The Firefighter Problem: A Structural Analysis

We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of bounded degree b+3 for any fixed budget b>=2 (Bazgan et al.,2012). In this paper, we provide further insight into the complexity landscape of the problem by showing that the pathwidth and the maximum degree of the input graph govern its complexity. More precisely, we first prove that the problem is NP-complete even on trees of pathwidth at most three for any fixed budget b>=1. We then show that the problem turns out to be fixed parameter-tractable with respect to the combined parameter "pathwidth" and "maximum degree" of the input graph

A multimodal approach to cardiovascular risk stratification in patients with type 2 diabetes incorporating retinal, genomic and clinical features

Cardiovascular diseases are a public health concern; they remain the leading cause of morbidity and mortality in patients with type 2 diabetes. Phenotypic information available from retinal fundus images and clinical measurements, in addition to genomic data, can identify relevant biomarkers of cardiovascular health. In this study, we assessed whether such biomarkers stratified risks of major adverse cardiac events (MACE). A retrospective analysis was carried out on an extract from the Tayside GoDARTS bioresource of participants with type 2 diabetes (n = 3,891). A total of 519 features were incorporated, summarising morphometric properties of the retinal vasculature, various single nucleotide polymorphisms (SNPs), as well as routine clinical measurements. After imputing missing features, a predictive model was developed on a randomly sampled set (n = 2,918) using L1-regularised logistic regression (lasso). The model was evaluated on an independent set (n = 973) and its performance associated with overall hazard rate after censoring (log-rank p < 0.0001), suggesting that multimodal features were able to capture important knowledge for MACE risk assessment. We further showed through a bootstrap analysis that all three sources of information (retinal, genetic, routine clinical) offer robust signal. Particularly robust features included: tortuousity, width gradient, and branching point retinal groupings; SNPs known to be associated with blood pressure and cardiovascular phenotypic traits; age at imaging; clinical measurements such as blood pressure and high density lipoprotein. This novel approach could be used for fast and sensitive determination of future risks associated with MACE

On conditional skewness with applications to environmental data

The statistical literature contains many univariate and multivariate skewness measures that allow two datasets to be compared, some of which are defined in terms of quantile values. In most situations, the comparison between two random vectors focuses on univariate comparisons of conditional random variables truncated in quantiles; this kind of comparison is of particular interest in the environmental sciences. In this work, we describe a new approach to comparing skewness in terms of the univariate convex transform ordering proposed by van Zwet (Convex transformations of random variables. Mathematical Centre Tracts, Amsterdam, 1964), associated with skewness as well as concentration. The key to these comparisons is the underlying dependence structure of the random vectors. Below we describe graphical tools and use several examples to illustrate these comparisons.The research of Félix Belzunce, Julio Mulero and José María Ruíz is partially funded by the Ministerio de Economía y Competitividad (Spain) under Grant MTM2012-34023-FEDER. Alfonso Suárez-Llorens acknowledges support received from the Ministerio de Economía y Competitividad (Spain) under Grant MTM2014-57559-P

Robustness of ranking and selection rules using generalised g-and-k distributions

A new class of distributions, including the MacGillivray adaptation of the g-and-h distributions and a new family called the g-and-k distributions, may be used to approximate a wide class of distributions, with the advantage of effectively controlling skewness and kurtosis through independent parameters. This separation can be used to advantage in the assessment of robustness to non-normality in frequentist ranking and selection rules. We consider the rule of selecting the largest of several means with some specified confidence. In general, we find that the frequentist selection rule is only robust to small changes in the distributional shape parameters g and k and depends on the amount of flexibility we allow in the specified confidence. This flexibility is exemplified through a quality control example in which a subset of batches of electrical transformers are selected as the most efficient with a specified confidence, based on the sample mean performance level far each batch. (C) 1997 Elsevier Science B.V

Education for a workplace statistician

Transitioning from university student to a statistician working as a collaborative researcher, consultant and workplace educator as well as a data scientist is a very daunting and challenging task. Statistical workplaces can involve at least some aspects of all these components, and some will more easily facilitate learning on the job than others. But all workplace statisticians need proficient statistical thinking, problem-solving and communication skills, as well as a sound statistics foundation for ongoing learning to competently understand, perform and possibly develop statistical analyses. This chapter discusses how early authentic experiential and constructive learning in statistical data analysis and problem-solving courses, combined with experience gained in a developmental and mentored program in tutoring such courses, build the key skills for a workplace statistician. This is illustrated by describing how this has proved invaluable in working as a statistician in a large tertiary hospital that also incorporates a basic science medical research institute