Contemporary issues in Australian family law: Do we need a more unified and interventionist judicial model

Recent decisions of the Family Court of Australian reflect concerns over the adversarial nature of the legal process. The processes and procedures of the judicial system militate against a detailed examination of the issues and rights of the parties in dispute. The limitations of the family law framework are particularly demonstrated in disputes over the custody of children where the Court has tended to neglect the rights and interests of the primary carer. An alternative "unified family court" framework will be examined in which the Court pursues a more active and interventionist approach in the determination of family law disputes.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Are the financial services external complaints resolution schemes subject to judicial review?

In Australia seven schemes (apart from the Superannuation Complaints Tribunal) provide alternative dispute resolution services for complaints brought by consumers against financial services industry members. Recently the Supreme Court of New South Wales held that the decisions of one scheme were amenable to judicial review at the suit of a financial services provider member and the Supreme Court of Victoria has since taken a similar approach. This article examines the juristic basis for such a challenge and contends that judicial review is not available, either at common law or under statutory provisions. This is particularly the case since Financial Industry Complaints Service Ltd v Deakin Financial Services Pty Ltd (2006) 157 FCR 229; 60 ACSR 372 decided that the jurisdiction of a scheme is derived from a contract made with its members. The article goes on to contend that the schemes are required to give procedural fairness and that equitable remedies are available if that duty is breached.

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Outrage management in cases of sexual harassment as revealed in judicial decisions

Sexual harassment can be conceptualized as a series of interactions between harassers and targets that either inhibit or increase outrage by third parties. The outrage management model predicts the kinds of actions likely to be used by perpetrators to minimize outrage, predicts the consequences of failing to use these tactics—namely backfire, and recommends countertactics to increase outrage. Using this framework, our archival study examined outrage-management tactics reported as evidence in 23 judicial decisions of sexual harassment cases in Australia. The decisions contained precise, detailed information about the circumstances leading to the claim; the events which transpired in the courtroom, including direct quotations; and the judges' interpretations and findings. We found evidence that harassers minimize outrage by covering up the actions, devaluing the target, reinterpreting the events, using official channels to give an appearance of justice, and intimidating or bribing people involved. Targets can respond using countertactics of exposure, validation, reframing, mobilization of support, and resistance. Although there are limitations to using judicial decisions as a source of information, our study points to the value of studying tactics and the importance to harassers of minimizing outrage from their actions. The findings also highlight that, given the limitations of statutory and organizational protections in reducing the incidence and severity of sexual harassment in the community, individual responses may be effective as part of a multilevel response in reducing the incidence and impact of workplace sexual harassment as a gendered harm.

Probability and statistics

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