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The bulk elemental composition of soil subsurface (B) horizons is influenced by environmental, biological, geological, and climatic factors. Because fossil soils (paleosols) are common in the geologic record, quantitative models that link climate to paleosol geochemistry are highly desirable in the paleoclimate community. Error associated with these models is typically reported as the root mean square error (RMSE) of a regression analysis and reflects the variability imparted by non-climatic influences on soil formation and the uncertainty associated with model fitting. However, for prediction purposes, the RMSE is well known to underestimate model uncertainty. In this work we re-evaluate a widely used transfer function for mean annual precipitation (MAP) based on the chemical index of alteration minus potassium (CIA-K) using data science best practices on two continental-scale soil data sets. Data set inter-comparisons and cross-validation of exponential regression models indicate that the root mean square prediction error (RMSPE) between CIA-K and MAP for soils representative of climates across the continental United States is around 299 mm, significantly higher than the currently accepted 182 mm RMSE. Further, CIA-K is unable to predict perhumid (>2000 mm MAP) climate zones. We show that transitioning from a simple regression framework to one of recursive partitioning via random forests can significantly increase prediction accuracy while automating variable selection. We introduce two new, widely applicable random forest models for MAP (RF-MAP) that use 10 elemental oxides as input variables and were calibrated on the Baylor University Soil Informatics (BU-SI) data set. RF-MAP version 1.0 (RF-MAP1.0) was generated using the entire BU-SI data set (n = 685) and can predict MAP values up to 6865 mm with a RMSPE of 395 mm. RF-MAP version 2.0 (RF-MAP2.0) was generated using a modification of the BU-SI data set (n = 642) and can predict MAP values up to ∼1600 mm with a RMSPE of 209 mm. Pruned regression trees provide insight into the mechanisms driving the random forest models and demonstrate the first empirical confirmation of the sensitivity of soil elemental responses to global climate zones. The RF-MAP1.0 and RF-MAP2.0 models predict MAP values comparable to independent proxy estimates for a range of deep-time paleosols. We advocate for application of RF-MAP1.0 in settings where no a priori information on paleoclimate is available, and encourage the use of either RF-MAP1.0 or RF-MAP2.0 if users have independent constraints that paleo-MAP was below 1600 mm.

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.

Standard prior elicitation procedures require experts to explicitly quantify their beliefs about parameters in the form of multiple summaries. In this article, we draw on recent advances in the statistical graphics and information visualization communities to propose a novel elicitation scheme that implicitly learns an expert’s opinions through their sequential selection of graphics of carefully constructed hypothetical future samples. While the scheme can be applied to a broad array of models, we use it to construct procedures for elicitation in data models commonly used in practice: Bernoulli, Poisson, and Normal. We also provide open-source, web-based Shiny implementations of the procedures.

This article provides necessary and sufficient conditions that characterize independence among sub-vectors of a singular multivariate skew-normal random vector.

Wald, profile likelihood, and marginal likelihood confidence intervals are derived for the ratio of two Poisson rates in the presence of one-way differentially misclassified data using double sampling. Monte Carlo simulations demonstrate the reliability and relative performance of the intervals, and an example from cancer epidemiology illustrates their application and interpretation in a real-world scenario. All of the methods described are implemented and freely available in the R package poisDoubleSamp on the Comprehensive R Archive Network (CRAN).

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.