Adjusted jackknife for imputation under unequal probability sampling without replacement

Imputation is commonly used to compensate for item non-response in sample surveys. If we treat the imputed values as if they are true values, and then compute the variance estimates by using standard methods, such as the jackknife, we can seriously underestimate the true variances. We propose a modified jackknife variance estimator which is defined for any without-replacement unequal probability sampling design in the presence of imputation and non-negligible sampling fraction. Mean, ratio and random-imputation methods will be considered. The practical advantage of the method proposed is its breadth of applicability.

Using phylogeny to investigate the origins of the Cape flora: the importance of taxonomic, gene and genome sampling strategies

Phylogenetic methods hold great promise for the reconstruction of the transition from precursor to modern flora and the identification of underlying factors which drive the process. The phylogenetic methods presently used to address the question of the origin of the Cape flora of South Africa are considered here. The sampling requirements of each of these methods, which include dating of diversifications using calibrated molecular trees, sister pair comparisons, lineage through time plots and biogeographical optimizations are reviewed. Sampling of genes, genomes and species are considered. Although increased higher-level studies and increased sampling are required for robust interpretation, it is clear that much progress is already made. It is argued that despite the remarkable richness of the flora, the Cape flora is a valuable model system to demonstrate the utility of phylogenetic methods in determining the history of a modern flora.

Variable step LMS algorithm using the accumulated instantaneous error concept

The convergence speed of the standard Least Mean Square adaptive array may be degraded in mobile communication environments. Different conventional variable step size LMS algorithms were proposed to enhance the convergence speed while maintaining low steady state error. In this paper, a new variable step LMS algorithm, using the accumulated instantaneous error concept is proposed. In the proposed algorithm, the accumulated instantaneous error is used to update the step size parameter of standard LMS is varied. Simulation results show that the proposed algorithm is simpler and yields better performance than conventional variable step LMS.

Improvement of classification accuracy for stochastic discrimination - Multi-class classification

In this paper, an improved stochastic discrimination (SD) is introduced to reduce the error rate of the standard SD in the context of multi-class classification problem. The learning procedure of the improved SD consists of two stages. In the first stage, a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. In the second stage, the standard SD is modified by (i) restricting sampling in the important space; and (ii) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but smaller variance than that of standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples axe provided to demonstrate the effectiveness of the proposed improved SD.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.

On improvement of classification accuracy for stochastic discrimination

Stochastic discrimination (SD) depends on a discriminant function for classification. In this paper, an improved SD is introduced to reduce the error rate of the standard SD in the context of a two-class classification problem. The learning procedure of the improved SD consists of two stages. Initially a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. Then the standard SD is modified by 1) restricting sampling in the important space, and 2) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but with a smaller variance than that of the standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples are provided to demonstrate the effectiveness of the proposed improved SD.

Insights into redox cycling of sulfur and iron in peatlands using high-resolution diffusive equilibrium thin film (DET) gel probe sampling

High spatial resolution vertical profiles of pore-water chemistry have been obtained for a peatland using diffusive equilibrium in thin films (DET) gel probes. Comparison of DET pore-water data with more traditional depth-specific sampling shows good agreement and the DET profiling method is less invasive and less likely to induce mixing of pore-waters. Chloride mass balances as water tables fell in the early summer indicate that evaporative concentration dominates and there is negligible lateral flow in the peat. Lack of lateral flow allows element budgets for the same site at different times to be compared. The high spatial resolution of sampling also enables gradients to be observed that permit calculations of vertical fluxes. Sulfate concentrations fall at two sites with net rates of 1.5 and 5.0nmol cm− 3 day− 1, likely due to a dominance of bacterial sulfate reduction, while a third site showed a net gain in sulfate due to oxidation of sulfur over the study period at an average rate of 3.4nmol cm− 3 day− 1. Behaviour of iron is closely coupled to that of sulfur; there is net removal of iron at the two sites where sulfate reduction dominates and addition of iron where oxidation dominates. The profiles demonstrate that, in addition to strong vertical redox related chemical changes, there is significant spatial heterogeneity. Whilst overall there is evidence for net reduction of sulfate within the peatland pore-waters, this can be reversed, at least temporarily, during periods of drought when sulfide oxidation with resulting acid production predominates.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

A note on the analysis error associated with 3D-FGAT

The analysis-error variance of a 3D-FGAT assimilation is examined analytically using a simple scalar equation. It is shown that the analysis-error variance may be greater than the error variances of the inputs. The results are illustrated numerically with a scalar example and a shallow-water model.