Introduction

The Statistics Consortium at the University of Maryland, College Park, hosted a two-day workshop on Bayesian Methods that Frequentists Should Know during April 30--May 1, 2008. The event was co-sponsored by the Institute of Mathematical Statistics (IMS), Office of Research and Methodology, National Center for Health Statistics, Survey Research Methods Section (SRMS) of the American Statistical Association, and Washington Statistical Society. The workshop was intended to bring out the positive features of Bayesian statistics in solving real-life problems, including complex problems in sample surveys and production of high-quality official statistics.Comment: Published in at http://dx.doi.org/10.1214/11-STS359 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

CooccurrenceAffinity: An R package for computing a novel metric of affinity in co-occurrence data that corrects for pervasive errors in traditional indices.

1. Analysis of co-occurrence data with traditional indices has led to many problems such as sensitivity of the indices to prevalence and the same value representing either a strong positive or strong negative association across different datasets. In our recent study (Mainali et al 2022), we revealed the source of the problems that make the traditional indices fundamentally flawed and unreliable-namely that the indices in common use have no target of estimation quantifying degree of association in the non-null case-and we further developed a novel parameter of association, alpha, with complete formulation of the null distribution for estimating the mechanism of affinity. We also developed the maximum likelihood estimate (MLE) of alpha in our previous study. 2. Here, we introduce the CooccurrenceAffinity R package that computes the MLE for alpha. We provide functions to perform the analysis based on a 2×2 contingency table of occurrence/co-occurrence counts as well as a m×n presence-absence matrix (e.g., species by site matrix). The flexibility of the function allows a user to compute the alpha MLE for entity pairs on matrix columns based on presence-absence states recorded in the matrix rows, or for entity pairs on matrix rows based on presence-absence recorded in columns. We also provide functions for plotting the computed indices. 3. As novel components of this software paper not reported in the original study, we present theoretical discussion of a median interval and of four types of confidence intervals. We further develop functions (a) to compute those intervals, (b) to evaluate their true coverage probability of enclosing the population parameter, and (c) to generate figures. 4. CooccurrenceAffinity is a practical and efficient R package with user-friendly functions for end-to-end analysis and plotting of co-occurrence data in various formats, making it possible to compute the recently developed metric of alpha MLE as well as its median and confidence intervals introduced in this paper. The package supplements its main output of the novel metric of association with the three most common traditional indices of association in co-occurrence data: Jaccard, Sørensen-Dice, and Simpson

Null model analyses are not adequate to summarize strong associations: Rebuttal to Ulrich et al. (2022)

We recently developed a novel metric of association in pairwise co-occurrence data (Mainali et al., 2022) to address fundamental flaws in traditional indices, as elaborately discussed and conclusively shown in our published paper. Our new metric, the maximum likelihood estimator (MLE) alpha-hat of a statistical parameter alpha, quantifies the degree of association between species occupancy at ecological sites, and it is insensitive to the species prevalences and number of sites. In contrast, we showed that classic indices of co-occurrence (Jaccard, Simpson, Sørensen–Dice) can be highly sensitive to fixed margins of contingency tables, estimating wildly variable degrees of association and even reversing the direction of association for tables with different margins but the same degree-of-association alpha.https://doi.org/10.1111/jbi.1475

A better index for analysis of co-occurrence and similarity

Scientists often need to know whether pairs of entities tend to occur together or independently. Standard approaches to this issue use co-occurrence indices such as Jaccard, Sørensen-Dice, and Simpson. We show that these indices are sensitive to the prevalences of the entities they describe and that this invalidates their interpretability. We propose an index, α, that is insensitive to prevalences. Published datasets reanalyzed with both α and Jaccard’s index ( J ) yield profoundly different biological inferences. For example, a published analysis using J contradicted predictions of the island biogeography theory finding that community stability increased with increasing physical isolation. Reanalysis of the same dataset with the estimator α ˆ reversed that result and supported theoretical predictions. We found similarly marked effects in reanalyses of antibiotic cross-resistance and human disease biomarkers. Our index α is not merely an improvement; its use changes data interpretation in fundamental ways. </jats:p