Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Closed-form solutions for low-rank non-rigid reconstruction

Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation. We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model. We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. [1], which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.

A new data source for fisheries resource assessment: genetic estimates of the effective number of spawners. Final Report to the Fisheries Research and Development Corporation.

The development of innovative methods of stock assessment is a priority for State and Commonwealth fisheries agencies. It is driven by the need to facilitate sustainable exploitation of naturally occurring fisheries resources for the current and future economic, social and environmental well being of Australia. This project was initiated in this context and took advantage of considerable recent achievements in genomics that are shaping our comprehension of the DNA of humans and animals. The basic idea behind this project was that genetic estimates of effective population size, which can be made from empirical measurements of genetic drift, were equivalent to estimates of the successful number of spawners that is an important parameter in process of fisheries stock assessment. The broad objectives of this study were to 1. Critically evaluate a variety of mathematical methods of calculating effective spawner numbers (Ne) by a. conducting comprehensive computer simulations, and by b. analysis of empirical data collected from the Moreton Bay population of tiger prawns (P. esculentus). 2. Lay the groundwork for the application of the technology in the northern prawn fishery (NPF). 3. Produce software for the calculation of Ne, and to make it widely available. The project pulled together a range of mathematical models for estimating current effective population size from diverse sources. Some of them had been recently implemented with the latest statistical methods (eg. Bayesian framework Berthier, Beaumont et al. 2002), while others had lower profiles (eg. Pudovkin, Zaykin et al. 1996; Rousset and Raymond 1995). Computer code and later software with a user-friendly interface (NeEstimator) was produced to implement the methods. This was used as a basis for simulation experiments to evaluate the performance of the methods with an individual-based model of a prawn population. Following the guidelines suggested by computer simulations, the tiger prawn population in Moreton Bay (south-east Queensland) was sampled for genetic analysis with eight microsatellite loci in three successive spring spawning seasons in 2001, 2002 and 2003. As predicted by the simulations, the estimates had non-infinite upper confidence limits, which is a major achievement for the application of the method to a naturally-occurring, short generation, highly fecund invertebrate species. The genetic estimate of the number of successful spawners was around 1000 individuals in two consecutive years. This contrasts with about 500,000 prawns participating in spawning. It is not possible to distinguish successful from non-successful spawners so we suggest a high level of protection for the entire spawning population. We interpret the difference in numbers between successful and non-successful spawners as a large variation in the number of offspring per family that survive – a large number of families have no surviving offspring, while a few have a large number. We explored various ways in which Ne can be useful in fisheries management. It can be a surrogate for spawning population size, assuming the ratio between Ne and spawning population size has been previously calculated for that species. Alternatively, it can be a surrogate for recruitment, again assuming that the ratio between Ne and recruitment has been previously determined. The number of species that can be analysed in this way, however, is likely to be small because of species-specific life history requirements that need to be satisfied for accuracy. The most universal approach would be to integrate Ne with spawning stock-recruitment models, so that these models are more accurate when applied to fisheries populations. A pathway to achieve this was established in this project, which we predict will significantly improve fisheries sustainability in the future. Regardless of the success of integrating Ne into spawning stock-recruitment models, Ne could be used as a fisheries monitoring tool. Declines in spawning stock size or increases in natural or harvest mortality would be reflected by a decline in Ne. This would be good for data-poor fisheries and provides fishery independent information, however, we suggest a species-by-species approach. Some species may be too numerous or experiencing too much migration for the method to work. During the project two important theoretical studies of the simultaneous estimation of effective population size and migration were published (Vitalis and Couvet 2001b; Wang and Whitlock 2003). These methods, combined with collection of preliminary genetic data from the tiger prawn population in southern Gulf of Carpentaria population and a computer simulation study that evaluated the effect of differing reproductive strategies on genetic estimates, suggest that this technology could make an important contribution to the stock assessment process in the northern prawn fishery (NPF). Advances in the genomics world are rapid and already a cheaper, more reliable substitute for microsatellite loci in this technology is available. Digital data from single nucleotide polymorphisms (SNPs) are likely to super cede ‘analogue’ microsatellite data, making it cheaper and easier to apply the method to species with large population sizes.

Unsupervised Domain Adaptation by Domain Invariant Projection

Domain-invariant representations are key to addressing the domain shift problem where the training and test exam- ples follow different distributions. Existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space. This space, however, may not be di- rectly suitable for such a comparison, since some of the fea- tures may have been distorted by the domain shift, or may be domain specific. In this paper, we introduce a Domain Invariant Projection approach: An unsupervised domain adaptation method that overcomes this issue by extracting the information that is invariant across the source and tar- get domains. More specifically, we learn a projection of the data to a low-dimensional latent space where the distance between the empirical distributions of the source and target examples is minimized. We demonstrate the effectiveness of our approach on the task of visual object recognition and show that it outperforms state-of-the-art methods on a stan- dard domain adaptation benchmark dataset

Effect of changes in hook pattern and size on catch rate, hooking location, injury and bleeding for a number of tropical reef fish species

The Queensland Great Barrier Reef line fishery in Australia is regulated via a range of input and output controls including minimum size limits, daily catch limits and commercial catch quotas. As a result of these measures a substantial proportion of the catch is released or discarded. The fate of these released fish is uncertain, but hook-related mortality can potentially be decreased by using hooks that reduce the rates of injury, bleeding and deep hooking. There is also the potential to reduce the capture of non-target species though gear selectivity. A total of 1053 individual fish representing five target species and three non-target species were caught using six hook types including three hook patterns (non-offset circle, J and offset circle), each in two sizes (small 4/0 or 5/0 and large 8/0). Catch rates for each of the hook patterns and sizes varied between species with no consistent results for target or non-target species. When data for all of the fish species were aggregated there was a trend for larger hooks, J hooks and offset circle hooks to cause a greater number of injuries. Using larger hooks was more likely to result in bleeding, although this trend was not statistically significant. Larger hooks were also more likely to foul-hook fish or hook fish in the eye. There was a reduction in the rates of injuries and bleeding for both target and non-target species when using the smaller hook sizes. For a number of species included in our study the incidence of deep hooking decreased when using non-offset circle hooks, however, these results were not consistent for all species. Our results highlight the variability in hook performance across a range of tropical demersal finfish species. The most obvious conservation benefits for both target and non-target species arise from using smaller sized hooks and non-offset circle hooks. Fishers should be encouraged to use these hook configurations to reduce the potential for post-release mortality of released fish.

A consensus genetic map of sorghum that integrates multiple component maps and high-throughput Diversity Array Technology (DArT) markers

Background: Sorghum genome mapping based on DNA markers began in the early 1990s and numerous genetic linkage maps of sorghum have been published in the last decade, based initially on RFLP markers with more recent maps including AFLPs and SSRs and very recently, Diversity Array Technology (DArT) markers. It is essential to integrate the rapidly growing body of genetic linkage data produced through DArT with the multiple genetic linkage maps for sorghum generated through other marker technologies. Here, we report on the colinearity of six independent sorghum component maps and on the integration of these component maps into a single reference resource that contains commonly utilized SSRs, AFLPs, and high-throughput DArT markers. Results: The six component maps were constructed using the MultiPoint software. The lengths of the resulting maps varied between 910 and 1528 cM. The order of the 498 markers that segregated in more than one population was highly consistent between the six individual mapping data sets. The framework consensus map was constructed using a "Neighbours" approach and contained 251 integrated bridge markers on the 10 sorghum chromosomes spanning 1355.4 cM with an average density of one marker every 5.4 cM, and were used for the projection of the remaining markers. In total, the sorghum consensus map consisted of a total of 1997 markers mapped to 2029 unique loci ( 1190 DArT loci and 839 other loci) spanning 1603.5 cM and with an average marker density of 1 marker/0.79 cM. In addition, 35 multicopy markers were identified. On average, each chromosome on the consensus map contained 203 markers of which 58.6% were DArT markers. Non-random patterns of DNA marker distribution were observed, with some clear marker-dense regions and some marker-rare regions. Conclusion: The final consensus map has allowed us to map a larger number of markers than possible in any individual map, to obtain a more complete coverage of the sorghum genome and to fill a number of gaps on individual maps. In addition to overall general consistency of marker order across individual component maps, good agreement in overall distances between common marker pairs across the component maps used in this study was determined, using a difference ratio calculation. The obtained consensus map can be used as a reference resource for genetic studies in different genetic backgrounds, in addition to providing a framework for transferring genetic information between different marker technologies and for integrating DArT markers with other genomic resources. DArT markers represent an affordable, high throughput marker system with great utility in molecular breeding programs, especially in crops such as sorghum where SNP arrays are not publicly available.

Demography of feral camels in central Australia and its relevance to population control

Since their release over 100 years ago, camels have spread across central Australia and increased in number. Increasingly, they are being seen as a pest, with observed impacts from overgrazing and damage to infrastructure such as fences. Irregular aerial surveys since 1983 and an interview-based survey in 1966 suggest that camels have been increasing at close to their maximum rate. A comparison of three models of population growth fitted to these, albeit limited, data suggests that the Northern Territory population has indeed been growing at an annual exponential rate of r = 0.074, or 8% per year, with little evidence of a density-dependent brake. A stage-structured model using life history data from a central Australian camel population suggests that this rate approximates the theoretical maximum. Elasticity analysis indicates that adult survival is by far the biggest influence on rate of increase and that a 9% reduction in survival from 96% is needed to stop the population growing. In contrast, at least 70% of mature females need to be sterilised to have a similar effect. In a benign environment, a population of large mammals such as camels is expected to grow exponentially until close to carrying capacity. This will frustrate control programs, because an ever-increasing number of animals will need to be removed for zero growth the longer that culling or harvesting effort is delayed. A population projection for 2008 suggests ~10 500 animals need to be harvested across the Northern Territory. Current harvests are well short of this. The ability of commercial harvesting to control camel populations in central Australia will depend on the value of animals, access to animals and the presence of alternative species to harvest when camels are at low density.

Analysis of the distribution of the number of bidders in construction contract auctions

The number of bidders, N, involved in a construction procurement auction is known to have an important effect on the value of the lowest bid and the mark up applied by bidders. In practice, for example, it is important for a bidder to have a good estimate of N when bidding for a current contract. One approach, instigated by Friedman in 1956, is to make such an estimate by statistical analysis and modelling. Since then, however, finding a suitable model for N has been an enduring problem for researchers and, despite intensive research activity in the subsequent thirty years little progress has been made - due principally to the absence of new ideas and perspectives. This paper resumes the debate by checking old assumptions, providing new evidence relating to concomitant variables and proposing a new model. In doing this and in order to assure universality, a novel approach is developed and tested by using a unique set of twelve construction tender databases from four continents. This shows the new model provides a significant advancement on previous versions. Several new research questions are also posed and other approaches identified for future study.

On the number of two-line and three-line latin rectangles - an alternative approach

The number of two-line and three-line Latin rectangles is obtained by recursive methods in a setting slightly more general than usually considered. We show how this leads to a generalisation which is proved elsewhere.

QTL for root angle and number in a population developed from bread wheats (Triticum aestivum) with contrasting adaptation to water-limited environments

Root architecture traits in wheat are important in deep soil moisture acquisition and may be used to improve adaptation to water-limited environments. The genetic architecture of two root traits, seminal root angle and seminal root number, were investigated using a doubled haploid population derived from SeriM82 and Hartog. Multiple novel quantitative trait loci (QTL) were identified, each one having a modest effect. For seminal root angle, four QTL (-log10(P) >3) were identified on 2A, 3D, 6A and 6B, and two suggestive QTL (-log10(P) >2) on 5D and 6B. For root number, two QTL were identified on 4A and 6A with four suggestive QTL on 1B, 3A, 3B and 4A. QTL for root angle and root number did not co-locate. Transgressive segregation was found for both traits. Known major height and phenology loci appear to have little effect on root angle and number. Presence or absence of the T1BL.1RS translocation did not significantly influence root angle. Broad sense heritability (h 2) was estimated as 50 % for root angle and 31 % for root number. Root angle QTL were found to be segregating between wheat cultivars adapted to the target production region indicating potential to select for root angle in breeding programs. © 2013 Springer-Verlag Berlin Heidelberg.

The identification of teaching interactions used in one-to-one teaching of number in the early years of schooling

This research paper reports on phase one of an investigation of video recorded intensive one-to-one teaching interactions with 6–7-year-old students who were in their second year of schooling in Australia and identified by the their teacher as low attaining in early number. The two-phased study from which this paper emerges was originally conducted in 1998 as part of my Bachelor of Teaching Honours (Research) program at Southern Cross University Lismore, New South Wales. That study identified teaching interactions particularly suited to one-to-one teaching in the Maths Recovery Program, a program designed for these students who were at risk of failure in early number. Since that time a great deal has not changed with limited literature available that comprehensively reports on teaching interactions in intensive one-to-one settings. Revisiting the original study is considered timely given the increasing number of withdrawal and intensive programs now funded and adopted by schools and yet, rarely reported on in terms of the effectiveness of the teaching interactions that occur in such settings. This paper then presents a discussion of a preliminary series of teaching interactions that either positively and or negatively influence an intensive one-to-one teaching and learning setting