A simple demonstration of the relationship between classification and canonical variates analysis
No abstract available.
American Statistician↗
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Simulation testing of unbiasedness of variance estimators
In this article I address the evaluation of estimators of variance for parameter estimates. Given an unbiased estimator X of a parameter θ, and an estimator V of the variance of X , how does one test (via simulation) whether V is an unbiased estimator of the variance of X? The derivation of the test statistic illustrates the need for care in substituting consistent estimators for unknown parameters.
American Statistician↗
Making Recursive Bayesian inference accessible
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior distributions resulting from former studies. Two existing Recursive Bayesian methods are: Prior- and Proposal-Recursive Bayes. Prior-Recursive Bayes uses Bayesian updating, fitting models to partitions of data sequentially, and provides a way to accommodate new data as they become available using the posterior from the previous stage as the prior in the new stage based on the latest data. ProposalRecursive Bayes is intended for use with hierarchical Bayesian models and uses a set of transient priors in first stage independent analyses of the data partitions. The second stage of Proposal-Recursive Bayes uses the posteriors from the first stage as proposals in an MCMC algorithm to fit the full model. We combine Prior- and Proposal-Recursive concepts to fit any Bayesian model, and often with computational improvements. We demonstrate our method with two case studies. Our approach has implications for big data, streaming data, and optimal adaptive design situations.
American Statistician↗
Estimation of contact time among animals from telemetry data
Continuous processes in most applications are measured discretely with error. This complicates the task of detecting intersections and the number of intersections between two continuous processes (i.e., when the processes have the same value). Intersections of continuous processes are scientifically important but challenging to estimate from data. For example, in the field of animal ecology, intersections of the paths of moving animals tracked with satellite technologies can be used to understand disease transmission. We illustrate how to quantify contact between animals using telemetry data (i.e., the recorded locations of an animal over time). We introduce our method to quantify contact time with accessible concepts from introductory stochastic process literature, such as Brownian motion. Then, we provide two data examples using white-tailed deer ( Odocoileus virginianus ) and mule deer ( Odocoileus hemionus) telemetry data in a region with high prevalence of chronic wasting disease. Our work provides a needed connection between existing model-based literature for animal movement and rule-based literature for animal interaction. Further, our work illustrates a unique statistical problem receiving minimal attention with broad applicability in human and livestock tracking.
The American Statistician↗
Book review: Bayesian analysis for population ecology
Brian Dennis described the field of ecology as “fertile, uncolonized ground for Bayesian ideas.” He continued: “The Bayesian propagule has arrived at the shore. Ecologists need to think long and hard about the consequences of a Bayesian ecology. The Bayesian outlook is a successful competitor, but is it a weed? I think so.” (Dennis 2004) Review info: Bayesian Analysis for Population Ecology. By Ruth King, Byron J. T. Morgan, Olivier Gimenez, and Stephen P. Brooks, 2010. ISBN: 978-1439811870, xvii, 442 pp.
American Statistician↗
Moving beyond p<0.05 in ecotoxicology: A guide for practitioners
Statistical inferences play a critical role in ecotoxicology. Historically, Null Hypothesis Significance Testing (NHST) has been the dominant method for inference in ecotoxicology. As a brief and informal definition of the NHST approach, researchers compare (or test) an experimental treatment or observation against a hypothesis of no relationship or effect (the null hypothesis) using the collected data to see if the observed values are statistically significant given predefined error rates. The resulting probability of observing a value equal to or greater than the observed value assuming the null hypothesis is true is the p-value. Historically, criticisms of NHST have existed for almost a century and more recently these have grown to the point where statisticians, including the American Statistical Association, have felt the need to clarify the role of NHST and p-values in science beyond their current, common use. These limitations also exist in ecotoxicology. For example, a review of the 2010 Environmental Toxicology & Chemistry (ET&C) volume found many authors did not correctly report p-values. We repeated this review looking at the 2019 volume of ET&C and the incorrect reporting of p-values still occurred almost a decade later. Problems with NHST and p-values highlight the need for statistical inferences besides NHST, something that has long been known in ecotoxicology and the broader scientific and statistical communities. Furthermore, concerns such as these led the Executive Director of the American Statistical Association to recommend against use of statistical significance in 2019. In light of these criticisms, however, ecotoxicologists require alternative methods. In this paper, we describe some alternative methods including confidence intervals, regression analysis, dose-response curves, Bayes factors, survival analysis, and model selection. Lastly, we provide insights for what ecotoxicology might look like in a post-p-value world.
Environmental Toxicology and Chemistry↗
Estimating population trends with a linear model: Technical comments
Controversy has sometimes arisen over whether there is a need to accommodate the limitations of survey design in estimating population change from the count data collected in bird surveys. Analyses of surveys such as the North American Breeding Bird Survey (BBS) can be quite complex; it is natural to ask if the complexity is necessary, or whether the statisticians have run amok. Bart et al. (2003) propose a very simple analysis involving nothing more complicated than simple linear regression, and contrast their approach with model-based procedures. We review the assumptions implicit to their proposed method, and document that these assumptions are unlikely to be valid for surveys such as the BBS. One fundamental limitation of a purely design-based approach is the absence of controls for factors that influence detection of birds at survey sites. We show that failure to model observer effects in survey data leads to substantial bias in estimation of population trends from BBS data for the 20 species that Bart et al. (2003) used as the basis of their simulations. Finally, we note that the simulations presented in Bart et al. (2003) do not provide a useful evaluation of their proposed method, nor do they provide a valid comparison to the estimating- equations alternative they consider.
Condor↗
Book review: Bird census techniques, Second edition
Conservation concerns, federal mandates to monitor birds, and citizen science programs have spawned a variety of surveys that collect information on bird populations. Unfortunately, all too frequently these surveys are poorly designed and use inappropriate counting methods. Some of the flawed approaches reflect a lack of understanding of statistical design; many ornithologists simply are not aware that many of our most entrenched counting methods (such as point counts) cannot appropriately be used in studies that compare densities of birds over space and time. It is likely that most of the readers of The Condor have participated in a bird population survey that has been criticized for poor sampling methods. For example, North American readers may be surprised to read in Bird Census Techniques that the North American Breeding Bird Survey 'is seriously flawed in its design,' and that 'Analysis of trends is impossible from points that are positioned along roads' (p. 109). Our conservation efforts are at risk if we do not acknowledge these concerns and improve our survey designs. Other surveys suffer from a lack of focus. In Bird Census Techniques, the authors emphasize that all surveys require clear statements of objectives and an understanding of appropriate survey designs to meet their objectives. Too often, we view survey design as the realm of ornithologists who know the life histories and logistical issues relevant to counting birds. This view reflects pure hubris: survey design is a collaboration between ornithologists, statisticians, and managers, in which goals based on management needs are met by applying statistical principles for design to the biological context of the species of interest. Poor survey design is often due to exclusion of some of these partners from survey development. Because ornithologists are too frequently unaware of these issues, books such as Bird Census Techniques take on added importance as manuals for educating ornithologists about the relevance of survey design and methods and the often subtle interdisciplinary nature of surveys. Review info: Bird Census Techniques, Second Edition. By Colin J. Bibby, Neil D. Burgess, David A. Hill, and Simon H. Mustoe. 2000. Academic Press, London, UK. xvii 1 302 pp. ISBN 0- 12-095831-7.
Condor↗