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Until about two hundred years ago, no gemological distinction was made between ruby and spinel. Red spinel and red ruby are not infrequently found together and though gem cutters and engravers noticed and commented on the difference in hardness, the assumption was that spinel was simply an \"unripe\" version of ruby. Additionally, ruby and sapphire are both versions of the mineral corundum, distinguished only by color and minute traces of the metal oxides that caused these different colors. Sapphires may be pink, yellow, and green as well as blue, while rubies come in many shades of red which, inevitably causes confusion as one person's pale red ruby is another's pink sapphire--there are no absolutes. Consequently, the nomenclature is confused, both within early texts, and also in later translations of those texts. The ancient authors could only report on the basis of the information available to them at the time, while those writing the later translations were fine textual scholars or epigraphers, but not infrequently poor gemologists, not familiar with the mineralogical distinctions between the gems. It has often been difficult to get an overarching view of the many different factors that all played a part in the spread of precious gems and of the dissemination of knowledge about them. Given the paucity of available information concentrating exclusively on the use of ancient precious gemstones, the author combed the literature for relevant references. A surprising amount of descriptive and factual information was found, mostly scattered throughout early texts. The most interesting passages were selected and wherever possible the original authors' words were quoted rather than paraphrased. The early translations in the languages used by 17th-19th century scholars are given, names of people, places or objects that otherwise might have remained obscure are explained. Gems travel. They follow wealth and because of their natural immutability, the only way they can be identified by culture is by the way man has affected their appearance, deliberately or accidentally. The dating of gems that are still in original period settings is easier because the dated typology of rings and jewelry settings generally, is more secure than the study of gem shapes, while the study and dating of specific faceting styles of unmounted stones is still in its infancy.

Gelman and Rubin's (Statist. Sci. 7 (1992) 457–472) convergence diagnostic is one of the most popular methods for terminating a Markov chain Monte Carlo (MCMC) sampler. Since the seminal paper, researchers have developed sophisticated methods for estimating variance of Monte Carlo averages. We show that these estimators find immediate use in the Gelman–Rubin statistic, a connection not previously established in the literature. We incorporate these estimators to upgrade both the univariate and multivariate Gelman–Rubin statistics, leading to improved stability in MCMC termination time. An immediate advantage is that our new Gelman–Rubin statistic can be calculated for a single chain. In addition, we establish a one-to-one relationship between the Gelman–Rubin statistic and effective sample size. Leveraging this relationship, we develop a principled termination criterion for the Gelman–Rubin statistic. Finally, we demonstrate the utility of our improved diagnostic via examples.

\"When Adrienne Rubin enters into the jewelry business in 1970s Los Angeles, she is a maverick in a world dominated by men. She soon meets a young hotshot salesman who doesn't seem to struggle at all, and when he asks her to be his partner, she is excited to join him. She doesn't know him well, but she does know his father, and she believes he is as trustworthy as the day is long... Diamonds and Scoundrels shows us how a woman in a man's world, with tenacity and sheer determination, can earn respect and obtain a true sense of accomplishment. Following Rubin's experiences in the jewelry industry through the '70s, '80s, and '90s--with the ups and downs, good guys and bad--this is a tale of personal growth, of how to overcome challenges with courage and resilience. It's a story for the woman today who, in addition to a rich family life, seeks a self-realized, fulfilling path toward a life well lived\"--Publisher's description.

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for defining, identifying, and estimating causal effects. In this paper, we review the potential outcomes framework with a focus on potential outcomes notation to define individual and average causal effects. We then show how three canonical assumptions, Unconfoundedness, Positivity, and Consistency, may be used to identify average causal effects. The identification results motivate methods for estimating causal effects in practice, which include model-based estimators, such as regression, inverse probability weighting, and doubly robust estimation, and procedures that target covariate balance, such as matching and stratification. Examples and discussion are grounded in the context of a running example of a study aimed at assessing the causal effect of receipt of special education services on 5th grade mathematics achievement in school-aged children. Practical considerations for education research are discussed.

We follow a post hoc, “user-agnostic” approach to false discovery control in a large-scale multiple testing framework, as introduced by Genovese and Wasserman [J. Amer. Statist. Assoc. 101 (2006) 1408–1417], Goeman and Solari [Statist. Sci. 26 (2011) 584–597]: the statistical guarantee on the number of correct rejections must hold for any set of candidate items, possibly selected by the user after having seen the data. To this end, we introduce a novel point of view based on a family of reference rejection sets and a suitable criterion, namely the joint familywise error rate over that family (JER for short). First, we establish how to derive post hoc bounds from a given JER control and analyze some general properties of this approach. We then develop procedures for controlling the JER in the case where reference regions are p-value level sets. These procedures adapt to dependencies and to the unknown quantity of signal (via a step-down principle). We also show interesting connections to confidence envelopes of Meinshausen [Scand. J. Stat. 33 (2006) 227–237]; Genovese and Wasserman [J. Amer. Statist. Assoc. 101 (2006) 1408–1417], the closed testing based approach of Goeman and Solari [Statist. Sci. 26 (2011) 584–597] and to the higher criticism of Donoho and Jin [Ann. Statist. 32 (2004) 962–994]. Our theoretical statements are supported by numerical experiments.

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates. If there are a large number of covariates relative to the number of observations, regression may perform poorly because of overfitting. In such cases, the least absolute shrinkage and selection operator (Lasso) may be helpful. We study the resulting Lasso-based treatment effect estimator under the Neyman–Rubin model of randomized experiments. We present theoretical conditions that guarantee that the estimator is more efficient than the simple difference-of-means estimator, and we provide a conservative estimator of the asymptotic variance, which can yield tighter confidence intervals than the difference-of-means estimator. Simulation and data examples show that Lasso-based adjustment can be advantageous even when the number of covariates is less than the number of observations. Specifically, a variant using Lasso for selection and ordinary least squares (OLS) for estimation performs particularly well, and it chooses a smoothing parameter based on combined performance of Lasso and OLS.

Travel to the most sophisticated telescope ever built, in Chile, and learn what it can do.

Most library leaders are made in the field, whether assuming vacant positions, falling into the role by chance, or taking it on from a sense of duty to maintain the stability of their unit or department. Those who are lucky find a mentor, but often, little training is offered. The goal of this article is to inspire new and seasoned leaders to examine their position and evaluate how their leadership style can inspire and motivate members of their team to achieve their best work while thriving within their organization. It is also inspired by concepts presented in popular works on leadership, motivation, and productivity, chief among these Gretchen Rubin’s The Four Tendencies, Liz Wiseman and Greg McKeown’s Multipliers, and Cal Newport’s Deep Work.

Vera Cooper Rubin was a pioneering astronomer, an admired role model and a passionate champion of female scientists. Her groundbreaking work confirmed the existence of dark matter and demonstrated that galaxies are embedded in dark-matter halos, which we now know contain most of the mass in the Universe.

A poem is presented.