Probability and statistics

Now in its sixth edition, the Traffic Engineering Handbook continues to be a must have publication in the transportation industry, as it has been for the past 60 years. The new edition provides updated information for people entering the practice and for those already practicing. The handbook is a convenient desk reference, as well as an all in one source of principles and proven techniques in traffic engineering. Most chapters are presented in a new format, which divides the chapters into four areas-basics, current practice, emerging trends and information sources. Chapter topics include road users, vehicle characteristics, statistics, planning for operations, communications, safety, regulations, traffic calming, access management, geometrics, signs and markings, signals, parking, traffic demand, maintenance and studies. In addition, as the focus in transportation has shifted from project based to operations based, two new chapters have been added-"Planning for Operations" and "Managing Traffic Demand to Address Congestion: Providing Travelers with Choices." The Traffic Engineering Handbook continues to be one of the primary reference sources for study to become a certified Professional Traffic Operations Engineer™. Chapters are authored by notable and experienced authors, and reviewed and edited by a distinguished panel of traffic engineering experts.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

Probability and story-telling : normative and descriptive models of juridical proof

The operation of the law rests on the selection of an account of the facts. Whether this involves prediction or postdiction, it is not possible to achieve certainty. Any attempt to model the operation of the law completely will therefore raise questions of how to model the process of proof. In the selection of a model a crucial question will be whether the model is to be used normatively or descriptively. Focussing on postdiction, this paper presents and contrasts the mathematical model with the story model. The former carries the normative stamp of scientific approval, whereas the latter has been developed by experimental psychologists to describe how humans reason. Neil Cohen's attempt to use a mathematical model descriptively provides an illustration of the dangers in not clearly setting this parameter of the modelling process. It should be kept in mind that the labels 'normative' and 'descriptive' are not eternal. The mathematical model has its normative limits, beyond which we may need to critically assess models with descriptive origins.

On the optimality of sample-based estimates of the expectation of the empirical minimizer

We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates expectations to sample averages. Second, we show that these structural upper bounds can be loose, compared to previous bounds. In particular, we demonstrate a class for which the expectation of the empirical minimizer decreases as O(1/n) for sample size n, although the upper bound based on structural properties is Ω(1). Third, we show that this looseness of the bound is inevitable: we present an example that shows that a sharp bound cannot be universally recovered from empirical data.

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.

Two dynamic discrete choice estimation problems and simulation method solutions

This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in both cases, for this application, simpler methods also provide reasonably good results.

Expectation and variation with a virtual die

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the advantage they offer is a familiar context within which to explore much more complex concepts. If the basic chance mechanism of the device is understood, it is possible to enter quickly into an arena of more complex concepts. This is what happened with a two hour activity engaged in by four classes of Grade 6 students in the same school. The activity targeted the concepts of variation and expectation. The teachers held extended discussions with their classes on variation and expectation at the beginning of the activity, with students contributing examples of the two concepts from their own experience. These notions are quite sophisticated for Grade 6, but the underlying concepts describe phenomena that students encounter every day. For example, time varies continuously; sporting results vary from game to game; the maximum temperature varies from day to day. However, there is an expectation about tomorrow’s maximum temperature based on the expert advice from the weather bureau. There may also be an expectation about a sporting result based on the participants’ previous results. It is this juxtaposition that makes life interesting. Variation hence describes the differences we see in phenomena around us. In a scenario displaying variation, expectation describes the effort to characterise or summarise the variation and perhaps make a prediction about the message arising from the scenario. The explicit purpose of the activity described here was to use the familiar scenario of rolling a die to expose these two concepts. Because the students had previously experienced rolling physical dice they knew instinctively about the variation that occurs across many rolls and about the theoretical expectation that each side should “come up” one-sixth of the time. They had observed the instances of the concepts in action, but had not consolidated the underlying terminology to describe it. As the two concepts are so fundamental to understanding statistics, we felt it would be useful to begin building in the familiar environment of rolling a die. Because hand-held dice limit the explorations students can undertake, the classes used the soft-ware TinkerPlots (Konold & Miller, 2011) to simulate rolling a die multiple times.

Can Risk Management boost the supply of Affordable Housing Development and Management?

A shortage of affordable housing is a major problem in Australia today. This is mainly due to the limited supply of affordable housing that is provided by the non-government housing sector. Some private housing developers see the provision of affordable housing for lower income people as a high risk investment which offers a lower return than broader market-based housing. The scarcity of suitable land, a limited government ‘subsidy’, and increasing housing costs have not provided sufficient development incentives to encourage their investment despite the existing high demand for affordable housing. This study analyses the risk management process conducted by some private and not-for-profit housing providers in South East Queensland, and draws conclusions about the relationship between risk assessments/responses and past experiences. In-depth interviews of selected non-government housing providers have been conducted to facilitate an understanding of their approach to risk assessment/response in developing and in managing affordable housing projects. These developers use an informal risk management process as part of their normal business process in accordance with industry standards. A simple qualitative matrix has been used to analyse probability and impacts using a qualitative scale - low, medium and high. For housing providers who have considered investing in affordable housing but have not yet implemented any such projects, affordable housing development is seen as an opportunity that needs to be approached with caution. The risks associated with such projects and the levels of acceptance of these are not consistently identified by current housing providers. Many interviewees agree that the recognition of financial risk and the fear of community rejection of such housing projects have restrained them from committing to such investment projects. This study suggests that implementing improvements to the risk mitigation and management framework may assist in promoting the supply of affordable housing by non-government providers.

The Impact of Globalization and Corruption on Extraordinary Wealth: An Empirical Analysis

The billionaires of the world attract significant attention from the media and the public. The popular press is full of books selling formulas on how to become rich. Surprisingly, only a limited number of studies have explored empirically the determinants of extraordinary wealth. Using a large data set we explore whether globalization and corruption affect extreme wealth accumulation. We find evidence that an increase in globalization increases super-richness. In addition, we also find that an increase in corruption leads to an increase in the creation of super fortune. This supports the argument that in kleptocracies large sums are transferred into the hands of a small group of individuals.

Governors highway safety associations and transportation planning: Exploratory factor analysis and structural equation modeling

The Intermodal Surface Transportation Efficiency Act (ISTEA) of 1991 mandated the consideration of safety in the regional transportation planning process. As part of National Cooperative Highway Research Program Project 8-44, "Incorporating Safety into the Transportation Planning Process," we conducted a telephone survey to assess safety-related activities and expertise at Governors Highway Safety Associations (GHSAs), and GHSA relationships with metropolitan planning organizations (MPOs) and state departments of transportation (DOTs). The survey results were combined with statewide crash data to enable exploratory modeling of the relationship between GHSA policies and programs and statewide safety. The modeling objective was to illuminate current hurdles to ISTEA implementation, so that appropriate institutional, analytical, and personnel improvements can be made. The study revealed that coordination of transportation safety across DOTs, MPOs, GHSAs, and departments of public safety is generally beneficial to the implementation of safety. In addition, better coordination is characterized by more positive and constructive attitudes toward incorporating safety into planning.

Gender inequality and the spread of HIV-AIDS in India

Purpose The purpose of the paper is to analyze the low status of women as being a major contributor for the observed gender inequality in the spread of HIV/AIDS in India. Design/methodology/approach The paper uses data from National Aids Control Organization (NACO), National Family Health Survey (NFHS 3), and the Directorate of Economics and Statistics. Findings This study highlights the problems facing women in deterring the spread of HIV/AIDS in India. The status and empowerment of women are important variables in combating the disease among both men and women in India. Literacy, education, exposure to the media, labor market participation, awareness of HIV/AIDS, and economic independence are important considerations in improving the status of women in India. Policymakers need to focus on gender inequality in order to combat the spread of HIV/AIDS in India. Originality/value While absolute figures indicate men are more likely to be infected with HIV/AIDS, the rate of decline is higher for men compared to women in India. We explore several plausible explanations for such observed inequality in the spread of HIV/AIDS across gender. In particular, a potentially important factor - the low status of women in society is attributable as an impediment to the spread of the disease. A case study of the relationship between gender empowerment and the spread of HIV/AIDS in the state with the highest concentration, Manipur, provides more insight to the difficulties faced by women in combating HIV/AIDS in India.

Non-compositional concepts and quantum tests

Compositionality is a frequently made assumption in linguistics, and yet many human subjects reveal highly non-compositional word associations when confronted with novel concept combinations. This article will show how a non-compositional account of concept combinations can be supplied by modelling them as interacting quantum systems.

Can water security be achieved in the urban environment through the implementation of the Neo Institutional theory government regulation and legislation?

The research seeks to address the current global water crisis and the built environments effect on the increasing demand for sustainability and water security. The fundamental question in determining the correct approach for water security in the built environment is whether government regulation and legislation could provide the framework for sustainable development and the conscious shift providing that change is the only perceivable option, there is no alternative. This article will attempt to analyse the value of the neo institutional theory as a method for directing individuals and companies to conform to water saving techniques. As is highlighted throughout the article, it will be investigated whether an incentive verse punishment approach to government legislations and regulations would provide the framework required to ensure water security within the built environment. Individuals and companies make certain choices or perform certain actions not because they fear punishment or attempt to conform; neither do they do so because an action is appropriate or feels some sort of social obligation. Instead, the cognitive element of neo institutionalism suggests that individuals make certain choices because they can conceive no alternative. The research seeks to identify whether sustainability and water security can become integrated into all aspects of design and architecture through the perception that 'there is no alternative.' This report seeks to address the omission of water security in the built environment by reporting on a series of investigations, interviews, literature reviews, exemplars and statistics relating to the built environment and the potential for increased water security. The results and analysis support the conclusions that through the support of government and local council, sustainability in the built environment could be achieved and become common practice for developments. Highlighted is the approach required for water management systems integration into the built environment and how these can be developed and maintained effectively between cities, states, countries and cultures.