Equitability revisited: why the “equitable threat score” is not equitable

In the forecasting of binary events, verification measures that are “equitable” were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used “equitable threat score” (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as “asymptotically equitable.” In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around −0.5, reducing in magnitude to −0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphy’s two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures

Asia-Pacific Regional Integration Index: Construction, Interpretation, and Comparison

We develop an index to measure the degree of regional integration in Asia and the Pacific (48 economies in six subregions). The index comprises 26 indicators in six dimensions of regional integration, i.e., trade and investment, money and finance, regional value chains, infrastructure and connectivity, free movement of people, and institutional and social integration. We use principal component analysis to apportion a weight to each dimension and indicator to construct composite indexes. The resulting indexes help assess the state of regional integration on diverse socioeconomic dimensions, evaluate progress against goals, identify strengths and weaknesses, and track progress. Cross-country, cross-regional comparisons also allow policy makers to prioritize areas for further efforts

Development and Feasibility of a Smartphone, ECG and GPS Based System for Remotely Monitoring Exercise in Cardiac Rehabilitation

Background Despite its efficacy and cost-effectiveness, exercise-based cardiac rehabilitation is undertaken by less than one-third of clinically eligible cardiac patients in every country for which data is available. Reasons for non-participation include the unavailability of hospital-based rehabilitation programs, or excessive travel time and distance. For this reason, there have been calls for the development of more flexible alternatives. Methodology and Principal Findings We developed a system to enable walking-based cardiac rehabilitation in which the patient's single-lead ECG, heart rate, GPS-based speed and location are transmitted by a programmed smartphone to a secure server for real-time monitoring by a qualified exercise scientist. The feasibility of this approach was evaluated in 134 remotely-monitored exercise assessment and exercise sessions in cardiac patients unable to undertake hospital-based rehabilitation. Completion rates, rates of technical problems, detection of ECG changes, pre- and post-intervention six minute walk test (6 MWT), cardiac depression and Quality of Life (QOL) were key measures. The system was rated as easy and quick to use. It allowed participants to complete six weeks of exercise-based rehabilitation near their homes, worksites, or when travelling. The majority of sessions were completed without any technical problems, although periodic signal loss in areas of poor coverage was an occasional limitation. Several exercise and post-exercise ECG changes were detected. Participants showed improvements comparable to those reported for hospital-based programs, walking significantly further on the post-intervention 6 MWT, 637 m (95% CI: 565–726), than on the pre-test, 524 m (95% CI: 420–655), and reporting significantly reduced levels of cardiac depression and significantly improved physical health-related QOL. Conclusions and Significance The system provided a feasible and very flexible alternative form of supervised cardiac rehabilitation for those unable to access hospital-based programs, with the potential to address a well-recognised deficiency in health care provision in many countries. Future research should assess its longer-term efficacy, cost-effectiveness and safety in larger samples representing the spectrum of cardiac morbidity and severity

Роман Э. М. Форстера «Поездка в Индию» сквозь призму аналитической психологии К. Г. Юнга

По мнению большинства критиков и исследователей творчества английского прозаика Эдуарда Моргана Форстера (Edward Morgan Forster, 1879-1970), роман «Поездка в Индию» (“A Passage to India”, 1924) считается его наиболее значительным произведением, которое и по сей день вызывает многочисленные интерпретации. В силу известных причин в советском литературоведении роман изучался преимущественно в свете общественно-политической проблематики; магистральными мотивами выделялись политические и антиколониальные. Безусловно, не стоит преуменьшать социально-политическое значение романа – политическая проблематика занимает важное место в произведении, однако, вряд ли стоит ее и преувеличивать

DALASS: Variable selection in discriminant analysis via the LASSO

The objective of DALASS is to simplify the interpretation of Fisher’s discriminant function coefficients. The DALASS problem—discriminant analysis (DA) modified so that the canonical variates satisfy the LASSO constraint—is formulated as a dynamical system on the unit sphere. Both standard and orthogonal canonical variates are considered. The globally convergent continuous-time algorithms are illustrated numerically and applied to some well-known data sets

A clustering approach to interpretable principal components

A new method for constructing interpretable principal components is proposed. The method first clusters the variables, and then interpretable (sparse) components are constructed from the correlation matrices of the clustered variables. For the first step of the method, a new weighted-variances method for clustering variables is proposed. It reflects the nature of the problem that the interpretable components should maximize the explained variance and thus provide sparse dimension reduction. An important feature of the new clustering procedure is that the optimal number of clusters (and components) can be determined in a non-subjective manner. The new method is illustrated using well-known simulated and real data sets. It clearly outperforms many existing methods for sparse principal component analysis in terms of both explained variance and sparseness

Independent component analysis for three-way data with an application from atmospheric science

In this paper, a new approach to independent component analysis (ICA) for three-way data is considered. The rotational freedom of the three-mode component analysis (Tucker3) model is exploited to implement ICA in one mode of the data. The performance of the proposed approach is evaluated by means of numerical experiments. An illustration with real data from atmospheric science is presented, where the first mode is spatial location, the second is time and the third is a set of different meteorological variables representing geopotential heights at various vertical pressure levels. The results show that the three-mode decomposition finds spatial patterns of climate anomalies which can be interpreted in a meteorological sense and as such gives an insightful low-dimensional representation of the data