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.

Collaborative destination branding : planning for tourism development through design in the Waterfall Way, NSW, Australia

This thesis develops, applies and analyses a collaborative design methodology for branding a tourism destination. The area between the Northern Tablelands and the Mid-North Coast of New South Wales, Australia, was used as a case study for this research. The study applies theoretical concepts of systems thinking and complexity to the real world, and tests the use of design as a social tool to engage multiple stakeholders in planning. In this research I acknowledge that places (and destinations) are socially constructed through people's interactions with their physical and social environments. This study explores a methodology that is explicit about the uncertainties of the destination’s system, and that helps to elicit knowledge and system trends. The collective design process used the creation of brand concepts, elements and strategies as instruments to directly engage stakeholders in the process of reflecting about their places and the issues related to tourism activity in the region. The methods applied included individual conversations and collaborative design sessions to elicit knowledge from local stakeholders. Concept maps were used to register and interpret information released throughout the process. An important aspect of the methodology was to bring together different stakeholder groups and translate the information into a common language that was understandable by all participants. This work helped release significant information as to what kind of tourism activity local stakeholders are prepared to receive and support. It also helped the emergence of a more unified regional identity. The outcomes delivered by the project (brand, communication material and strategies) were of high quality and in line with the desires and expectation of the local hosts. The process also reinforced local sense of pride, belonging and conservation. Furthermore, interaction between participants from different parts of the region triggered some self organising activity around the brand they created together. A major contribution of the present work is the articulation of an inclusive methodology to facilitate the involvement of locals into the decision-making process related to tourism planning. Of particular significance is the focus on the social construction of meaning in and through design, showing that design exercises can have significant social impact – not only on the final product, but also on the realities of the people involved in the creative process.

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.

Virion : new media and the development of the discursive museum

The historical rhetoric established with the very first public art museums declared that the purpose of such institutions was to provide a space where art could be accessible to all citizens. However contrary to this aim, studies show that art museums are one of the least accessed cultural institutions in the western world. The prevailing consensus for this can be attributed to the perception that museums are elitist, irrelevant and restricted to a small and privileged group. The focus of this research project is to address the issues that lead to these perceptions, and to identify possible curatorial strategies to encourage greater access to, and participation in the visual arts. This will be done through designing and curating an open submission exhibition that utilises new media technologies to increase access and dialogue between artists and audiences. This is part of a hybrid practice-based methodology that also includes scholarly research to critically investigate a number of historical and contemporary theories concerned with public museums and approaches to curatorial practice. This research will culminate in the development of Virion, an Internet based exhibition that aims to develop a curatorial model that facilitates open and democratic participation in arts practice from a diverse public audience.

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.