Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.

The relationship between building characteristics and the chemical composition of surface films found on glass windows in Brisbane, Australia

Films found on the windows of residential buildings have been studied. The main aim of the paper was to assess the roles of the films in the accumulation of potentially toxic chemicals in residential buildings. Thus the elemental and polycyclic aromatic hydrocarbon compositions of the surface films from the glass windows of eighteen residential buildings were examined. The presence of sample amounts of inorganic elements (4.0–1.2 × 106 μg m−2) and polycyclic aromatic hydrocarbons in the films (BDL - 620.1 ng m−2) has implications for human exposure and the fate of pollutants in the urban environment. To facilitate the interpretation of the results, data matrices consisting of the chemical composition of the films and the building characteristics were subjected to multivariate data analysis methods, and these revealed that the accumulation of the chemicals was strongly dependent on building characteristics such as the type of glass used for the window, the distance from a major road, age of the building, distance from an industrial activity, number of smokers in the building and frequency of cooking in the buildings. Thus, building characteristics which minimize the accumulation of pollutants on the surface films need to be encouraged.

School system as axiological medium : the state's primary macro-proposing context and its expanding moral role in Australia

This paper analyses the Australian Values Education Program (VEP) within the framework of late-classical political economy. using analytical methods from systemic functional linguistics and critical discourse analysis, we demonstrate that the VEP is an unwitting restatement of the principles of ideology as developed by the likes of Destutt de Tracy and the Young Hegelians. We conclude that the sudden shock of globalisation and the post-national cultures this has entailed is in many ways similar to the shock of formal nationalism that emerged in the late-Seventeenth and early- Eighteenth centuries. The overall result of the VEP for the Australian school system is a massive procedural burden that is unlikely to produce the results at which the program is aimed.

Boosting the margin: A new explanation for the effectiveness of voting methods

One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition.

On the consistency of multiclass classification methods

Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that not all generalizations preserve the nice property of Bayes consistency. We provide a necessary and sufficient condition for consistency which applies to a large class of multiclass classification methods. The approach is illustrated by applying it to some multiclass methods proposed in the literature.

On the consistency of multiclass classification methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.