

Fuhlbohm (Family)

Kraus, Peter -- Biography.

Huppatz (Family).

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 two major companies cited what they considered onerous divestiture requirements from the U.S. Department of Justice as the reason behind their joint decision.

The post McGraw-Hill and Cengage Abandon Merger Plans 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.

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.

Saint Paul schools are in the market for a vendor to provide background checks, while the Education Technology Joint Powers Authority is seeking media repositories. A Texas district wants quotes on technology for new campuses.

The post Calif. Ed-Tech Consortium Seeks Media Repository Solutions; Saint Paul District Needs Background Check Services appeared first on Market Brief.

Three children have now died in New York state from a possible complication from the coronavirus involving swollen blood vessels and heart problems, Gov. Andrew Cuomo said Saturday. At least 73 children in New York have been diagnosed with symptoms similar to Kawasaki disease — a rare inflammatory condition in children — and toxic shock syndrome.

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.

A train in India on Friday plowed through a group of migrant workers who fell asleep on the tracks after walking back home from a coronavirus lockdown, killing 15, the Railways Ministry said. Early this week the government started running trains to carry stranded workers to their home states.

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.

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 infections and deaths are spread across roughly two farms and 189 meat and processed food factories.

Some Buckeyes are not comfortable being told by a "woman in power" to quarantine, one expert said.

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

The Democracy Fund + UCLA Nationscape Project found some misinformation about the coronavirus is more widespread that you might think.

Kurtis Shuler, Marilou Sison-Mangus, Juhee Lee.

Source: Bayesian Analysis, Volume 15, Number 2, 559--578.

Abstract:
We propose a Bayesian sparse multivariate regression method to model the relationship between microbe abundance and environmental factors for microbiome data. We model abundance counts of operational taxonomic units (OTUs) with a negative binomial distribution and relate covariates to the counts through regression. Extending conventional nonlocal priors, we construct asymmetric nonlocal priors for regression coefficients to efficiently identify relevant covariates and their effect directions. We build a hierarchical model to facilitate pooling of information across OTUs that produces parsimonious results with improved accuracy. We present simulation studies that compare variable selection performance under the proposed model to those under Bayesian sparse regression models with asymmetric and symmetric local priors and two frequentist models. The simulations show the proposed model identifies important covariates and yields coefficient estimates with favorable accuracy compared with the alternatives. The proposed model is applied to analyze an ocean microbiome dataset collected over time to study the association of harmful algal bloom conditions with microbial communities.

Cristiano Villa, Jeong Eun Lee.

Source: Bayesian Analysis, Volume 15, Number 2, 533--558.

Abstract:
In this work we propose a novel model prior for variable selection in linear regression. The idea is to determine the prior mass by considering the worth of each of the regression models, given the number of possible covariates under consideration. The worth of a model consists of the information loss and the loss due to model complexity. While the information loss is determined objectively, the loss expression due to model complexity is flexible and, the penalty on model size can be even customized to include some prior knowledge. Some versions of the loss-based prior are proposed and compared empirically. Through simulation studies and real data analyses, we compare the proposed prior to the Scott and Berger prior, for noninformative scenarios, and with the Beta-Binomial prior, for informative scenarios.

Maxim Rabinovich, Aaditya Ramdas, Michael I. Jordan, Martin J. Wainwright.

Source: Bayesian Analysis, Volume 15, Number 2, 505--532.

Abstract:
Slow mixing is the central hurdle is applications of Markov chains, especially those used for Monte Carlo approximations (MCMC). In the setting of Bayesian inference, it is often only of interest to estimate the stationary expectations of a small set of functions, and so the usual definition of mixing based on total variation convergence may be too conservative. Accordingly, we introduce function-specific analogs of mixing times and spectral gaps, and use them to prove Hoeffding-like function-specific concentration inequalities. These results show that it is possible for empirical expectations of functions to concentrate long before the underlying chain has mixed in the classical sense, and we show that the concentration rates we achieve are optimal up to constants. We use our techniques to derive confidence intervals that are sharper than those implied by both classical Markov-chain Hoeffding bounds and Berry-Esseen-corrected central limit theorem (CLT) bounds. For applications that require testing, rather than point estimation, we show similar improvements over recent sequential testing results for MCMC. We conclude by applying our framework to real-data examples of MCMC, providing evidence that our theory is both accurate and relevant to practice.

Xuan Cao, Kshitij Khare, Malay Ghosh.

Source: Bayesian Analysis, Volume 15, Number 1, 241--262.

Abstract:
The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an important tuning parameter which reflects the dispersion of the non-local prior density around zero, and implicitly determines the size of the regression coefficients that will be shrunk to zero. Current approaches treat the scale parameter as given, and suggest choices based on prior coverage/asymptotic considerations. In this paper, we consider the fully Bayesian approach introduced in (Wu, 2016) with the pMOM non-local prior and an appropriate Inverse-Gamma prior on the tuning parameter to analyze the underlying theoretical property. Under standard regularity assumptions, we establish strong model selection consistency in a high-dimensional setting, where $p$ is allowed to increase at a polynomial rate with $n$ or even at a sub-exponential rate with $n$ . Through simulation studies, we demonstrate that our model selection procedure can outperform other Bayesian methods which treat the scale parameter as given, and commonly used penalized likelihood methods, in a range of simulation settings.

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.

Fangzheng Xie, Yanxun Xu.

Source: Bayesian Analysis, Volume 15, Number 1, 159--186.

Abstract:
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal contraction rate of the full posterior distribution up to a logarithmic factor by estimating metric entropies of certain function classes. Under the assumption that the degree of the polynomials is larger than the unknown smoothness level of the true function, the posterior contraction behavior can adapt to this smoothness level provided an upper bound is known. We also provide a frequentist sieve maximum likelihood estimator with a near-optimal convergence rate. We further investigate the application of the kernel mixture of polynomials to partial linear models and obtain both the near-optimal rate of contraction for the nonparametric component and the Bernstein-von Mises limit (i.e., asymptotic normality) of the parametric component. The proposed method is illustrated with numerical examples and shows superior performance in terms of computational efficiency, accuracy, and uncertainty quantification compared to the local polynomial regression, DiceKriging, and the robust Gaussian stochastic process.

Antony Overstall, James McGree.

Source: Bayesian Analysis, Volume 15, Number 1, 103--131.

Abstract:
A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models. Although straightforward in principle, there are several challenges to finding Bayesian designs in practice. Firstly, the utility and expected utility are rarely available in closed form and require approximation. Secondly, the design space can be of high-dimensionality. In the case of intractable likelihood models, these problems are compounded by the fact that the likelihood function, whose evaluation is required to approximate the expected utility, is not available in closed form. A strategy is proposed to find Bayesian designs for intractable likelihood models. It relies on the development of an automatic, auxiliary modelling approach, using multivariate Gaussian process emulators, to approximate the likelihood function. This is then combined with a copula-based approach to approximate the marginal likelihood (a quantity commonly required to evaluate many utility functions). These approximations are demonstrated on examples of stochastic process models involving experimental aims of both parameter estimation and model comparison.

Federico Camerlenghi, David B. Dunson, Antonio Lijoi, Igor Prünster, Abel Rodríguez.

Source: Bayesian Analysis, Volume 14, Number 4, 1303--1356.

Abstract:
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalizing to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop a Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by-product. The results and their inferential implications are showcased on synthetic and real data.

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.

Gemma E. Moran, Veronika Ročková, Edward I. George.

Source: Bayesian Analysis, Volume 14, Number 4, 1091--1119.

Abstract:
Consider the problem of high dimensional variable selection for the Gaussian linear model when the unknown error variance is also of interest. In this paper, we show that the use of conjugate shrinkage priors for Bayesian variable selection can have detrimental consequences for such variance estimation. Such priors are often motivated by the invariance argument of Jeffreys (1961). Revisiting this work, however, we highlight a caveat that Jeffreys himself noticed; namely that biased estimators can result from inducing dependence between parameters a priori . In a similar way, we show that conjugate priors for linear regression, which induce prior dependence, can lead to such underestimation in the Bayesian high-dimensional regression setting. Following Jeffreys, we recommend as a remedy to treat regression coefficients and the error variance as independent a priori . Using such an independence prior framework, we extend the Spike-and-Slab Lasso of Ročková and George (2018) to the unknown variance case. This extended procedure outperforms both the fixed variance approach and alternative penalized likelihood methods on simulated data. On the protein activity dataset of Clyde and Parmigiani (1998), the Spike-and-Slab Lasso with unknown variance achieves lower cross-validation error than alternative penalized likelihood methods, demonstrating the gains in predictive accuracy afforded by simultaneous error variance estimation. The unknown variance implementation of the Spike-and-Slab Lasso is provided in the publicly available R package SSLASSO (Ročková and Moran, 2017).

Claudia Kirch, Matthew C. Edwards, Alexander Meier, Renate Meyer.

Source: Bayesian Analysis, Volume 14, Number 4, 1037--1073.

Abstract:
Nonparametric Bayesian inference has seen a rapid growth over the last decade but only few nonparametric Bayesian approaches to time series analysis have been developed. Most existing approaches use Whittle’s likelihood for Bayesian modelling of the spectral density as the main nonparametric characteristic of stationary time series. It is known that the loss of efficiency using Whittle’s likelihood can be substantial. On the other hand, parametric methods are more powerful than nonparametric methods if the observed time series is close to the considered model class but fail if the model is misspecified. Therefore, we suggest a nonparametric correction of a parametric likelihood that takes advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. We use a nonparametric Bernstein polynomial prior on the spectral density with weights induced by a Dirichlet process and prove posterior consistency for Gaussian stationary time series. Bayesian posterior computations are implemented via an MH-within-Gibbs sampler and the performance of the nonparametrically corrected likelihood for Gaussian time series is illustrated in a simulation study and in three astronomy applications, including estimating the spectral density of gravitational wave data from the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO).

Miguel de Carvalho, Garritt L. Page, Bradley J. Barney.

Source: Bayesian Analysis, Volume 14, Number 4, 1013--1036.

Abstract:
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer.

Jon Cockayne, Chris J. Oates, Ilse C.F. Ipsen, Mark Girolami.

Source: Bayesian Analysis, Volume 14, Number 3, 937--1012.

Abstract:
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about, for example, the magnitude of the error. In this paper we propose a novel statistical model for this error, set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging.

Joseph Antonelli, Giovanni Parmigiani, Francesca Dominici.

Source: Bayesian Analysis, Volume 14, Number 3, 825--848.

Abstract:
In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders ( $p$ ) is larger than the number of observations ( $n$ ), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable $X_{j}$ is strongly associated with the treatment $T$ but weakly with the outcome $Y$ , the coefficient $eta_{j}$ will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients $eta_{j}$ corresponding to the potential confounders $X_{j}$ . Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients ( $eta_{j}$ s) of the $X_{j}$ s that are strongly associated with $T$ but weakly associated with $Y$ . We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels.

Stefano Peluso, Siddhartha Chib, Antonietta Mira.

Source: Bayesian Analysis, Volume 14, Number 3, 727--751.

Abstract:
We develop a general Bayesian semiparametric change-point model in which separate groups of structural parameters (for example, location and dispersion parameters) can each follow a separate multiple change-point process, driven by time-dependent transition matrices among the latent regimes. The distribution of the observations within regimes is unknown and given by a Dirichlet process mixture prior. The properties of the proposed model are studied theoretically through the analysis of inter-arrival times and of the number of change-points in a given time interval. The prior-posterior analysis by Markov chain Monte Carlo techniques is developed on a forward-backward algorithm for sampling the various regime indicators. Analysis with simulated data under various scenarios and an application to short-term interest rates are used to show the generality and usefulness of the proposed model.

Luis Gutiérrez, Andrés F. Barrientos, Jorge González, Daniel Taylor-Rodríguez.

Source: Bayesian Analysis, Volume 14, Number 2, 649--675.

Abstract:
We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.