Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Estimating the spatial scale of herbicide and soil interactions by nested sampling, hierarchical analysis of variance and residual maximum likelihood

An unbalanced nested sampling design was used to investigate the spatial scale of soil and herbicide interactions at the field scale. A hierarchical analysis of variance based on residual maximum likelihood (REML) was used to analyse the data and provide a first estimate of the variogram. Soil samples were taken at 108 locations at a range of separating distances in a 9 ha field to explore small and medium scale spatial variation. Soil organic matter content, pH, particle size distribution, microbial biomass and the degradation and sorption of the herbicide, isoproturon, were determined for each soil sample. A large proportion of the spatial variation in isoproturon degradation and sorption occurred at sampling intervals less than 60 m, however, the sampling design did not resolve the variation present at scales greater than this. A sampling interval of 20-25 m should ensure that the main spatial structures are identified for isoproturon degradation rate and sorption without too great a loss of information in this field.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

The automation and evaluation of nested clade phylogeographic analysis

Nested clade phylogeographic analysis (NCPA) is a popular method for reconstructing the demographic history of spatially distributed populations from genetic data. Although some parts of the analysis are automated, there is no unique and widely followed algorithm for doing this in its entirety, beginning with the data, and ending with the inferences drawn from the data. This article describes a method that automates NCPA, thereby providing a framework for replicating analyses in an objective way. To do so, a number of decisions need to be made so that the automated implementation is representative of previous analyses. We review how the NCPA procedure has evolved since its inception and conclude that there is scope for some variability in the manual application of NCPA. We apply the automated software to three published datasets previously analyzed manually and replicate many details of the manual analyses, suggesting that the current algorithm is representative of how a typical user will perform NCPA. We simulate a large number of replicate datasets for geographically distributed, but entirely random-mating, populations. These are then analyzed using the automated NCPA algorithm. Results indicate that NCPA tends to give a high frequency of false positives. In our simulations we observe that 14% of the clades give a conclusive inference that a demographic event has occurred, and that 75% of the datasets have at least one clade that gives such an inference. This is mainly due to the generation of multiple statistics per clade, of which only one is required to be significant to apply the inference key. We survey the inferences that have been made in recent publications and show that the most commonly inferred processes (restricted gene flow with isolation by distance and contiguous range expansion) are those that are commonly inferred in our simulations. However, published datasets typically yield a richer set of inferences with NCPA than obtained in our random-mating simulations, and further testing of NCPA with models of structured populations is necessary to examine its accuracy.

The automation of nested clade phylogeographic analysis

ANeCA is a fully automated implementation of Nested Clade Phylogeographic Analysis. This was originally developed by Templeton and colleagues, and has been used to infer, from the pattern of gene sequence polymorphisms in a geographically structured population, the historical demographic processes that have shaped its evolution. Until now it has been necessary to perform large parts of the procedure manually. We provide a program that will take data in Nexus sequential format, and directly output a set of inferences. The software also includes TCS v1.18 and GeoDis v2.2 as part of automation.

Nested parallelism for multi-core HPC systems using Java

Since its introduction in 1993, the Message Passing Interface (MPI) has become a de facto standard for writing High Performance Computing (HPC) applications on clusters and Massively Parallel Processors (MPPs). The recent emergence of multi-core processor systems presents a new challenge for established parallel programming paradigms, including those based on MPI. This paper presents a new Java messaging system called MPJ Express. Using this system, we exploit multiple levels of parallelism - messaging and threading - to improve application performance on multi-core processors. We refer to our approach as nested parallelism. This MPI-like Java library can support nested parallelism by using Java or Java OpenMP (JOMP) threads within an MPJ Express process. Practicality of this approach is assessed by porting to Java a massively parallel structure formation code from Cosmology called Gadget-2. We introduce nested parallelism in the Java version of the simulation code and report good speed-ups. To the best of our knowledge it is the first time this kind of hybrid parallelism is demonstrated in a high performance Java application. (C) 2009 Elsevier Inc. All rights reserved.

Four-dimensional variational data assimilation for high resolution nested models

Four-dimensional variational data assimilation (4D-Var) is used in environmental prediction to estimate the state of a system from measurements. When 4D-Var is applied in the context of high resolution nested models, problems may arise in the representation of spatial scales longer than the domain of the model. In this paper we study how well 4D-Var is able to estimate the whole range of spatial scales present in one-way nested models. Using a model of the one-dimensional advection–diffusion equation we show that small spatial scales that are observed can be captured by a 4D-Var assimilation, but that information in the larger scales may be degraded. We propose a modification to 4D-Var which allows a better representation of these larger scales.

Correction of atmospheric delay effects in radar interferometry using a nested mesoscale atmospheric model

The temporal variability of the atmosphere through which radio waves pass in the technique of differential radar interferometry can seriously limit the accuracy with which the method can measure surface motion. A forward, nested mesoscale model of the atmosphere can be used to simulate the variable water content along the radar path and the resultant phase delays. Using this approach we demonstrate how to correct an interferogram of Mount Etna in Sicily associated with an eruption in 2004-5. The regional mesoscale model (Unified Model) used to simulate the atmosphere at higher resolutions consists of four nested domains increasing in resolution (12, 4, 1, 0.3 km), sitting within the analysis version of a global numerical model that is used to initiate the simulation. Using the high resolution 3D model output we compute the surface pressure, temperature and the water vapour, liquid and solid water contents, enabling the dominant hydrostatic and wet delays to be calculated at specific times corresponding to the acquisition of the radar data. We can also simulate the second-order delay effects due to liquid water and ice.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.