Summary1. The mvabund package for R provides tools for model-based analysis of multivariate abundance data in ecology. 2. This includes methods for visualising data, fitting predictive models, checking model assumptions, as well as testing hypotheses about the community-environment association.3. This paper briefly introduces the package and demonstrates its functionality by example.

Summary 1.A critical property of count data is its mean-variance relationship, yet this is rarely considered in multivariate analysis in ecology. 2. This study considers what is being implicitly assumed about the mean-variance relationship in distance-based analyses -multivariate analyses based on a matrix of pairwise distances -and what the effect is of any misspecification of the mean-variance relationship. 3. It is shown that distance-based analyses make implicit assumptions that are typically out-of-step with what is observed in real data, which has major consequences. 4. Potential consequences of this mean-variance misspecification are: confounding location and dispersion effects in ordinations; misleading results when trying to identify taxa in which an effect is expressed; failure to detect a multivariate effect unless it is expressed in high-variance taxa. 5. Data transformation does not solve the problem. 6. A solution is to use generalised linear models and their recent multivariate generalisations, which is shown here to have desirable properties.

Abstract-In this paper, we have proposed a fingerprint orientation model based on 2D Fourier expansions (FOMFE) in the phase plane. The FOMFE does not require prior knowledge of singular points (SPs). It is able to describe the overall ridge topology seamlessly, including the SP regions, even for noisy fingerprints. Our statistical experiments on a public database show that the proposed FOMFE can significantly improve the accuracy of fingerprint feature extraction and thus that of fingerprint matching. Moreover, the FOMFE has a low-computational cost and can work very efficiently on large fingerprint databases. The FOMFE provides a comprehensive description for orientation features, which has enabled its beneficial use in feature-related applications such as fingerprint indexing. Unlike most indexing schemes using raw orientation data, we exploit FOMFE model coefficients to generate the feature vector. Our indexing experiments show remarkable results using different fingerprint databases.

Bootstrap methods are widely used in statistics, and bootstrapping of residuals can be especially useful in the regression context. However, difficulties are encountered extending residual resampling to regression settings where residuals are not identically distributed (thus not amenable to bootstrapping)—common examples including logistic or Poisson regression and generalizations to handle clustered or multivariate data, such as generalised estimating equations. We propose a bootstrap method based on probability integral transform (PIT-) residuals, which we call the PIT-trap, which assumes data come from some marginal distribution F of known parametric form. This method can be understood as a type of “model-free bootstrap”, adapted to the problem of discrete and highly multivariate data. PIT-residuals have the key property that they are (asymptotically) pivotal. The PIT-trap thus inherits the key property, not afforded by any other residual resampling approach, that the marginal distribution of data can be preserved under PIT-trapping. This in turn enables the derivation of some standard bootstrap properties, including second-order correctness of pivotal PIT-trap test statistics. In multivariate data, bootstrapping rows of PIT-residuals affords the property that it preserves correlation in data without the need for it to be modelled, a key point of difference as compared to a parametric bootstrap. The proposed method is illustrated on an example involving multivariate abundance data in ecology, and demonstrated via simulation to have improved properties as compared to competing resampling methods.

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