Environmetrics 

About: Environmetrics is an academic journal published by Wiley-Blackwell. The journal publishes majorly in the area(s): Estimator & Computer science. It has an ISSN identifier of 1099-095X. Over the lifetime, 1690 publications have been published receiving 41148 citations. The journal is also known as: Environ metrics & EnvironMetrics (Chichester).

Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values†

Abstract: A new variant ‘PMF’ of factor analysis is described. It is assumed that X is a matrix of observed data and σ is the known matrix of standard deviations of elements of X. Both X and σ are of dimensions n × m. The method solves the bilinear matrix problem X = GF + E where G is the unknown left hand factor matrix (scores) of dimensions n × p, F is the unknown right hand factor matrix (loadings) of dimensions p × m, and E is the matrix of residuals. The problem is solved in the weighted least squares sense: G and F are determined so that the Frobenius norm of E divided (element-by-element) by σ is minimized. Furthermore, the solution is constrained so that all the elements of G and F are required to be non-negative. It is shown that the solutions by PMF are usually different from any solutions produced by the customary factor analysis (FA, i.e. principal component analysis (PCA) followed by rotations). Usually PMF produces a better fit to the data than FA. Also, the result of PF is guaranteed to be non-negative, while the result of FA often cannot be rotated so that all negative entries would be eliminated. Different possible application areas of the new method are briefly discussed. In environmental data, the error estimates of data can be widely varying and non-negativity is often an essential feature of the underlying models. Thus it is concluded that PMF is better suited than FA or PCA in many environmental applications. Examples of successful applications of PMF are shown in companion papers.

Large scale wildlife monitoring studies: statistical methods for design and analysis

Abstract: Techniques for estimation of absolute abundance of wildlife populations have received a lot of attention in recent years. The statistical research has been focused on intensive small-scale studies. Recently, however, wildlife biologists have desired to study populations of animals at very large scales for monitoring purposes. Population indices are widely used in these extensive monitoring programs because they are inexpensive compared to estimates of absolute abundance. A crucial underlying assumption is that the population index (C) is directly proportional to the population density (D). The proportionality constant, β, is simply the probability of ‘detection’ for animals in the survey. As spatial and temporal comparisons of indices are crucial, it is necessary to also assume that the probability of detection is constant over space and time. Biologists intuitively recognize this when they design rigid protocols for the studies where the indices are collected. Unfortunately, however, in many field studies the assumption is clearly invalid. We believe that the estimation of detection probability should be built into the monitoring design through a double sampling approach. A large sample of points provides an abundance index, and a smaller sub-sample of the same points is used to estimate detection probability. There is an important need for statistical research on the design and analysis of these complex studies. Some basic concepts based on actual avian, amphibian, and fish monitoring studies are presented in this article. Copyright © 2002 John Wiley & Sons, Ltd.

Bayesian stable isotope mixing models

Abstract: In this paper, we review recent advances in stable isotope mixing models (SIMMs) and place them into an overarching Bayesian statistical framework, which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixture. The most widely used application is quantifying the diet of organisms based on the food sources they have been observed to consume. At the centre of the multivariate statistical model we propose is a compositional mixture of the food sources corrected for various metabolic factors. The compositional component of our model is based on the isometric log-ratio transform. Through this transform, we can apply a range of time series and non-parametric smoothing relationships. We illustrate our models with three case studies based on real animal dietary behaviour.

Spatial Modelling Using a New Class of Nonstationary Covariance Functions.

Abstract: We introduce a new class of nonstationary covariance functions for spatial modelling. Nonstationary covariance functions allow the model to adapt to spatial surfaces whose variability changes with location. The class includes a nonstationary version of the Matern stationary covariance, in which the differentiability of the spatial surface is controlled by a parameter, freeing one from fixing the differentiability in advance. The class allows one to knit together local covariance parameters into a valid global nonstationary covariance, regardless of how the local covariance structure is estimated. We employ this new nonstationary covariance in a fully Bayesian model in which the unknown spatial process has a Gaussian process (GP) prior distribution with a nonstationary covariance function from the class. We model the nonstationary structure in a computationally efficient way that creates nearly stationary local behavior and for which stationarity is a special case. We also suggest non-Bayesian approaches to nonstationary kriging.To assess the method, we use real climate data to compare the Bayesian nonstationary GP model with a Bayesian stationary GP model, various standard spatial smoothing approaches, and nonstationary models that can adapt to function heterogeneity. The GP models outperform the competitors, but while the nonstationary GP gives qualitatively more sensible results, it shows little advantage over the stationary GP on held-out data, illustrating the difficulty in fitting complicated spatial data.

Characterization of the trophic conditions of marine coastal waters with special reference to the NW Adriatic Sea: Proposal for a trophic scale, turbidity and generalized water quality index

Abstract: In pursuing earlier attempts to characterize the trophic state of inland waters, a new trophic index (TRIX) based on chlorophyll, oxygen saturation, mineral and total nitrogen and phosphorus, and applicable to coastal marine waters, is proposed. Numerically, the index is scaled from 0 to 10, covering a wide range of trophic conditions from oligotrophy to eutrophy. Secchi disk transparency combined with chlorophyll, instead, defines a turbidity index (TRBIX) that serves as complementary water quality index. The two indices are combined in a general water quality index (GWQI). Statistical properties and application of these indices to specific situations are discussed on examples pertaining to the NW Adriatic Sea. It is believed that these indices will simplify and make comparison between different spatial and temporal trophic situations of marine coastal waters more consistent. © 1998 John Wiley & Sons, Ltd.