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.

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Texture enhancement is an important component of image processing that finds extensive application in science and engineering. The quality of medical images, quantified using the imaging texture, plays a significant role in the routine diagnosis performed by medical practitioners. Most image texture enhancement is performed using classical integral order differential mask operators. Recently, first order fractional differential operators were used to enhance images. Experimentation with these methods led to the conclusion that fractional differential operators not only maintain the low frequency contour features in the smooth areas of the image, but they also nonlinearly enhance edges and textures corresponding to high frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we apply the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other first order fractional differential operators, we find that our new algorithms provide higher signal to noise values and superior image quality.

A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.

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.