Split Sampling: Expectations, Normalisation and Rare Events

In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution. We illustrate our method with two applications. First, we compute a shortest network path rare event probability and compare our method to estimation to a cross entropy approach. Then, we compute a normalisation constant of a high dimensional mixture of Gaussians and compare our estimate to one based on nested sampling. We discuss the relationship between our method and other alternatives such as the product of conditional probability estimator and importance sampling. The methods developed here are available in the R package: SplitSampling

Demand for Wine in Australia: Systems Versus Single Equation Approach

The objective of the study is to estimate demand for wine in Australia, based on both the systems approach and the single equation approach. Both approaches consider demand for three categories of alcoholic drinks (beer, wine and spirits) in a seemingly unrelated regression framework to take account of cross-equation correlations. Time series data on retail price indexes and apparent per capita consumption of alcoholic beverages for Australia for the period 1975/76 to 1998/99 are used for econometric estimation. The results show that over the short run, beer and wine are necessities; however, over the long run, wine becomes a luxury good. Beer and wine are complements. Demand for all three beverages is price inelastic. The study also found that the behaviour of wine consumers reflect past consumption patterns, indicating that wine is more addictive than either beer or spirits. A structural change in consumer preferences away from cheaper cask wines to more expensive bottled table wines has a significant impact on the volume of wine consumption. Finally, wine consumption has increased over time. The study re-confirms the importance of developing a model that considers the impacts of both economic and non-economic variables on wine consumption.wine demand, demand analysis, almst ideal demand system, Demand and Price Analysis,

Sharp Threshold Asymptotics for the Emergence of Additive Bases

A subset A of {0,1,...,n} is said to be a 2-additive basis for {1,2,...,n} if each j in {1,2,...,n} can be written as j=x+y, x,y in A, x<=y. If we pick each integer in {0,1,...,n} independently with probability p=p_n tending to 0, thus getting a random set A, what is the probability that we have obtained a 2-additive basis? We address this question when the target sum-set is [(1-alpha)n,(1+alpha)n] (or equivalently [alpha n, (2-alpha) n]) for some 0<alpha<1. Under either model, the Stein-Chen method of Poisson approximation is used, in conjunction with Janson's inequalities, to tease out a very sharp threshold for the emergence of a 2-additive basis. Generalizations to k-additive bases are then given.Comment: 22 page

Brain awareness week and beyond: encouraging the next generation.

The field of neuroscience is generating increased public appetite for information about exciting brain research and discoveries. As stewards of the discipline, together with FUN and others, the Society for Neuroscience (SfN) embraces public outreach and education as essential to its mission of promoting understanding of the brain and nervous system. The Society looks to its members, particularly the younger generation of neuroscientists, to inspire, inform and engage citizens of all ages, and most importantly our youth, in this important endeavor. Here we review SfN programs and resources that support public outreach efforts to inform, educate and tell the story of neuroscience. We describe the important role the Brain Awareness campaign has played in achieving this goal and highlight opportunities for FUN members and students to contribute to this growing effort. We discuss specific programs that provide additional opportunities for neuroscientists to get involved with K-12 teachers and students in ways that inspire youth to pursue further studies and possible careers in science. We draw attention to SfN resources that support outreach to broader audiences. Through ongoing partnerships such as that between SfN and FUN, the neuroscience community is well positioned to pursue novel approaches and resources, including harnessing the power of the Internet. These efforts will increase science literacy among our citizens and garner more robust support for scientific research

Practical Attacks on Cryptographically End-to-end Verifiable Internet Voting Systems

Cryptographic end-to-end verifiable voting technologies concern themselves with the provision of a more trustworthy, transparent, and robust elections. To provide voting systems with more transparency and accountability throughout the process while preserving privacy which allows voters to express their true intent. Helios Voting is one of these systems---an online platform where anyone can easily host their own cryptographically end-to-end verifiable election, aiming to bring verifiable voting to the masses. Helios does this by providing explicit cryptographic checks that an election was counted correctly, checks that any member of the public can independently verify. All of this while still protecting one of the essential properties of open democracy, voter privacy. In spite of these cryptographic checks and the strong mathematical assertions of correctness they provide, this thesis discusses the discovery and exploit of three vulnerabilities. The first is the insufficient validation of cryptographic elements in Helios ballots uploaded by users. This allows a disgruntled voter to cast a carefully crafted ballot which will prevent an election from being tallied. The second vulnerability is the insufficient validation of cryptographic parameters used in ElGamal by an election official. This leads to an attack where the election official can upload weak parameters allowing the official to cast arbitrary votes in a single ballot. The final attack is a cross-site scripting attack that would allow anyone to steal or re-cast ballots on behalf of victims. We coordinated disclosure with the Helios developers and provided fixes for all the vulnerabilities outlined in the thesis. Additionally, this thesis adds to the body of work highlighting the fragility of internet voting applications and discusses the unique challenges faced by internet voting applications

Evaluating the reliability of four-dimensional computed tomography scans of the wrist

Introduction: Four-dimensional CT (or 4D CT) scans are a novel approach to diagnosing musculoskeletal pathology. Although still in its infancy, there has been a surge of interest in identifying clinical applications for musculoskeletal 4D CT. The scapholunate joint has received the most attention thus far due to the complex articulations and challenges faced with prompt diagnosis of scapholunate injuries. The objective of this thesis is to review current literature on musculoskeletal 4D CT and to evaluate the inter- and intra-rater reliability of the assessment of scapholunate stability in 4D CT wrist scans. Methodology: 4D CT scans of thirteen healthy volunteers and four patients were prepared. Seven orthopaedic and plastic surgeons were recruited to qualitatively assess the stability of the scapholunate joint in the 4D CT scans. Statistical analysis included percent agreement, Fleiss’ kappa, and Gwet’s AC1 coefficient. Results: The percent agreement amongst all raters was 0.80392 (95% CI: 0.675 - 0.932). Fleiss’ Kappa was 0.54895 (95% CI: 0.252 - 0.846) and Gwet’s AC₁ was 0.54895 (95% CI: 0.391 - 0.915). The intraclass correlation coefficient (ICC) for intra-rater reliability was 0.71631 (95% CI: 0.5567 – 0.8423). Conclusion: Our pilot study suggests good inter- and intra-rater reliability for the qualitative assessment of scapholunate instability in 4D CT scans. Although further studies are required, this thesis highlights the vast potential of 4D CT as a non-invasive diagnostic technique of dynamic musculoskeletal injuries

Information Uncertainty and the Momentum Effect

I identify simple proxies for uncertainty and attempt to determine if the returns to a momentum strategy vary with these proxies. The proxies identified include the stock’s daily 6-month historical return volatility, the magnitude of alpha in a 6-month historical regression of the stock’s daily returns on the Fama-French factors and the (1-R2) value of the regression. The exposures to each of the risk factors were also tested as possible proxies for uncertainty related to the factors. Using daily stock return data from CRSP from 1926 to 2006, stocks are first sorted into quintiles based on these proxies. A momentum strategy is pursued in each uncertainty quintile by taking long and short positions in the deciles with the highest and lowest past returns respectively over a 6 month ranking period, and holding these positions for a further 6 months. It was found that with greater volatility, momentum returns are higher. Similarly, as the magnitude of alphas rises, momentum returns increase. These results support the hypothesis that greater uncertainty contributes to momentum. Finally, momentum returns are higher with larger exposures to the market factor, but show no statistically significant trends with the size and book-to-market factors. When (1-R2) values increase however, momentum returns decline, in contradiction with the hypothesis that greater uncertainty contributes to momentum. Stocks were also sorted into industry groups according to Kenneth French’s twelve industry portfolio classification. The industries were ranked according to the volatility of their daily returns and the returns to a momentum strategy within the industry. There was no clear relationship between the volatility of daily returns and momentum returns of the twelve industry portfolios