Statistical tests of the primality of some numbers look similar to statistical tests of many nonmathematical, clearly empirical propositions. Yet interpretations of probability prima facie appear to preclude the possibility of statistical tests of mathematical propositions. For example, it is hard to understand how the statement that n is prime could have a frequentist probability other than 0 or 1. On the other hand, subjectivist approaches appear to be saddled with ‘coherence’ constraints on rational probabilities that require (...) rational agents to assign extremal probabilities to logical and mathematical propositions. In the light of these problems, many philosophers have come to think that there must be some way to generalize a Bayesian statistical account. In this article I propose that a classical frequentist approach should be reconsidered. I conclude that we can give a conditional justification of statistical testing of at least some mathematical hypotheses: if statistical tests provide us with reasons to believe or bet on empirical hypotheses in the standard situations, then they also provide us with reasons to believe or bet on mathematical hypotheses in the structurally similar mathematical cases. (shrink)

This study examines the Programme for International Student Assessment (PISA), one of the most influential tools of global education reform discourses in the 21st century. The study focuses on the governing role of statistical data in the discourse constructed by the international comparative assessment, referring to the global educational governance of the OECD. Disturbingly, the systematic collection and distribution of data does not merely quantify student achievement. Rather, students and participating countries are also qualified and classified. Here, (...) OECD’s PISA statistics act as a governing technology enabling the comparisons; through PISA’s statistics, the OECD has largely fostered the test-driven education reform trends worldwide. In this study, statistical data are examined as political instruments visualizing intangible concepts, constructing definitions of good practice and improvement, and fabricating the individuals whose knowledge and skills are normalized. In conclusion, it is necessary to rethink the new sociopolitical instrument – PISA’s statistics – not as a master rationale to reform the educational system of each country, but as a mere reference point based on the system’s distinctiveness. (shrink)

Peter Spirtes. Building Causal Graphs from Statistical Data in the Presence of Latent Variables.

This article is a longitudinal analysis of the relation between gendered labour divisions and new data processing technologies at the Dutch Central Bureau of Statistics. Following social-constructivist and evolutionary economic approaches, the authors hold that the relation between technology and work organization is a two-way process. This means that technology does not only affect the relations between men and women at work, but that these relations also influence technological choices. The proportional numbers of men and women on the labour (...) market and changing conceptions of which work is deemed appropriate for women have been important factors in the strongly varying extent to which women participated in office work. They have also been important factors in determining the course of technological development. Shortages of women on the labour market have even determined search heuristics for new technological solutions in specific directions. (shrink)

Statistical methods used by healthcare entities enable the collection of various information about the structure and characteristics of treated patients. They are an important source of knowledge, and form a database that plays an important role in entity management theory. In the presented study, we analysed the hospital stays of patients treated in all hospital wards of the 3rd City Hospital in Łodź during 2012. The following, in particular, were taken into account: admittance procedure, discharge procedure, age and sex (...) of hospitalised persons. Patients in over 55% of cases were admitted using the sud- den admittance procedure. At the same time, over 3/4 of the stays ended with a referral for further treatment in ambulatory conditions, and death occurred in approx. 5% of hospitalisations. By comparing the discharge procedures, the percentage of deaths in the Anaesthesiology and Intensive Care Wards can be seen clearly. Internal wards are next in turn. The biggest differences in the length of hospitalisation between the studied institution and the NFZ data concern the E77, A49, A48, A87, A33, D18, E16, E61 and G37 groups. (shrink)

Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further (...) progress in data analysis. (shrink)

Combining information from two or possibly several blocks of data is gaining increased attention and importance in several areas of science and industry. Typical examples can be found in chemistry, spectroscopy, metabolomics, genomics, systems biology and sensory science. Many methods and procedures have been proposed and used in practice. The area goes under different names: data integration, data fusion, multiblock analyses, multiset analyses and a few more. This book is an attempt to give an up-to-date treatment of (...) the most used and important methods within an important branch of the area; namely methods based on so-called components or latent variables. These methods have already obtained an enormous attention in for instance chemometrics, bioinformatics, machine learning and sensometrics and have proved to be important both for prediction and interpretation. The book is primarily a description of methodologies, but most of the methods will be illustrated by examples from the above-mentioned areas. The book is written such that both users of the methods as well as method developers will hopefully find sections of interest. In the end of the book there is a description of a software package developed particularly for the book. This package is freely available in R and covers many of the methods discussed. To distinguish the different type of methods from each other, the book is divided into five parts. Part I is introduction and preliminary concepts. Part II is the core of the book containing the main unsupervised and supervised methods. Part III deals with more complex structures and, finally, Part IV discusses alternative unsupervised and supervised methods. The book ends with Part V discussing the available software. Our recommendation for reading the book are as follows. A minimum read of the book would involve chapters 1, 2, 3, 5 and 7. Chapters 4, 6 and 8 are more specialized and chapters 9 and 10 contain methods we think are more advanced or less obvious to use. We feel privileged to have so many friendly colleagues who were willing to spend their time on helping us to improve the book by reading separate chapters. We would like to express our thanks to: Rasmus Bro, Margriet Hendriks, Ulf Indahl, Henk Kiers, Ingrid MaÌ⁽ge, Federico Marini, AÌ⁽smund Rinnan, Rosaria Romano, Lars Erik Solberg, Marieke Timmerman, Oliver Tomic, Johan Westerhuis and Barry Wise. Of course, the correctness of the final text is fully our responsibility! (shrink)

The rise of Big Data changes the context in which organisations producing official statistics operate. Big Data provides opportunities, but in order to make optimal use of Big Data, a number of challenges have to be addressed. This stimulates increased collaboration between National Statistical Institutes, Big Data holders, businesses and universities. In time, this may lead to a shift in the role of statistical institutes in the provision of high-quality and impartial statistical information (...) to society. In this paper, the changes in context, the opportunities, the challenges and the way to collaborate are addressed. The collaboration between the various stakeholders will involve each partner building on and contributing different strengths. For national statistical offices, traditional strengths include, on the one hand, the ability to collect data and combine data sources with statistical products and, on the other hand, their focus on quality, transparency and sound methodology. In the Big Data era of competing and multiplying data sources, they continue to have a unique knowledge of official statistical production methods. And their impartiality and respect for privacy as enshrined in law uniquely position them as a trusted third party. Based on this, they may advise on the quality and validity of information of various sources. By thus positioning themselves, they will be able to play their role as key information providers in a changing society. (shrink)

Statistical significance is almost universally equated with the attribution to some population of nonchance influences as the source of structure in the data. But statistical significance can be divorced from both parameter estimation and probability as, instead, a statement about the atypicality or lack of exchangeability over some distinction of the data relative to some set. From this perspective, the criticisms of significance tests evaporate.

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of means, coefficient of variation, and number of observations, by measuring eye fixations, accuracy, and confidence when assessing differences between number sets. Results indicated that participants implicitly create (...) and compare approximate summary values that include information about mean and variance, with no evidence of explicit calculation. Accuracy and confidence increased, while the number of fixations decreased as sets became more distinct , demonstrating that the statistical properties of datasets were highly related to comparisons. The discussion includes a model proposing how reasoners summarize and compare datasets within the architecture for approximate number representation. (shrink)

The quality of the products coming from different lines of production requires some tests called comparative life tests. For lines having the same facility, the lifetime of the product is distributed by Burr XII, the lifetime distribution, and units are tested under type-I generalized hybrid censoring scheme. The observed censoring data are used under maximum likelihood and the Bayes method to estimate the model parameters. The theoretical results are discussed and assessed through data analysis and Monte Carlo simulation (...) study. Finally, we reported some brief comments obtained from numerical computation. (shrink)

The exponential growth of social data both in volume and complexity has increasingly exposed many of the shortcomings of the conventional frequentist approach to statistics. The scientific community has called for careful usage of the approach and its inference. Meanwhile, the alternative method, Bayesian statistics, still faces considerable barriers toward a more widespread application. The bayesvl R package is an open program, designed for implementing Bayesian modeling and analysis using the Stan language’s no-U-turn (NUTS) sampler. The package combines the (...) ability to construct Bayesian network models using directed acyclic graphs (DAGs), the Markov chain Monte Carlo (MCMC) simulation technique, and the graphic capability of the ggplot2 package. As a result, it can improve the user experience and intuitive understanding when constructing and analyzing Bayesian network models. A case example is offered to illustrate the usefulness of the package for Big Data analytics and cognitive computing. (shrink)

Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the (...) logarithm transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution. (shrink)

There is an increasing interest in expanding the one-parameter Lindley distribution to two-parameter, three-parameter, and five-parameter. The univariate one-parameter Lindley distribution is still one of the most applicable distributions in data analysis especially in lifetime data. Modeling dependent random quantities required bivariate parametric probability distributions. This study presents a new bivariate three-parameter probability distribution called bivariate modified Lindley distribution. The one-parameter modified Lindley distribution is used as a base line to construct the new model. Its statistical properties (...) including cumulative function, density function, marginals, moments, conditional distributions, and copula are discussed. Simulation is constructed to declare theoretical properties, to show the flexibility of the new model and to investigate the goodness of fit. Two sets of real data, financial data and UEFA Champion’s League data, are used to show the applicability of the proposed model for different types of data. (shrink)

Evidence, as viewed through the lens of statistical significance, is not always as it appears! In the investigation of clinical research findings arising from statistical analyses, a fundamental initial step for the emerging fraud detective is to retrieve the source data for cross-examination with the study data. Recognizing that source data are not always forthcoming and that, realistically speaking, the investigator may be uninitiated in fraud detection and investigation, this paper will highlight some key methodological (...) procedures for providing a sounder evidence base for withdrawing from a study on grounds of integrity. The promotion of patient safety is paramount. However, there is a broader rationale for disseminating these ideas. This includes empowering researchers to optimize their personal integrity, make informed choices regarding membership of future research collaborations and successfully voice their concerns to journal editors, particularly where a conflict of interests can render such dialogues particularly difficult. Recommendations will be supported by topical case studies and practical steps involving data exploration, testing of baseline data and application of Benford’s Law. While this paper has a clinical focus, the advice provided is transferrable to a wide range of multidisciplinary research settings outside of Medicine. (shrink)

The diversity of state confidentiality laws governing public health data presents a significant challenge for public health initiatives. This challenge is further complicated by the array of confidentially laws that are relevant within a state as disclosure and usage standards vary depending upon data holder, type, and source. These laws often have not been updated to address modern confidentiality risks such as unlawful data linkage or breach, leaving many public health organizations without clear guidance in the contentious (...) area of individual privacy. To address these challenges, public health organizations have increasingly turned to the science of de-identification, but whether de-identification adequately meets the many and varied state confidentiality legal requirements remains an unanswered question. (shrink)

This book examines several epistemological regimes in studies of numerical data over the last four centuries. It distinguishes these regimes and mobilises questions present in the philosophy of science, sociology and historical works throughout the 20th century. Attention is given to the skills of scholars and their methods, their assumptions, and the socio-historical conditions that made calculations and their interpretations possible. In doing so, questions posed as early as Émile Durkheim’s and Ernst Cassirer’s ones are revisited and the concept (...) of symbolic form is put to the test in this particular survey, conducted over long period of time. Although distinct from a methodological and epistemological point of view, today these regimes may be found together in the toolbox of statisticians and those who comment on their conclusions. As such, the book is addressed to social scientists and historians and all those who are interested in numerical productions. (shrink)

In European countries (excluding the UK and Ireland), official statistics do not use racial or ethnic categories, but instead rely on proxies to collect data about discrimination. In the German microcensus, the proxy category adopted is ‘migration background’ (Migrationshintergrund): an individual has a ‘migration background’ when one or more of their parents does not have German citizenship by birth. We apply a coupled ethical-epistemic analysis to the ‘migration background’ category to illuminate how the epistemic issues contribute to ethical ones. (...) Our central claim is that these ethical-epistemic issues with the ‘migration background’ category are best analysed in terms of Charles Mills's ‘white ignorance’. Appealing to Annette Martín's structural account of white ignorance, we highlight the cyclical reinforcement of ignorance and racial injustice in the use of the ‘migration background’ variable. Colourblind eliminativism about race perpetuates the use of ‘migration background’, which sustains and intensifies racial injustices. (shrink)

Madole & Harden argue that the Mendelian reshuffling of genes and genomes is analogous to randomised controlled trials. We are not convinced by their arguments. First, their recipe for meeting the demands on randomised experiments is inherently inconsistent. Second, disequilibrium across chromosomes conflicts with their assumption of statistical independence. Third, the genome-wide association study (GWAS) method has many pitfalls, including low repeatability.

In typical statistical learning studies, researchers define sequences in terms of the probability of the next item in the sequence given the current item (or items), and they show that high probability sequences are treated as more familiar than low probability sequences. Existing accounts of these phenomena all assume that participants represent statistical regularities more or less as they are defined by the experimenters—as sequential probabilities of symbols in a string. Here we offer an alternative, or possibly supplementary, (...) hypothesis. Specifically, rather than identifying or labeling individual stimuli discretely in order to predict the next item in a sequence, we need only assume that the participant is able to represent the stimuli as evincing particular similarity relations to one another, with sequences represented as trajectories through this similarity space. We present experiments in which this hypothesis makes sharply different predictions from hypotheses based on the assumption that sequences are learned over discrete, labeled stimuli. We also present a series of simulation models that encode stimuli as positions in a continuous two‐dimensional space, and predict the next location from the current location. Although no model captures all of the data presented here, the results of three critical experiments are more consistent with the view that participants represent trajectories through similarity space rather than sequences of discrete labels under particular conditions. (shrink)

People made forecasts from graphically presented time series. Series were sinusoids overlaid by a zero or positive linear trend and a zero, low, moderate, or high level of noise. Forecasting performance was affected by both these variables. However, it did not correlate with ability to identify the trend and correlated significantly with ability to detect the sinusoidal pattern only when series were noise-free. A second experiment showed that the effect of data noise was not influenced by the number of (...) forecasts that people made from a series. These findings are consistent with the view that data noise does not affect the way that forecasts are made but that it impairs them for two reasons. First, it renders the anchor-and-adjust heuristics underlying them less effective. Second, it causes people to add more noise to their judgements in their attempts to make them representative of the data. (shrink)

We present a statistical analysis of the realization of definiteness in Tunisian Arabic (TA) texts written in Arabizi, a hybrid system reflecting some features of TA phonetics (assimilation), but also showing orthographic features, as the use of arithmographs. In §1, we give an overview of definiteness in TA from a semantic and syntactic point of view. In §2 we outline a typology of definite articles and show that TA normally marks definiteness with articles or similar devices, but also presents (...) zero-markings or weak definites. In §3 we discuss TA and how definiteness is instantiated in TA. In §4, we present data from the Tunisian Arabizi Corpus (TAC), a multidisciplinary work with a hybrid approach based on dialectological questions, corpus linguistics standards, and deep learning techniques. In §5 we define the behavior of TA with respect to what we observed in §1, §2 and §3, describing our TAC-based analysis. (shrink)

The approaching ways in religious phenomenon quantitative studies are, most of the times, based only on the evolution of adherent flows and population structure from a religious point of view. In this pape, an integrated statistical indicators system will be designed. The main purpose of the system is to enhance the quality and coherence of the religious phenomenon. The most important indicators from the integrated system are: context indicators (political, economical, socio-cultural, demographical), basic indicators, level and structure indicators, participation (...) indicators, resource indicators (spiritual, human and pecuniary), quality, efficiency and outcomes (religious freedom, social connections, international relationships). Designing a complete, coherent system of indicators is necessary for a correct approach in studying the religious phenomenon. Statistical indicators can supply quantitative data for the operational description of the religious phenomenon. The indicators’ system makes possible not only a descriptive analysis but also some advanced statistical techniques (e.g. regression and correlation method). (shrink)

Next SectionThe precise nature and scope of healthcare confidentiality has long been the subject of debate. While the obligation of confidentiality is integral to professional ethical codes and is also safeguarded under English law through the equitable remedy of breach of confidence, underpinned by the right to privacy enshrined in Article 8 of the Human Rights Act 1998, it has never been regarded as absolute. But when can and should personal information be made available for statistical and research purposes (...) and what if the information in question is highly sensitive information, such as that relating to the termination of pregnancy after 24 weeks? This article explores the case of In the Matter of an Appeal to the Information Tribunal under section 57 of the Freedom of Information Act 2000, concerning the decision of the Department of Health to withhold some statistical data from the publication of its annual abortion statistics. The specific data being withheld concerned the termination for serious fetal handicap under section 1(1)d of the Abortion Act 1967. The paper explores the implications of this case, which relate both to the nature and scope of personal privacy. It suggests that lessons can be drawn from this case about public interest and use of statistical information and also about general policy issues concerning the legal regulation of confidentiality and privacy in the future. (shrink)

Biomarkers are widely used not only as prognostic or diagnostic indicators, or as surrogate markers of disease in clinical trials, but also to formulate theories of pathogenesis. We identify two problems in the use of biomarkers in mechanistic studies. The first problem arises in the case of multifactorial diseases, where different combinations of multiple causes result in patient heterogeneity. The second problem arises when a pathogenic mediator is difficult to measure. This is the case of the oxidative stress (OS) theory (...) of disease, where the causal components are reactive oxygen species (ROS) that have very short half-lives. In this case, it is usual to measure the traces left by the reaction of ROS with biological molecules, rather than the ROS themselves. Borrowing from the philosophical theories of signs, we look at the different facets of biomarkers and discuss their different value and meaning in multifactorial diseases and system medicine to inform their use in patient stratification in personalized medicine. (shrink)

The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, (...) characterized by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. (shrink)

A key motivation for Universal Grammar (UG) is developmental: UG can help children acquire the linguistic knowledge that they do as quickly as they do from the data that's available to them. Some of the most fruitful recent work in language acquisition has combined ideas about different hypothesis space building blocks with domain‐general statistical learning. Statistical learning can then provide a way to help navigate the hypothesis space in order to converge on the correct hypothesis. Reinforcement learning (...) is a principled way to update the probability of a categorical option that's in competition with other categorical options. There are two prominent options for linking theory theoretical representations: the Uniformity of Theta Assignment Hypothesis (UTAH) and the relativized form of that theory, relativized UTAH. The learning strategy of Pearl and Sprouse shares the intuition with subjacency that there's a local structural anomaly when syntactic islands occur. (shrink)

This paper shows how to define probability distributions over linguistically realistic syntactic structures in a way that permits us to define language learning and language comprehension as statistical problems. We demonstrate our approach using lexical‐functional grammar (LFG), but our approach generalizes to virtually any linguistic theory. Our probabilistic models are maximum entropy models. In this paper we concentrate on statistical inference procedures for learning the parameters that define these probability distributions. We point out some of the practical problems (...) that make straightforward ways of estimating these distributions infeasible, and develop a “pseudo‐likelihood” estimation procedure that overcomes some of these problems. This method raises interesting questions concerning the nature of the data available to a language learner and the modularity of language learning and processing. (shrink)

Unsupervised statistical learning is the standard setting for the development of the only advanced visual system that is both highly sophisticated and versatile, and extensively studied: that of monkeys and humans. In this extended abstract, we invoke philosophical observations, computational arguments, behavioral data and neurobiological findings to explain why computer vision researchers should care about (1) unsupervised learning, (2) statistical inference, and (3) the visual brain. We then outline a neuromorphic approach to structural primitive learning motivated by (...) these considerations, survey a range of neurobiological findings and behavioral data consistent with it, and conclude by mentioning some of the more challenging directions for future research. (shrink)