Katz, King, and Rosenblatt (2020, American Political Science Review 114, 164–178) introduces a theoretical framework for understanding redistricting and electoral systems, built on basic statistical and social science principles of inference. DeFord et al. (2021, Political Analysis, this issue) instead focuses solely on descriptive measures, which lead to the problems identified in our article. In this article, we illustrate the essential role of these basic principles and then offer statistical, mathematical, and substantive corrections required to apply DeFord et al.’s calculations to social science questions of interest, while also showing how to easily resolve all claimed paradoxes and problems. We are grateful to the authors for their interest in our work and for this opportunity to clarify these principles and our theoretical framework.

We develop a model that successfully learns social and organizational human network structure using ambient sensing data from distributed plug load energy sensors in commercial buildings. A key goal for the design and operation of commercial buildings is to support the success of organizations within them. In modern workspaces, a particularly important goal is collaboration, which relies on physical interactions among individuals. Learning the true socio-organizational relational ties among workers can therefore help managers of buildings and organizations make decisions that improve collaboration. In this paper, we introduce the Interaction Model, a method for inferring human network structure that leverages data from distributed plug load energy sensors. In a case study, we benchmark our method against network data obtained through a survey and compare its performance to other data-driven tools. We find that unlike previous methods, our method infers a network that is correlated with the survey network to a statistically significant degree (graph correlation of 0.46, significant at the 0.01 confidence level). We additionally find that our method requires only 10 weeks of sensing data, enabling dynamic network measurement. Learning human network structure through data-driven means can enable the design and operation of spaces that encourage, rather than inhibit, the success of organizations.

Quantitative comparative social scientists have long worried about the performance of multilevel models when the number of upper-level units is small. Adding to these concerns, an influential Monte Carlo study by Stegmueller (2013) suggests that standard maximum-likelihood (ML) methods yield biased point estimates and severely anti-conservative inference with few upper-level units. In this article, the authors seek to rectify this negative assessment. First, they show that ML estimators of coefficients are unbiased in linear multilevel models. The apparent bias in coefficient estimates found by Stegmueller can be attributed to Monte Carlo Error and a flaw in the design of his simulation study. Secondly, they demonstrate how inferential problems can be overcome by using restricted ML estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible within the framework that most practitioners are familiar with, even if there are only a few upper-level units.

Intensive week-long Summer Schools in Statistics for Astronomers were initiated at Penn State in 2005 and have been continued annually. Due to their popularity and high demand, additional full summer schools have been organized in India, Brazil, Space Telescope Science Institute.

The Summer Schools seek to give a broad exposure to fundamental concepts and a wide range of resulting methods across many fields of statistics. The Summer Schools in statistics and data analysis for young astronomers present concepts and methodologies with hands on tutorials using the data from astronomical surveys.

In this paper, we use queuing theory to model the number of insured households in an insurance portfolio. The model is based on an idea from Boucher and Couture-Piché (2015), who use a queuing theory model to estimate the number of insured cars on an insurance contract. Similarly, the proposed model includes households already insured, but the modeling approach is modified to include new households that could be added to the portfolio. For each household, we also use the queuing theory model to estimate the number of insured cars. We analyze an insurance portfolio from a Canadian insurance company to support this discussion. Statistical inference techniques serve to estimate each parameter of the model, even in cases where some explanatory variables are included in each of these parameters. We show that the proposed model offers a reasonable approximation of what is observed, but we also highlight the situations where the model should be improved. By assuming that the insurance company makes a $1 profit for each one-year car exposure, the proposed approach allows us to determine a global value of the insurance portfolio of an insurer based on the customer equity concept.

Visual displays of data in the parasitology literature are often presented in a way which is not very informative regarding the distribution of the data. An example being simple barcharts with half an error bar on top to display the distribution of parasitaemia and biomarkers of host immunity. Such displays obfuscate the shape of the data distribution through displaying too few statistical measures to explain the spread of all the data and selecting statistical measures which are influenced by skewness and outliers. We describe more informative, yet simple, visual representations of the data distribution commonly used in statistics and provide guidance with regards to the display of estimates of population parameters (e.g. population mean) and measures of precision (e.g. 95% confidence interval) for statistical inference. In this article we focus on visual displays for numerical data and demonstrate such displays using an example dataset consisting of total IgG titres in response to three Plasmodium blood antigens measured in pregnant women and parasitaemia measurements from the same study. This tutorial aims to highlight the importance of displaying the data distribution appropriately and the role such displays have in selecting statistics to summarize its distribution and perform statistical inference.

There is burgeoning interest in predicting road development because of the wide ranging important socioeconomic and environmental issues that roads present, including the close links between road development, deforestation and biodiversity loss. This is especially the case in developing nations, which are high in natural resources, where road development is rapid and often not centrally managed. Characterization of large scale spatio-temporal patterns in road network development has been greatly overlooked to date. This paper examines the spatio-temporal dynamics of road density across the Brazilian Amazon and assesses the relative contributions of local versus neighbourhood effects for temporal changes in road density at regional scales. To achieve this, a combination of statistical analyses and model-data fusion techniques inspired by studies of spatio-temporal dynamics of populations in ecology and epidemiology were used. The emergent development may be approximated by local growth that is logistic through time and directional dispersal. The current rates and dominant direction of development may be inferred, by assuming that roads develop at a rate of 55 km per year. Large areas of the Amazon will be subject to extensive anthropogenic change should the observed patterns of road development continue.

In this paper, following an open portfolio approach, we show how to estimate a Bonus-malus system evolution.

Considering a model for the number of new annual policies, we obtain ML estimators, asymptotic distributions and confidence regions for the expected number of new policies entering the portfolio in each year, as well as for the expected number and proportion of insureds in each bonus class, by year of enrollment. Confidence regions for the distribution of policyholders result in confidence regions for optimal bonus scales.

Our treatment is illustrated by an example with numerical results.

Based on the concept of multipower variation we establish a class of easily computable and robust estimators for the integrated volatility, especially including the squared integrated volatility, in Lévy-type stochastic volatility models. We derive consistency and feasible distributional results for the estimators. Furthermore, we discuss the applications to time-changed CGMY, normal inverse Gaussian, and hyperbolic models with and without leverage, where the time-changes are based on integrated Cox-Ingersoll-Ross or Ornstein-Uhlenbeck-type processes. We deduce which type of market microstructure does not affect the estimates.

S. James Press's many contributions to statistical research, lecturing, mentoring students, the statistics profession, etc., are summarized. Then some new developments in Bayesian analysis are described and remarks on the future of Bayesian analysis are presented.

We develop and apply bootstrap methods for diffusion models when fitted to the long run as characterized by the stationary distribution of the data. To obtain bootstrap refinements to statistical inference, we simulate candidate diffusion processes. We use these bootstrap methods to assess measurements of local mean reversion or “pull” to the center of the distribution for short-term interest rates. We also use them to evaluate the fit of the model to the empirical density.