Recurrence Relations Among Moments of Order Statistics from Two Related Outlier Models

It is shown that the moments of order statistics in samples drawn from a continuous population with pdf f(x) symmetric about zero comprising a single outlier with pdf g(x) symmetric about zero can be expressed in terms of the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero and the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero comprising a single outlier with pdf obtained by folding g(x) at zero. The cumulative round off error involved in numerical evaluation of the moments of order statistics from the symmetric-outlier model, using a table of the moments of order statistics from the folded population and the moments of order statistics from the folded-outlier model, is not serious.     

Robust Hotelling-Type T2 Statistics

To test an assumed mean vector, and to test the equality of two mean vectors, robust statistics are developed which have exactly the same form as the Hotelling T² statistics. These statistics are shown to have remarkable type I error robustness and power.     

Comparing Power Behaviours for Some Goodness-of-Fit Test Statistics in Sparse Multinomials

This paper is concerned with the power behaviour of four goodness-of-fit test statistics in sparse multinomials with k cells. Most previous work has been concerned only with both Pearson's X² and the likelihood ratio test statistics. We consider in this study, two additional test statistics, namely, the Cressie-Read test statistic – I(2/3) and the modified Freeman-Tukey test (FT) statistic. Because k ≥ 10 in this study, a Monte Carlo procedure based on 1000 simulated samples is used to estimate the powers for the four test statistics. Alternatives on various line segments are employed. Results suggest that none of the test statistics completely dominate the other and that the choice of which test to use depends on the nature of the alternative hypothesis. These results are consistent with those obtained by West and Kempthorne (1972), although, the Pearson's χ² test statistic may be preferred because of its closer approximation to the χ² distribution in terms of the attained α levels.     

Testing Equality of Correlated Means in the Presence of Unequal Variances and Missing Values

Several statistics are proposed for testing the hypothesis of equality of the means of bivariate normal distribution with unknown variances and correlation coefficient when observations are missing on both variatea. The null distributions of the statistics are approximated by well-known distributions. The empirical sizes and powers of the statistics are computed and compared with paired t test and some of the known statistics based on available data. The comparisons support the use of two of the statistics proposed in this paper.     

Point count summary statistics differentially predict reproductive activity in bird-habitat relationship studies

Point count summary statistics (e.g. mean abundance, maximum abundance, frequency and presence/absence) reflect different assumptions about behavioral and population processes. In this paper we (1) determine the frequency and usage trends of different point count summary statistics in recent ornithological literature, and (2) assess how well point count data, summarized using five common statistics, predict an alternate measure of habitat quality–reproductive activity. For the 100 journal years we reviewed (10 journals over 10 years), 148 papers used point counts to evaluate bird habitat relationships. The number of papers using point counts has increased over the decade. Mean abundance, the most common summary statistic, was used more than twice as frequently as the next most common summary statistics. Only 25.7% (38 papers) provided a justification for use of a particular summary technique. We conducted point counts in three Canadian study regions (New Brunswick, Nova Scotia, and Newfoundland and Labrador) comprised of two ecosystem types (forest and grassland). While there was a statistically significant positive correlation between point count data and reproductive activity data for most species, we found that point counts were often unsuccessful at predicting reproductive activity in forest birds. For species where point counts adequately predicted reproductive activity mean abundance and frequency were consistently the best predictors. Our results indicate that statistics using information on intra-season (multiple-visit) occupancy tend to be better estimators of reproductive activity.     

General Analysis of Covariance Models for the Split Block and Related Block Designs

Exact test statistics and confidence intervals for a general split block ANOCOVA model are derived. With a single covariate, each statistic for testing main effect A, main effect B, and the AxB interaction has one less numerator degree of freedom than its counterpart in the ordinary ANOVA without a covariate. Sufficient conditions on the model parameters which allow these lost numerator degrees of freedom to be regained are given, as are exact statistics and confidence intervals for the corresponding reduced models. A note of caution is offered when constructing test statistics for reduced versions of the general model using the method of generalized least squares. General analysis of covariance models for two other block designs are presented.     

Weighted Logrank Testing Procedures for the Simple Tree Alternatives

Weighted logrank testing procedures for comparing r treatments with a control when some of the data are randomly censored are discussed. Four kinds of test statistics for the simple tree alternatives are considered. The weighted logrank statistics based on pairwise ranking scheme is proposed and the covariances of the test statistics are explicitly obtained. This class of test statistics can be viewed as the general statistics of constructing the test procedures for various order restricted alternatives by modifying weights. Four kinds of weighted logrank tests are illustrated with an example. Simulation studies are performed to compare the sizes and the powers of the considered tests with the other.     

Model life tables for the smaller new world monkeys

Mortality statistics from five populations of small New World monkeys (includinsg Callithrix jaccus, Leontopithecus rosalia, Saguinus fuscicollis, and Saguinus oedipus) were combined to generate a standard model life table reflecting the mortality patterns of these primates. The model is applied to three individual populations to illustrate a strategy for smoothing and interpolating mortality statistics of varying completeness and quality. © 1993 Wiley-Liss, Inc.     

Comparisons of Some Chi-squared Tests for the Test of Independence in Sparse Two-Way Contingency Tables

We consider in this paper, the behaviour of a class of the CRESSIE READ (1984) power divergence test statistics indexed by parameter λ - I (λ), with the modified X₂ test statistics (LU) proposed by LAWAL and UPTON (1984), for sparse contingency tables ranging from the 3×3 to the 10×10. We present a sample of our results here. The results indicate that the LU test out-performs either the Cressie-Read suggested test I(2/3) or the Pearson's test - I(1). Our results further show that the modification to the likelihood ratio test [Y₂ = I'(0)] proposed by WILLIAMS (1976) performs like the parent Y₂ test, very poorly compared with either the I(2/3), X₂ or the LU test statistics. Power results also indicate that the powers of the LU test are in all cases considered in this study slightly higher than those of X₂ and I(2/3) tests. The LU test is therefore strongly recommended for use with sparse two-way contingency tables because in all of the cases considered, none of the other test statistics consistently out-performs the LU test with respect to attained α level or power.     

Distribution of the number of false discoveries in large-scale family-based association testing with application to the association between <Emphasis Type="Italic">PTPN1</Emphasis> and hypertension and obesity

We present a model-free approach to the study of the number of false discoveries for large-scale simultaneous family-based association tests (FBATs) in which the set of discoveries is decided by applying a threshold to the test statistics. When the association between a set of markers in a candidate gene and a group of phenotypes is studied by a class of FBATs, we indicate that a joint null hypothesis distribution for these statistics can be obtained by the fundamental statistical method of conditioning on sufficient statistics for the null hypothesis. Based on the joint null distribution of these statistics, we can obtain the distribution of the number of false discoveries for the set of discoveries defined by a threshold; the size of this set is referred to as its tail count. Simulation studies are presented to demonstrate that the conditional, not the unconditional, distribution of the tail count is appropriate for the study of false discoveries. The usefulness of this approach is illustrated by re-examining the association between PTPN1 and a group of blood-pressure-related phenotypes reported by Olivier et al. (Hum Mol Genet 13:1885–1892, 2004); our results refine and reinforce this association.     

Evaluating,partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records

Most species data display spatial autocorrelation that can affect ecological niche models (ENMs) accuracy‐statistics, affecting its ability to infer geographic distributions. Here we evaluate whether the spatial autocorrelation underlying species data affects accuracy‐statistics and map the uncertainties due to spatial autocorrelation effects on species range predictions under past and future climate models. As an example, ENMs were fitted to Qualea grandiflora (Vochysiaceae), a widely distributed plant from Brazilian Cerrado. We corrected for spatial autocorrelation in ENMs by selecting sampling sites equidistant in geographical (GEO) and environmental (ENV) spaces. Distributions were modelled using 13 ENMs evaluated by two accuracy‐statistics (TSS and AUC), which were compared with uncorrected ENMs. Null models and the similarity statistics I were used to evaluate the effects of spatial autocorrelation. Moreover, we applied a hierarchical ANOVA to partition and map the uncertainties from the time (across last glacial maximum, pre‐insustrial, and 2080 time periods) and methodological components (ENMs and autocorrelation corrections). The GEO and ENV models had the highest accuracy‐statistics values, although only the ENV model had values higher than expected by chance alone for most of the 13 ENMs. Uncertainties from time component were higher in the core region of the Brazilian Cerrado where Q. grandiflora occurs, whereas methodological components presented higher uncertainties in the extreme northern and southern regions of South America (i.e. outside of Brazilian Cerrado). Our findings show that accounting for autocorrelation in environmental space is more efficient than doing so in geographical space. Methodological uncertainties were concentrated in outside the core region of Q. grandiflora's habitat. Conversely, uncertainty due to time component in the Brazilian Cerrado reveals that ENMs were able to capture climate change effects on Q. grandiflora distributions.     

Ascertainment Bias and the Pattern of Nucleotide Diversity at the Human ALDH2 Locus in a Japanese Population

Many East Asian human populations harbor a high-frequency deficiency allele for the aldehyde dehydrogenase 2 (ALDH2) enzyme, a critical protein involved in the metabolism of ethanol. Here we use resequencing and long-range SNP haplotype data from a Japanese sample to test whether patterns of nucleotide diversity and linkage disequilibrium at this locus are compatible with a standard neutral model of evolution. Examination of the pattern of polymorphism at a locus such as this, where the frequency of a common allele is known a priori, introduces an ascertainment bias that must be corrected for in analyses of the frequency spectrum of polymorphisms. We apply a flexible and generally applicable simulation approach to correct for this bias in our ALDH2 data and, also, to explore the effect of bias on the commonly used summary statistics Tajima’s D, Fu and Li’s D, and Fay and Wu’s H. Our study finds no evidence that the pattern of genetic variation at ALDH2 differs from that expected under a standard neutral model. However, our general examination of ascertainment bias indicates that a priori knowledge of segregating alleles greatly affects the expected distributions of summary statistics. Under many parameter combinations we find that ascertainment bias introduces an elevated rate of false positives when summary statistics are used to test for deviations from a standard neutral model. However, we also show that over a wide range of conditions the power of all summary statistics can be greatly increased by incorporating prior knowledge of segregating alleles. [Reviewing Editor: Dr. Martin Kreitman]     

Analysis of Trends in Proportions with an Ordinally Scaled Determinant

In this paper the analysis of several proportions in a comparative study setting is discussed. The case of ordinal grouping variates is considered. F statistics are formulated to test for trend in the proportions over the scored values of the determinant variate. The null chi-square or F (t square) functions are presented separately for the unstratified and stratified analysis, and in either situation the corresponding functions with angular transformed proportions are also expressed. Generalizations to deal with the parameters in the nonnull range are outlined. Throughout, the intimate relation between the presented statistics and standard methods is pointed out.     

Trimmed Weighted Simes' Test for Two One‐Sided Hypotheses With Arbitrarily Correlated Test Statistics

The two‐sided Simes test is known to control the type I error rate with bivariate normal test statistics. For one‐sided hypotheses, control of the type I error rate requires that the correlation between the bivariate normal test statistics is non‐negative. In this article, we introduce a trimmed version of the one‐sided weighted Simes test for two hypotheses which rejects if (i) the one‐sided weighted Simes test rejects and (ii) both p‐values are below one minus the respective weighted Bonferroni adjusted level. We show that the trimmed version controls the type I error rate at nominal significance level α if (i) the common distribution of test statistics is point symmetric and (ii) the two‐sided weighted Simes test at level 2α controls the level. These assumptions apply, for instance, to bivariate normal test statistics with arbitrary correlation. In a simulation study, we compare the power of the trimmed weighted Simes test with the power of the weighted Bonferroni test and the untrimmed weighted Simes test. An additional result of this article ensures type I error rate control of the usual weighted Simes test under a weak version of the positive regression dependence condition for the case of two hypotheses. This condition is shown to apply to the two‐sided p‐values of one‐ or two‐sample t‐tests for bivariate normal endpoints with arbitrary correlation and to the corresponding one‐sided p‐values if the correlation is non‐negative. The Simes test for such types of bivariate t‐tests has not been considered before. According to our main result, the trimmed version of the weighted Simes test then also applies to the one‐sided bivariate t‐test with arbitrary correlation.     

StructureSelector: A web‐based software to select and visualize the optimal number of clusters using multiple methods

Inferences of population genetic structure are of great importance to the fields of ecology and evolutionary biology. The program structure has been widely used to infer population genetic structure. However, previous studies demonstrated that uneven sampling often leads to wrong inferences on hierarchical structure. The most widely used ΔK method tends to identify the uppermost hierarchy of population structure. Recently, four alternative statistics (medmedk , medmeak , maxmedk and maxmeak ) were proposed, which appear to be more accurate than the previously used methods for both even and uneven sampling data. However, the lack of easy‐to‐use software limits the use of these appealing new estimators. Here, we developed a web‐based user‐friendly software structureselector to calculate the four appealing alternative statistics together with the commonly used Ln Pr(X|K) and ΔK statistics. structureselector accepts the result files of structure , admixture or faststructure as input files. It reports the “best” K for each estimator, and the results are available as HTML or tab separated tables. The program can also generate graphical representations for specific K, which can be easily downloaded from the server. The software is freely available at http://lmme.qdio.ac.cn/StructureSelector/ .     

A Weibull statistics‐based lignocellulose saccharification model and a built‐in parameter accurately predict lignocellulose hydrolysis performance

Renewable energy from lignocellulosic biomass has been deemed an alternative to depleting fossil fuels. In order to improve this technology, we aim to develop robust mathematical models for the enzymatic lignocellulose degradation process. By analyzing 96 groups of previously published and newly obtained lignocellulose saccharification results and fitting them to Weibull distribution, we discovered Weibull statistics can accurately predict lignocellulose saccharification data, regardless of the type of substrates, enzymes and saccharification conditions. A mathematical model for enzymatic lignocellulose degradation was subsequently constructed based on Weibull statistics. Further analysis of the mathematical structure of the model and experimental saccharification data showed the significance of the two parameters in this model. In particular, the λ value, defined the characteristic time, represents the overall performance of the saccharification system. This suggestion was further supported by statistical analysis of experimental saccharification data and analysis of the glucose production levels when λ and n values change. In conclusion, the constructed Weibull statistics‐based model can accurately predict lignocellulose hydrolysis behavior and we can use the λ parameter to assess the overall performance of enzymatic lignocellulose degradation. Advantages and potential applications of the model and the λ value in saccharification performance assessment were discussed.     

Phylogeography of chamois (Rupicapra spp.) inferred from microsatellites

Evolutionary relationships among populations of chamois (Rupicapra spp.) across their current range from the Caucasus to the Cantabrian Mountains were investigated. The allelic variation in 23 microsatellite loci was assessed in eight geographical populations, recognised as subspecies of the two closely related species R. pyrenaica and R. rupicapra. Analysis of variance in allele frequencies (Fst, statistics) and in repeat numbers (Rst, statistics) showed these data to be highly structured. Two genetic distances between pairs of populations, Ds and (δμ)², were computed and phylogenetic trees were constructed. Similar patterns were produced by the different statistics. All trees indicate a deep divergence between the two recognised species, which is compatible with archaeological data that place their split in the Riss–Würm interglacial period. Genetic distances between pairs of populations are highly correlated with geographical distance. This suggests that the history of the genus during Pleistocene glacial-interglacial periods was dominated by expansions and contractions within limited geographic regions, leading to alternate contact and isolation of contiguous populations. In addition, the alpine barrier has played a substantial role in West–East differentiation.     

Using Discrete Distributions to Compute Powers for Goodness-of-Fit Test Statistics in a One-Way Multinomial Setting

Both the Bionomial and Poisson distributions are employed in this study to compute approximate powers for goodness-of-fit test statistics. The procedure adopted involves simulating 1000 samples from each of these distributions. These samples are then employed to compute both the randomized nominal critical values and estimated powers. The type I error rates returned from the use of the randomized critical levels Cα fall within the acceptable regions. We illustrate the use of the procedure with the Pearson's X² test statistic and show that this can readily be extended to any of the other well known goodness-of-fit test statistics.     

Mocapy++ - A toolkit for inference and learning in dynamic Bayesian networks

Background  

Mocapy++ is a toolkit for parameter learning and inference in dynamic Bayesian networks (DBNs). It supports a wide range of DBN architectures and probability distributions, including distributions from directional statistics (the statistics of angles, directions and orientations).     

Model life table for captive chimpanzees

Mortality statistics from three captive populations of chimpanzees (Pan troglodytes) were combined to generate standard model life tables for each sex in this species. The model is compared to an estimate of survivorship of a group of wild animals, and is applied to an incomplete data set to illustrate how the model may be used to extend estimates of mortality statistics to missing older ages. © 1995 Wiley-Liss, Inc.