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Algebraic methods have a long history in statistics. Apart from the ubiquitous applications of linear algebra, the most visible manifestations of modern algebra in statistics are found in the young field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to bear on statistical problems. Now over two decades old, algebraic statistics has applications in a wide range of theoretical and applied statistical domains. Nevertheless, algebraic statistical methods are still not mainstream, mostly due to a lack of easy off-the-shelf implementations. In this article we debut m2r, an R package that connects R to Macaulay2 through a persistent back-end socket connection running locally or on a cloud server. Topics range from basic use of m2r to applications and design philosophy.

One of the key advantages of the Bayesian paradigm is the ability to incorporate past experiences and expert opinion into statistical analyses. However, the principled, precise distillation of expert opinion into a probability distribution, a task known as prior elicitation, is challenging and involves considerations from psychology, computational science, software engineering, and other related fields. Moreover, for elicitation to be practical, applied statisticians need good computer tools to enable its use–to perform complex calculations and provide feedback. Such computer programs are called facilitators. Using the prior elicitation of a population proportion as a canonical example, in this article we contend that Wolfram Research Inc.’s Mathematica/CDF Player/CDF suite of technologies provides a new state-of-the-art platform for the development and dissemination of free facilitators. To illustrate its capabilities, we present a free facilitator that enables, in a real-time interactive environment, the computations and diagnostics required of an elicitation method known as the mode/percentile (MP) method.

Count data are subject to considerable sources of what is often referred to as non-sampling error. Errors such as misclassification, measurement error and unmeasured confounding can lead to substantially biased estimators. It is strongly recommended that epidemiologists not only acknowledge these sorts of errors in data, but incorporate sensitivity analyses into part of the total data analysis. We extend previous work on Poisson regression models that allow for misclassification by thoroughly discussing the basis for the models and allowing for extra-Poisson variability in the form of random effects. Via simulation we show the improvements in inference that are brought about by accounting for both the misclassification and the overdispersion.

Sample size determination is a vital part of clinical studies where cost and safety concerns lead to greater importance of not using more subjects and resources than are required. The Bayesian approach to sample size determination has the advantages of being able to use prior data and expert opinion to possibly reduce the total sample size while also acknowledging all uncertainty at the design stage. We apply a Bayesian decision theoretic approach to the problem of comparing two Poisson rates and find the required sample size to obtain a desired power while controlling the Type I error rate.