Learning detectors quickly with stationary statistics

Computer vision is increasingly becoming interested in the rapid estimation of object detectors. The canonical strategy of using Hard Negative Mining to train a Support Vector Machine is slow, since the large negative set must be traversed at least once per detector. Recent work has demonstrated that, with an assumption of signal stationarity, Linear Discriminant Analysis is able to learn comparable detectors without ever revisiting the negative set. Even with this insight, the time to learn a detector can still be on the order of minutes. Correlation filters, on the other hand, can produce a detector in under a second. However, this involves the unnatural assumption that the statistics are periodic, and requires the negative set to be re-sampled per detector size. These two methods differ chie y in the structure which they impose on the co- variance matrix of all examples. This paper is a comparative study which develops techniques (i) to assume periodic statistics without needing to revisit the negative set and (ii) to accelerate the estimation of detectors with aperiodic statistics. It is experimentally verified that periodicity is detrimental.

Cell image classification using histograms, higher order statistics and adaboost

A cell classification algorithm that uses first, second and third order statistics of pixel intensity distributions over pre-defined regions is implemented and evaluated. A cell image is segmented into 6 regions extending from a boundary layer to an inner circle. First, second and third order statistical features are extracted from histograms of pixel intensities in these regions. Third order statistical features used are one-dimensional bispectral invariants. 108 features were considered as candidates for Adaboost based fusion. The best 10 stage fused classifier was selected for each class and a decision tree constructed for the 6-class problem. The classifier is robust, accurate and fast by design.

Bluetooth vehicle trajectory by fusing Bluetooth and loops : motorway travel time statistics

Loop detectors are widely used on the motorway networks where they provide point speed and traffic volumes. Models have been proposed for temporal and spatial generalization of speed for average travel time estimation. Advancement in technology provides complementary data sources such as Bluetooth MAC Scanner (BMS), detecting the MAC ID of the Bluetooth devices transported by the traveller. Matching the data from two BMS stations provides individual vehicle travel time. Generally, on the motorways loops are closely spaced, whereas BMS are placed few kilometres apart. In this research, we fuse BMSs and loops data to define the trajectories of the Bluetooth vehicles. The trajectories are utilised to estimate the travel time statistics between any two points along the motorway. The proposed model is tested using simulation and validated with real data from Pacific motorway, Brisbane. Comparing the model with the linear interpolation based trajectory provides significant improvements.

Understanding the quantitative skill base on introductory statistics : a case study from business statistics

Basic mathematical skills are critical to a student’s ability to successfully undertake an introductory statistics course. Yet in business education this vitally important area of mathematics and statistics education is under-researched. The question therefore arises as to what level of mathematical skill a typical business studies student will possess as they enter the tertiary environment, and whether there are any common deficiencies that we can identify with a view to tackling the problem. This paper will focus on a study designed to measure the level of mathematical ability of first year business students. The results provide timely insight into a growing problem faced by many tertiary educators in this field.

Statistics critical in securing our food supply

“World food security … is at its lowest in half a century,” wrote Julian Cribb FTSE, a wellknown consultant in science communication and founding editor of www.sciencealert. com.au in the lead article in the 2008 ATSE Focus magazine issue entitled “Food for the world: the nation’s challenge”. Food security continues to be a key national and international concern and it is pleasing to see this issue of Focus again exploring aspects of the topic with the aim of continuing to raise awareness of issues and influencing relevant policy decisions. Statistics (or statistical science, more broadly) has been critical to the information and decision-making value chain needed to optimise agriculture and the food supply chain. The key steps are most often addressed by multidisciplinary research groups including statisticians in collaboration with life and physical scientists, agri-industry personnel and other relevant stakeholders.

Suicide, statistics and the coroner: A comparative study of death investigations

Australia has a significantly higher suicide rate than England. Rather than accepting that this ‘statistical fact’ is a direct reflection of some positivist truth, this paper begins with the premise that how suicide is counted depends upon what counts as suicide. This study involves semi-structured interviews with coroners both in Australia and England, as well as observations at inquests. Important differences between the two coronial systems include: first, quite different logics of operation; second, the burden of proof for reaching a finding of suicide is significantly higher in England; and third, the presence of family members at English inquests results in far greater pressure being brought to bear upon coroners. These combined factors result in a reduced likelihood of English coroners reaching a finding of suicide. The conclusions are twofold. First, this research supports existing criticisms of comparative suicide statistics. Second, this research adds theoretical weight to criticisms of positivist analyses of social phenomena.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

Phenotyping cotton ovule fibre initiation with spatial statistics

Yield in cultivated cotton (Gossypium spp.) is affected by the number and distribution of fibres initiated on the seed surface but, apart from simple statistical summaries, little has been done to assess this phenotype quantitatively. Here we use two types of spatial statistics to describe and quantify differences in patterning of cotton ovule fibre initials (FI). The following five different species of Gossypium were analysed: G. hirsutum L., G. barbadense L., G. arboreum, G. raimondii Ulbrich. and G. trilobum (DC.) Skovsted. Scanning electron micrographs of FIs were taken on the day of anthesis. Cell centres for fibre and epidermal cells were digitised and analysed by spatial statistics methods appropriate for marked point processes and tessellations. Results were consistent with previously published reports of fibre number and spacing. However, it was shown that the spatial distributions of FIs in all of species examined exhibit regularity, and are not completely random as previously implied. The regular arrangement indicates FIs do not appear independently of each other and we surmise there may be some form of mutual inhibition specifying fibre-initial development. It is concluded that genetic control of FIs differs from that of stomata, another well studied plant idioblast. Since spatial statistics show clear species differences in the distribution of FIs within this genus, they provide a useful method for phenotyping cotton. © CSIRO 2007.

Statistics at play

Three core components in developing children’s understanding and appreciation of data — establish a context, pose and answer statistical questions, represent and interpret data — lay the foundation for the fourth component: use data to enhance existing context.

Summarising and reporting sugarcane locomotive run statistics from TOTools and GPS data

The majority of sugar mill locomotives are equipped with GPS devices from which locomotive position data is stored. Locomotive run information (e.g. start times, run destinations and activities) is electronically stored in software called TOTools. The latest software development allows TOTools to interpret historical GPS information by combining this data with run information recorded in TOTools and geographic information from a GIS application called MapInfo. As a result, TOTools is capable of summarising run activity details such as run start and finish times and shunt activities with great accuracy. This paper presents 15 reports developed to summarise run activities and speed information. The reports will be of use pre-season to assist in developing the next year's schedule and for determining priorities for investment in the track infrastructure. They will also be of benefit during the season to closely monitor locomotive run performance against the existing schedule.

How do experts think about statistics? Hints for improving undergraduate and postgraduate training

Experts are increasingly being called upon to quantify their knowledge, particularly in situations where data is not yet available or of limited relevance. In many cases this involves asking experts to estimate probabilities. For example experts, in ecology or related fields, might be called upon to estimate probabilities of incidence or abundance of species, and how they relate to environmental factors. Although many ecologists undergo some training in statistics at undergraduate and postgraduate levels, this does not necessarily focus on interpretations of probabilities. More accurate elicitation can be obtained by training experts prior to elicitation, and if necessary tailoring elicitation to address the expert’s strengths and weaknesses. Here we address the first step of diagnosing conceptual understanding of probabilities. We refer to the psychological literature which identifies several common biases or fallacies that arise during elicitation. These form the basis for developing a diagnostic questionnaire, as a tool for supporting accurate elicitation, particularly when several experts or elicitors are involved. We report on a qualitative assessment of results from a pilot of this questionnaire. These results raise several implications for training experts, not only prior to elicitation, but more strategically by targeting them whilst still undergraduate or postgraduate students.

Introducing the practice of statistics: are we environmentally friendly?

The practice of statistics is the focus of the world in which professional statisticians live. To understand meaningfully what this practice is about, students need to engage in it themselves. Acknowledging the limitations of a genuine classroom setting, this study attempted to expose four classes of year 5 students (n=91) to an authentic experience of the practice of statistics. Setting an overall context of people’s habits that are considered environmentally friendly, the students sampled their class and set criteria for being environmentally friendly based on questions from the Australian Bureau of Statistics CensusAtSchool site. They then analysed the data and made decisions, acknowledging their degree of certainty, about three populations based on their criteria: their class, year 5 students in their school and year 5 students in Australia. The next step was to collect a random sample the size of their class from an Australian Bureau of Statistics ‘population’, analyse it and again make a decision about Australian year 5 students. At the end, they suggested what further research they might do. The analysis of students’ responses gives insight into primary students’ capacity to appreciate and understand decision making, and to participate in the practice of statistics, a topic that has received very little attention in the literature. Based on the total possible score of 23 from student workbook entries, 80 % of students achieved at least a score of 11.

Inferential, non-parametric statistics to assess quality of probabilistic forecast systems

Many statistical forecast systems are available to interested users. In order to be useful for decision-making, these systems must be based on evidence of underlying mechanisms. Once causal connections between the mechanism and their statistical manifestation have been firmly established, the forecasts must also provide some quantitative evidence of `quality’. However, the quality of statistical climate forecast systems (forecast quality) is an ill-defined and frequently misunderstood property. Often, providers and users of such forecast systems are unclear about what ‘quality’ entails and how to measure it, leading to confusion and misinformation. Here we present a generic framework to quantify aspects of forecast quality using an inferential approach to calculate nominal significance levels (p-values) that can be obtained either by directly applying non-parametric statistical tests such as Kruskal-Wallis (KW) or Kolmogorov-Smirnov (KS) or by using Monte-Carlo methods (in the case of forecast skill scores). Once converted to p-values, these forecast quality measures provide a means to objectively evaluate and compare temporal and spatial patterns of forecast quality across datasets and forecast systems. Our analysis demonstrates the importance of providing p-values rather than adopting some arbitrarily chosen significance levels such as p < 0.05 or p < 0.01, which is still common practice. This is illustrated by applying non-parametric tests (such as KW and KS) and skill scoring methods (LEPS and RPSS) to the 5-phase Southern Oscillation Index classification system using historical rainfall data from Australia, The Republic of South Africa and India. The selection of quality measures is solely based on their common use and does not constitute endorsement. We found that non-parametric statistical tests can be adequate proxies for skill measures such as LEPS or RPSS. The framework can be implemented anywhere, regardless of dataset, forecast system or quality measure. Eventually such inferential evidence should be complimented by descriptive statistical methods in order to fully assist in operational risk management.

From inferential statistics to climate knowledge

Climate variability and change are risk factors for climate sensitive activities such as agriculture. Managing these risks requires "climate knowledge", i.e. a sound understanding of causes and consequences of climate variability and knowledge of potential management options that are suitable in light of the climatic risks posed. Often such information about prognostic variables (e.g. yield, rainfall, run-off) is provided in probabilistic terms (e.g. via cumulative distribution functions, CDF), whereby the quantitative assessments of these alternative management options is based on such CDFs. Sound statistical approaches are needed in order to assess whether difference between such CDFs are intrinsic features of systems dynamics or chance events (i.e. quantifying evidences against an appropriate null hypothesis). Statistical procedures that rely on such a hypothesis testing framework are referred to as "inferential statistics" in contrast to descriptive statistics (e.g. mean, median, variance of population samples, skill scores). Here we report on the extension of some of the existing inferential techniques that provides more relevant and adequate information for decision making under uncertainty.