Evidential statistics as a statistical modern synthesis to support 21st century science

During the 20th century, population ecology and science in general relied on two very different statistical paradigms to solve its inferential problems: error statistics (also referred to as classical statistics and frequentist statistics) and Bayesian statistics. A great deal of good science was done using these tools, but both schools suffer from technical and philosophical difficulties. At the turning of the 21st century (Royall in Statistical evidence: a likelihood paradigm. Chapman & Hall, London, 1997 ; Lele in The nature of scientific evidence: statistical, philosophical and empirical considerations. The University of Chicago Press, Chicago, pp 191–216, 2004a ), evidential statistics emerged as a seriously contending paradigm. Drawing on and refining elements from error statistics, likelihoodism, Bayesian statistics, information criteria, and robust methods, evidential statistics is a statistical modern synthesis that smoothly incorporates model identification, model uncertainty, model comparison, parameter estimation, parameter uncertainty, pre-data control of error, and post-data strength of evidence into a single coherent framework. We argue that evidential statistics is currently the most effective statistical paradigm to support 21st century science. Despite the power of the evidential paradigm, we think that there is no substitute for learning how to clarify scientific arguments with statistical arguments. In this paper we sketch and relate the conceptual bases of error statistics, Bayesian statistics and evidential statistics. We also discuss a number of misconceptions about the paradigms that have hindered practitioners, as well as some real problems with the error and Bayesian statistical paradigms solved by evidential statistics.     

A Comparison of Three Weight-of-Evidence Approaches for Integrating Sediment Contamination Data within and Across Lines of Evidence

Multiple lines of evidence (LOE) are often considered when examining the potential impact of contaminated sediment. Three strategies are explored for combining information within and/or among different LOE. One technique uses a multivariate strategy for clustering sites into groups of similar impact. A second method employs meta-analysis to pool empirically derived P-values. The third method uses a quantitative estimation of probability derived from odds ratios. These three strategies are compared with respect to a set of data describing reference conditions and a contaminated area in the Great Lakes. Common themes in these three strategies include the critical issue of defining an appropriate set of reference/control conditions, the definition of impact as a significant departure from the normal variation observed in the reference conditions, and the use of distance from the reference distribution to define any of the effect measures. Reasons for differences in results between the three approaches are explored and strategies for improving the approaches are suggested.     

Generalization of the QST framework in hierarchically structured populations: Impacts of inbreeding and dominance

Q_ST is a differentiation parameter based on the decomposition of the genetic variance of a trait. In the case of additive inheritance and absence of selection, it is analogous to the genic differentiation measured on individual loci, F_ST. Thus, Q_ST?F_ST comparison is used to infer selection: selective divergence when Q_ST > F_ST, or convergence when Q_ST < F_ST. The definition of Q‐statistics was extended to two‐level hierarchical population structures with Hardy–Weinberg equilibrium. Here, we generalize the Q‐statistics framework to any hierarchical population structure. First, we developed the analytical definition of hierarchical Q‐statistics for populations not at Hardy–Weinberg equilibrium. We show that the Q‐statistics values obtained with the Hardy–Weinberg definition are lower than their corresponding F‐statistics when F_IS > 0 (higher when F_IS < 0). Then, we used an island model simulation approach to investigate the impact of inbreeding and dominance on the Q_ST?F_ST framework in a hierarchical population structure. We show that, while differentiation at the lower hierarchical level (Q_SR) is a monotonic function of migration, differentiation at the upper level (Q_RT) is not. In the case of additive inheritance, we show that inbreeding inflates the variance of Q_RT, which can increase the frequency of Q_RT > F_RT cases. We also show that dominance drastically reduces Q‐statistics below F‐statistics for any level of the hierarchy. Therefore, high values of Q‐statistics are good indicators of selection, but low values are not in the case of dominance.     

Bayesian statistical treatment of the fluorescence of AFLP bands leads to accurate genetic structure inference

Ever since the introduction of allozymes in the 1960s, evolutionary biologists and ecologists have continued to search for more powerful molecular markers to estimate important parameters such as effective population size and migration rates and to make inferences about the demographic history of populations, the relationships between individuals and the genetic architecture of phenotypic variation (Bensch & Akesson 2005; Bonin et al. 2007). Choosing a marker requires a thorough consideration of the trade-offs associated with the different techniques and the type of data obtained from them. Some markers can be very informative but require substantial amounts of start-up time (e.g. microsatellites), while others require very little time but are much less polymorphic. Amplified fragment length polymorphism (AFLP) is a firmly established molecular marker technique that falls in this latter category. AFLPs are widely distributed throughout the genome and can be used on organisms for which there is no a priori sequence information (Meudt & Clarke 2007). These properties together with their moderate cost and short start-up time have made them the method of choice for many molecular ecology studies of wild species (Bensch & Akesson 2005). However, they have a major disadvantage, they are dominant. This represents a very important limitation because many statistical genetics methods appropriate for molecular ecology studies require the use of codominant markers. In this issue, Foll et al. (2010) present an innovative hierarchical Bayesian method that overcomes this limitation. The proposed approach represents a comprehensive statistical treatment of the fluorescence of AFLP bands and leads to accurate inferences about the genetic structure of natural populations. Besides allowing a quasi-codominant treatment of AFLPs, this new method also solves the difficult problems posed by subjectivity in the scoring of AFLP bands.     

Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses

Throughout the last two decades, Bayesian statistical methods have proliferated throughout ecology and evolution. Numerous previous references established both philosophical and computational guidelines for implementing Bayesian methods. However, protocols for incorporating prior information, the defining characteristic of Bayesian philosophy, are nearly nonexistent in the ecological literature. Here, I hope to encourage the use of weakly informative priors in ecology and evolution by providing a ‘consumer's guide’ to weakly informative priors. The first section outlines three reasons why ecologists should abandon noninformative priors: 1) common flat priors are not always noninformative, 2) noninformative priors provide the same result as simpler frequentist methods, and 3) noninformative priors suffer from the same high type I and type M error rates as frequentist methods. The second section provides a guide for implementing informative priors, wherein I detail convenient ‘reference’ prior distributions for common statistical models (i.e. regression, ANOVA, hierarchical models). I then use simulations to visually demonstrate how informative priors influence posterior parameter estimates. With the guidelines provided here, I hope to encourage the use of weakly informative priors for Bayesian analyses in ecology. Ecologists can and should debate the appropriate form of prior information, but should consider weakly informative priors as the new ‘default’ prior for any Bayesian model.     

Model evaluation and spatial interpolation by Bayesian combination of observations with outputs from numerical models

Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models-3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models-3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models-3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models-3 output. We apply our methods to data on SO2 concentrations, and we obtain high-resolution SO2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO2 values are overestimated by the models.     

Formulas for the Computation of the WILCOXON Test and other Rank Statistics

A simple program for the computation of the WILCOXON test is introduced, which is suitable for implementation on a programmable desk computer. The allocation of ranks R_i is not necessary (see BERCHTOLD, 1979). In an analogous manner any ranks respectively rank sums also can be calculated, so that any test criterion or statistical estimate called rank statistic, may be completely constituted by computer programs without explicitely ranging of values.     

DNA序列的统计信息比较分析

我们从Genbank中选取灵长类、啮齿类、无脊椎类及细菌类的一部分DNA序列作了统计分析．为克服信息度量D_n的某些不足,引入了DI_1、DI_0和S三种信息统计量,得到了各大类及各类间差异的有关信息．     

Application of partial least squares discriminant analysis to two-dimensional difference gel studies in expression proteomics

Two-dimensional difference gel electrophoresis (DIGE) is a tool for measuring changes in protein expression between samples involving pre-electrophoretic labeling ith cyanine dyes. In multi-gel experiments, univariate statistical tests have been used to identify differential expression between sample types by looking for significant changes in spot volume. Multivariate statistical tests, which look for correlated changes between sample types, provide an alternate approach for identifying spots with differential expression. Partial least squares-discriminant analysis (PLS-DA), a multivariate statistical approach, was combined with an iterative threshold process to identify which protein spots had the greatest contribution to the model, and compared to univariate test for three datasets. This included one dataset where no biological difference was expected. The novel multivariate approach, detailed here, represents a method to complement the univariate approach in identification of differentially expressed protein spots. This new approach has the advantages of reduced risk of false-positives and the identification of spots that are significantly altered in terms of correlated expression rather than absolute expression values.     

Configural Frequency Analysis as a Parametric Method for the Search of Types and Antitypes

The article introduces Parametric Configural Frequency Analysis (CFA). It is argued that there are two types of parameters that can be of importance in CFA models. The first is effect parameters that are estimated from the data. This type of parameter is involved in almost all models of Classical, nonparametric CFA. The second type involves a priori or distributional parameters that can be used for estimation of expected frequencies. These parameters are specified a priori rather than estimated from data. A combination of models from Classical CFA and Parametric CFA is introduced as Semi-Parametric CFA. Data examples illustrate the new CFA models in comparison with the Classical CFA. Interpretational issues are discussed.     

Gaussian approximations for phylogenetic branch length statistics under stochastic models of biodiversity

Stein's method for Gaussian approximations and derived results are used to study the distribution of two phylogenetic branch length statistics: the total height of cherries and the sum of external branch lengths. The Gaussian approximations are obtained under a particular model of phylogenetic tree recently introduced by Popovic. Under an appropriate normalization the model is shown to behave similarly as the coalescent, and the approximations given here are also valid in this context.     

Population characteristics of extinct hominid endocranial volume

Distribution and variation statistics of hominid endocranial volume (ECV) have been investigated. Within the interpretative constraints imposed by (very) small sample sizes, the requirements for normality are met, as are those for heteroscedasticity. A significant difference in means can be demonstrated for only two comparisons. With one exception, overall distribution characteristics differ significantly in pairwise comparisons between taxa. The coefficient of variation of ECV that characterizes a group composed of all Plio-Pleistocene gracile hominids does not support a single polytypic species interpretation of this assemblage. Significant differences in the coefficient of variation exist between all possible pairs of taxa with the exception of Homo habilis and Homo erectus.     

农作物重大害虫发生规律研究与“九五”趋势分析

考查我国农作物重大害虫历史发生状况,研究粘虫Mythimna separata Walker、稻飞虱Nilaparvata lugens Sstal稻纵卷叶螟Cnaphalocrocis medinalis Guenee、二化螟Chilo sup pressalis Walker、三化螟Tryporyza incertulas Walker、麦蚜Schizaphis graminum Rondani、玉米螟Ostrinia furnacalis Guenee、棉铃虫Helicoverpar armigera (Hubner)等害虫的长期发生规律,初步发现粘虫、二化螟、稻飞虱、稻纵卷叶螟、玉米螟等长期变化有约16年周 期现象,稻飞虱、三化螟有12年左右周期性规律,二化螟、稻纵卷叶螟、麦蚜、棉铃虫等发生周期约11年。根据害虫规律性作出“九五”期间发展趋势预测。     

Identification and application of the concepts important for accurate and reliable protein secondary structure prediction.

A protein secondary structure prediction method from multiply aligned homologous sequences is presented with an overall per residue three-state accuracy of 70.1%. There are two aims: to obtain high accuracy by identification of a set of concepts important for prediction followed by use of linear statistics; and to provide insight into the folding process. The important concepts in secondary structure prediction are identified as: residue conformational propensities, sequence edge effects, moments of hydrophobicity, position of insertions and deletions in aligned homologous sequence, moments of conservation, auto-correlation, residue ratios, secondary structure feedback effects, and filtering. Explicit use of edge effects, moments of conservation, and auto-correlation are new to this paper. The relative importance of the concepts used in prediction was analyzed by stepwise addition of information and examination of weights in the discrimination function. The simple and explicit structure of the prediction allows the method to be reimplemented easily. The accuracy of a prediction is predictable a priori. This permits evaluation of the utility of the prediction: 10% of the chains predicted were identified correctly as having a mean accuracy of > 80%. Existing high-accuracy prediction methods are "black-box" predictors based on complex nonlinear statistics (e.g., neural networks in PHD: Rost & Sander, 1993a). For medium- to short-length chains (> or = 90 residues and < 170 residues), the prediction method is significantly more accurate (P < 0.01) than the PHD algorithm (probably the most commonly used algorithm). In combination with the PHD, an algorithm is formed that is significantly more accurate than either method, with an estimated overall three-state accuracy of 72.4%, the highest accuracy reported for any prediction method.     

Life‐History Data in Bioindication Procedures,Using the Example of Hoverflies (Diptera,Syrphidae) in the Elbe Floodplain

This is the first study to relate syrphid life history traits to environmental variables with a multi‐trait approach. We aimed to answer two questions: 1. Do syrphid species respond to small scale changes in environmental variables in seasonally flooded grasslands in a Central European floodplain (Elbe)? 2. Can species response to environmental variables be explained by the biological characteristics of the species expressed by their life history traits? Despite their large mobility, syrphids did respond significantly to small scale changes in environmental variables (groundwater (GW) depth, cation exchange capacity, amplitude of variation of the GW‐depth). On the other hand, the biological traits of the syrphids did not sufficiently explain syrphid occurrence at the sites. Possible explanations are discussed and an outlook for further studies is given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Basic data standards for primate colonies

A set of simple standards has been developed to ease the task of transferring primate colony data between institutions and computers, and to assure that colony vital statistics are appropriate for demographic and genetic analyses. The standards have been designed to be easily and inexpensively implemented from existing databases, and also may serve as a guide to the setup of new colony record-keeping systems. © 1993 Wiley-Liss, Inc.