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)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

Otsuka (2023) argues for a correspondence between data science and traditional epistemology: Bayesian statistics is internalist; classical (frequentist) statistics is externalist, owing to its reliabilist nature; model selection is pragmatist; and machine learning is a version of virtue epistemology. Where he sees diversity, I see an opportunity for unity. In this article, I argue that classical statistics, model selection, and machine learning share a foundation that is reliabilist in an unconventional sense that aligns with internalism. Hence a (...) unification under internalist reliabilism. (shrink)

This paper argues that unusual coincidences, particularly those involving historical events, can be viewed as design patterns, suggesting an intelligent influence over the course of events. A compelling case examined in detail using probability theory concerns the presidencies of Abraham Lincoln (1809–1865) and John F. Kennedy (1917–1963). This and other coincidences involving historical figures disfavor the materialistic perspective and point to the presence of an intelligent agent acting on a global scale, beyond the arrow of time, influencing human lives and (...) the course of history. (shrink)

In this article I investigate the extent to which perspectival realism (PR) agrees with frequentist statistical methodology and philosophy, with an emphasis on J. Neyman’s frequentist statistical methods and philosophy. PR is clarified in the context of frequentist statistics. Based on the example of the stopping rule problem, PR is shown to be able to naturally be associated with frequentist statistics in general. I show that there are explicit and implicit aspects of Neyman’s methods and philosophy that are (...) incompatible and both partially agree and disagree with PR. Additionally, I provide clarifications and interpretations to make Neyman’s methods and philosophy more coherent with the realist aspect of PR. Furthermore, I deliver an argument that, based on Neyman’s methods and philosophy, one is dealing with genuine and non-trivial perspectives. I argue that, despite Neyman being a normative anti-pluralist, there are some elements of perspectival pluralism present in his methods and philosophy. In conclusion, firstly, due to their ambivalence, Neyman’s conceptions align more closely with PR than with alternative, less moderate stances. Secondly, from the perspective of the statistical approach analysed, PR should be treated as a descriptive rather than a normative position, and as case (or aspect)-dependent, rather than a universal, absolute, or binding stance. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

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)

There are many philosophical questions surrounding the notion of lying. Is it ever morally acceptable to lie? Can we acquire knowledge from people who might be lying to us? More fundamental, however, is the question of what, exactly, constitutes the concept of lying. According to one traditional definition, lying requires intending to deceive (Augustine. (1952). Lying (M. Muldowney, Trans.). In R. Deferrari (Ed.), Treatises on various subjects (pp. 53?120). New York, NY: Catholic University of America). More recently, Thomas Carson (2006. (...) The definition of lying. Nous, 40, 284?306) has suggested that lying requires warranting the truth of what you do not believe. This paper examines these two prominent definitions and some cases that seem to pose problems for them. Importantly, theorists working on this topic fundamentally disagree about whether these problem cases are genuine instances of lying and, thus, serve as counterexamples to the definitions on offer. To settle these disputes, we elicited judgments about the proposed counterexamples from ordinary language users unfettered by theoretical bias. The data suggest that everyday speakers of English count bald-faced lies and proviso lies as lies. Thus, we claim that a new definition is needed to capture common usage. Finally, we offer some suggestions for further research on this topic and about the moral implications of our investigation into the concept of lying. (shrink)

With special attention being paid to recent developments in Artificial Intelligence and the Law, specifically related to evidentiary reasoning, this book ...

The Philosophy of Quantitative Methods undertakes a philosophical examination of a number of important quantitative research methods within the behavioral sciences in order to overcome the non-critical approaches typically provided by textbooks. These research methods are exploratory data analysis, statistical significance testing, Bayesian confirmation theory and statistics, meta-analysis, and exploratory factor analysis. Further readings are provided to extend the reader's overall understanding of these methods.

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of (...) Woodall et al [1]. We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals. We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses). (shrink)

Statistics play a critical role in biological and clinical research. However, most reports of scientific results in the published literature make it difficult for the reader to reproduce the statistical analyses performed in achieving those results because they provide inadequate documentation of the statistical tests and algorithms applied. The Ontology of Biological and Clinical Statistics (OBCS) is put forward here as a step towards solving this problem. Terms in OBCS, including ‘data collection’, ‘data transformation in statistics’, ‘data (...) visualization’, ‘statistical data analysis’, and ‘drawing a conclusion based on data’, cover the major types of statistical processes used in basic biological research and clinical outcome studies. OBCS is aligned with the Basic Formal Ontology (BFO) and extends the Ontology of Biomedical Investigations (OBI), an OBO (Open Biological and Biomedical Ontologies) Foundry ontology supported by over 20 research communities. We discuss two examples illustrating how the ontology is being applied. In the first (biological) use case, we describe how OBCS was applied to represent the high throughput microarray data analysis of immunological transcriptional profiles in human subjects vaccinated with an influenza vaccine. In the second (clinical outcomes) use case, we applied OBCS to represent the processing of electronic health care data to determine the associations between hospital staffing levels and patient mortality. Our case studies were designed to show how OBCS can be used for the consistent representation of statistical analysis pipelines under two different research paradigms. By representing statistics-related terms and their relations in a rigorous fashion, OBCS facilitates standard data analysis and integration, and supports reproducible biological and clinical research. (shrink)

The development of a biological notion of “population” over the first century of the theory of evolution has been commented upon by a number of historians and philosophers of biology. Somewhat less commonly discussed, however, is the parallel development of the statistical concept of a population over precisely the same period, in some cases driven by the same historical actors (such as Francis Galton and R. A. Fisher). We explore here these parallel developments, first from the perspective of a reconstruction (...) of the historical development of each concept, then with the aid of a digital analysis of a corpus of literature drawn from the journals Biometrika and Journal of Genetics, between 1900 and 1960. These twin analyses show both points of interesting overlap between these two historical trends as well as points of important divergence. The biological and statistical notions of “population” seem to be relatively clearly distinguishable over these six decades, in spite of the fact that a number of authors contributed clearly to both traditions. The complex interplay of continuity and discontinuity across these two notions of “population” makes them a particularly interesting case study of scientific conceptual change. (shrink)

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924–1925. Although it failed to attract the attention of Einstein’s contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein’s quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein’s confusion with his (...) initial success in extending Bose’s results and in realizing the consequences of what later came to be called Bose–Einstein statistics. We discuss Einstein’s motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein’s belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well known to Einstein from earlier work on Wien’s displacement law, Planck’s radiation theory and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory. (shrink)

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. (...) The relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed. (shrink)

Overstated generalizability is common in research. It may coexist with inflation of the magnitude and statistical support for effects and dismissal of internal validity problems. Generalizability may be secured before attempting replication of proposed discoveries or replication may precede efforts to generalize. These opposite approaches may decrease or increase, respectively, the use of inferential statistics with advantages and disadvantages.

In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi–Dirac statistics follows as a consequence of this coupling (...) while the Bose–Einstein follows by breaking it. In Sec. 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch–Gordan coefficients and the experimental evidence respectively, is presented. (shrink)

Since 1989, widely circulating statistics on gay teen suicide in the United States have acted as catalysts for institutional reforms, scientific research, and the creation of an identity category “gay youth.” While one figure has been replicated scientifically, these numbers originated not from a scientific research study but as risk estimates developed by a social worker and published in a government document. Many people within the public took up these original numbers, attributing their author the status of scientific researcher. (...) In effect, the numbers became “black boxed,” often traveling without citation. Drawing on Ian Hacking’s “dynamic nominalist” perspective, this article utilizes interviews with the author of these statistics and other key claimants, along with textual analysis, to trace the origins, uptake, and effects of these figures. While making vital policy contributions, the numbers have led to some ironic consequences including the fostering of gay youth identification with suicide as a potential correlate of their identity and the potential antigay redeployment of decontextualized numbers. They have also led to a reaction in the form of “resilience” narratives. (shrink)

When the state of a physical system is not fully determined by available data, it should be possible nevertheless to make a systematic guess concerning the unknown state by applying the principles of information theory. The resulting theoretical blend of informational and mechanical constructs should then constitute a modern structure for statistical physics. Such a program has been attempted by a number of authors, most notably Jaynes, with seeming success. However, we demonstrated in a recent publication that the standard list (...) of so-called “mutually exclusive and exhaustive” quantum states that is commonly employed by these authors is in fact not exhaustive. It follows that the information-theoretic foundations of quantum statistics must be reformulated. The present paper discusses the fundamental problems involved and establishes a format for the correct application of information theory to quantum mechanical situations. (shrink)

Are the categories used to study the social world and acting on it real or conventional ? An empirical answer to that question is given by an analysis of the debates about the quality of statistics produced by the European National Institues of statistics in the 1990s. Six criteria of quality were then specified: relevance, accuracy, timeliness, accessibility, comparability and coherence. How do statisticians and users of statistics deal with the tension produced by their objects being both (...) real (they exist before their measurement) and conventionally constructed (they are in a way, created by these conventions)? In particular, the technical and sociological distinction between the criteria of relevance and accuracy implies a realistic interpretation, desired by users, but that is nonetheless problematic. (shrink)

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector potential (...) that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)

Towards the end of her famous 1971 paper “Causality and Determination”, Elizabeth Anscombe discusses the controversial idea that “ ‘physical haphazard’ could be the only physical correlate of human freedom of action”. In order to illustrate how the high-level freedom of human action can go together with micro-indeterminism without creating a problem for micro-statistics, she provides the analogy of a glass box filled with minute coloured particles whose micro-dynamics is subject to statistical laws, while its outside reliably displays a (...) recognisable variation of a certain image created by an external cause. Anscombe’s example is somewhat enigmatic, and she provides no details to support its viability. In this paper we discuss the context of Anscombe’s analogy, and we provide basics of the theory and practice of building an Anscombe box. (shrink)

Objects in the world usually have names at different hierarchical levels (e.g., beagle, dog, animal). This research investigates adults' ability to use cross‐situational statistics to simultaneously learn object labels at individual and category levels. The results revealed that adults were able to use co‐occurrence information to learn hierarchical labels in contexts where the labels for individual objects and labels for categories were presented in completely separated blocks, in interleaved blocks, or mixed in the same trial. Temporal presentation schedules significantly (...) affected the learning of individual object labels, but not the learning of category labels. Learners' subsequent generalization of category labels indicated sensitivity to the structure of statistical input. (shrink)

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories, are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain (...) these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by first providing an analysis of the necessary and sufficient conditions for these properties, and second by advocating a particular account of explanation appropriate for this context. (shrink)