Suppose one hundred prisoners are in a yard under the supervision of a guard, and at some point, ninety-nine of them collectively kill the guard. If, after the fact, a prisoner is picked at random and tried, the probability of his guilt is 99%. But despite the high probability, the statistical chances, by themselves, seem insufficient to justify a conviction. The question is why. Two arguments are offered. The first, decision-theoretic argument shows that a conviction solely based on the (...) class='Hi'>statistics in the prisoner scenario is unacceptable so long as the goal of expected utility maximization is combined with fairness constraints. The second, risk-based argument shows that a conviction solely based on the statistics in the prisoner scenario lets the risk of mistaken conviction surge potentially too high. The same, by contrast, cannot be said of convictions solely based on DNA evidence or eyewitness testimony. A noteworthy feature of the two arguments in the paper is that they are not confined to criminal trials and can in fact be extended to civil trials. (shrink)

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

ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies (...) can provide additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education. (shrink)

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; (...) and pooling rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists. (shrink)

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional (...) Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment. (shrink)

The explanatory filter is a proposed method to detect design in nature with the aim of refuting Darwinian evolution. The explanatory filter borrows its logical structure from the theory of statistical hypothesis testing but we argue that, when viewed within this context, the filter runs into serious trouble in any interesting biological application. Although the explanatory filter has been extensively criticized from many angles, we present the first rigorous criticism based on the theory of mathematical statistics.

CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state of a physical system characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT (...) and Spin-Statistics theorems suggest about the ontology of RQFTs, and the extent to which this is compatible with the Received View. I will argue that such proofs suggest the Received View’s approach to ontology is flawed. (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.

Índice de autores/as y estadísticas del número | List of authors and issue statistics.

After sketching the conflict between objectivists and subjectivists on the foundations of statistics, this paper discusses an issue facing statisticians of both schools, namely, model validation. Statistical models originate in the study of games of chance, and have been successfully applied in the physical and life sciences. However, there are basic problems in applying the models to social phenomena; some of the difficulties will be pointed out. Hooke's law will be contrasted with regression models for salary discrimination, the latter (...) being a fairly typical application in the social sciences. (shrink)

The social and cognitive science replication crisis is partly due to the limitations of commonly used statistical tools. Inferential statistics require that unsystematic measurement variation is independent of system history, and weak relative to systematic or causal sources of variation. However, contemporary systems research underscores the dynamic, adaptive nature of social, cognitive, and behavioral systems. Variation in human activity includes the influences of intrinsic dynamics intertwined with changing contextual circumstances. Conventional inferential techniques presume milder forms of variability, such as (...) unsystematic measurement error, as in a Gaussian distribution. Inferential statistics indicate an elementary Newtonian cause-effect metaphor for change that is inconsistent with known principles of change in complex systems. Pattern formation in self-organizing systems and quantum probability are used to illustrate theoretical metaphors that instantiate alternative notions of change in complex systems. Inferential statistics and related techniques are crucial scientific resources. However, in the social and behavioral sciences, they must be practiced in conjunction with an appropriate general systems framework that accommodates intrinsic fluctuations and contextual adaptation. (shrink)

In The Empire of Chance, historians of science Gigerenzer et al. argue that statistical thinking has been “second to no other area of scientific endeavor” in its influence on “modern life and thought”. This article describes how quantitative descriptions of risk associated with industrialization and technological change became part of the mentality of ordinary Americans. It explains why Americans began counting accidents, tells what kinds of accidents they counted and how they counted them, and shows how statistical representations of risk (...) were used to justify prescriptions for public policy and individual behavior. On this frontier of the empire of chance, safety experts and self-styled “practical statisticians” were the principal colonizers. Distant from the centers of academic statistical science, they compromised rigorous scientific standards of methodology and accurate prediction in order to make convincing arguments outside their circles of expertise. To convey their point of view to audiences who were not literate in the field of statistics, they created a public language that conveyed statistical ideas through metaphors, graphic representations, and other rhetorical devices. They also engaged non-experts in collecting and analyzing data and, by the 1920s, even used quantitative self-measurement as a device to convince members of the public to alter their own risk-taking behaviors. (shrink)

There have been attempts to derive anti-haeccetistic conclusions from the fact that quantum mechanics (QM) appeals to non-standard statistics. Since in fact QM acknowledges two kinds of such statistics, Bose-Einstein and Fermi-Dirac, I argue that we could in the same vein derive the sharper anti-haeccetistic conclusion that bosons are bundles of tropes and fermions are bundles of universals. Moreover, since standard statistics is still appropriate at the macrolevel, we could also venture to say that no anti-haecceitistic conclusion (...) is warranted for ordinary objects, which could then tentatively be identified with substrates. In contrast to this, however, there has been so far no acknowledgement of the possibility of inclusivism, according to which ontological accounts of particulars as widely different as those can possibly coexist in one world picture. The success of the different statistics in physics at least calls for a revision in this respect. (shrink)

Much of the science and religion debate has focussed on statistics. The chapters in this section go beyond bare statistics by examining more nuanced studies of science, religion and education with the aim of developing a deeper understanding of the issues at play when attempting to deal with the issues of science and religion in the classroom.

The traditional standard theory of quantum mechanics is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper :858–873, 2015) we presented a proof of the spin–statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics”. In the present paper, by the same theory the proof of the spin–statistics theorem is extended to (...) the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin–statistics connection observed in Nature :858–873, 2015). The present proof of the spin–statistics theorem is simpler than the one presented in Santamato and De Martini :858–873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary. (shrink)

We start with the ambition -- dating back to the early days of the semantic web -- of assembling a significant portion human knowledge into a contradiction-free form using semantic web technology. We argue that this would not be desirable, because there are concepts, known as essentially contested concepts, whose definitions are contentious due to deep-seated ethical disagreements. Further, we argue that the ninetenth century hermeneutical tradition has a great deal to say, both about the ambition, and about why it (...) fails. We conclude with some remarks about statistics. (shrink)

We investigate the hypothesis that within a combination of a ‘number concept’ plus a ‘substantive concept’, such as ‘eleven animals’, the identity and indistinguishability present on the level of the concepts, i.e., all eleven animals are identical and indistinguishable, gives rise to a statistical structure of the Bose–Einstein type similar to how Bose–Einstein statistics is present for identical and indistinguishable quantum particles. We proceed by identifying evidence for this hypothesis by extracting the statistical data from the World-Wide-Web utilizing the (...) Google Search tool. By using the Kullback–Leibler divergence method, we then compare the obtained distribution with the Maxwell–Boltzmann as well as with the Bose–Einstein distributions and show that the Bose–Einstein’s provides a better fit as compared to the Maxwell–Boltzmann’s. (shrink)

In this essay David Labaree explores the historical and sociological elements that have made educational researchers dependent on statistics. He shows that educational research as a domain, with its focus on a radically soft and thoroughly applied form of knowledge and with its low academic standing, fits the pattern in which weak professions have been most likely to adopt quantification. One problem with educational researchers' seduction by the quantitative turn is that it deflects attention away from many of the (...) most important issues in the field, which are not easily reduced to standardized quanta. Another is that by adopting this rationalized, quantified, abstracted, statist, and reductionist vision of education, educational policymakers risk imposing reforms that will destroy the local practical knowledge that makes the ecology of the classroom function effectively. Quantification, Labaree suggests, may be useful for the professional interests of educational researchers, but it can be devastating for school and society. (shrink)

We have evolved to become who we are, at least in part, due to our general drive to create new things and ideas. When seeking to improve our creations, ideas, or situations, we systematically overlook opportunities to perform subtractive changes. For example, when tasked with giving feedback on an academic paper, reviewers will tend to suggest additional explanations and analyses rather than delete existing ones. Here, we show that this addition bias is systematically reflected in English language statistics along (...) several distinct dimensions. First, we show that words associated with an increase in quantity or number (e.g., add, addition, more, most) are more frequent than words associated with a decrease in quantity or number (e.g., subtract, subtraction, less, least). Second, we show that in binomial expressions, addition-related words are mentioned first, that is, add and subtract rather than subtract and add. Third, we show that the distributional semantics of verbs of change, such as to improve and to transform, overlap more with the distributional semantics of add/increase than subtract/decrease, which suggests that change verbs are implicitly biased toward addition. Fourth, addition-related words have more positive connotations than subtraction-related words. Fifth, we demonstrate that state-of-the-art large language models, such as the Generative Pre-trained Transformer (GPT-3), are also biased toward addition. We discuss the implications of our results for research on cognitive biases and decision-making. (shrink)

Jun Otsuka’s excellent book, Thinking about Statistics - the Philosophical Foundations (Otsuka 2023) is mostly organized around the idea that different statistical approaches can be illuminated by linking them to different ideas in general epistemology. Otsuka connects Bayesianism to internalism and foundationalism, frequentism to reliabilism, and the Akaike Information Criterion in model selection theory to instrumentalism. This useful mapping doesn’t cover all the interesting ideas he presents. His discussions of causal inference and machine learning are philosophically insightful, as is (...) his idea that statisticians embrace an assumption that is similar to Hume’s Principle of the Uniformity of Nature. I discuss these topics in what follows, sometimes disagreeing with details while at other times adding ideas that complement those presented in the book. (shrink)

ABSTRACT. Probability and statistics play an important role in contemporary -philosophy of causality. They are viewed as glasses through which we can see or detect causal relations. However, they may sometimes act as blinding glasses, as I will argue in this paper. In the 19th century, Francis Galton tried to statistically analyze hereditary phenomena. Although he was a far better statistician than Gregor Mendel, his biological theory turned out to be less fruitful. This was no sheer accident. His knowledge (...) of statistics generated two explananda (unknown to Mendel) which in turn generated constraints for any theory of heredity. These constraints misguided Galtons search for the causal mechanism of inheritance. This is not just. an interesting case for philosophers and historians of ·science. Notwithstanding the progress made by statitics, Galtons problem is still relevant today. In the final section, I briefly explore the implications for statistical techniques such as structural equation modelling. (shrink)

Quantification has been constitutive of psychology since its inception and is core to its scientific status. The adoption of qualitative methods eschewing inferential statistics is therefore unlikely to obtain. Rather than discarding useful tools because of improper use, we recommend highlighting how inferential statistics can be more thoughtfully applied.

This festschrift for Teddy Seidenfeld is a collection of newly commissioned essays on imprecise probability by leading experts in the field. Each contribution touches on Teddy’s seminal contributions to the field of imprecise probability, and gives an up-to-date state of the field that cannot be found elsewhere. The title, “a reflection on the foundations of probability and statistics”, calls back to Teddy’s seminal book, “Rethinking the Foundations of Probability and Statistics”, bookends to a career that has made fundamental (...) contributions to the foundations of probability and statistics, and shaped the field of imprecise probability. It is aimed at scholars engaged in probability and statistics. (shrink)

This essay examines Tocqueville's interest in statistics, and how it informed his analysis of democracy. It explores his early engagement with the discipline and shows how this proved critical to his and Beaumont's 1833 study of the American penitentiary system. It shows that Tocqueville's interest in statistics was long lasting. And it pays particular attention to his links with the British Association for the Advancement of Science, examining his attendance at the statistical section meetings of the BAAS conference (...) in Dublin in 1835. It shows how material presented at this conference appeared in a number of Tocqueville's works. The essay argues against the thesis that Tocqueville resisted the primacy of the social. Rather, it shows that his interest in statistics underscored the importance he attached to the social in his analysis of modern democracy. (shrink)

We contrast two theoretical positions on the relation between phenomenal and access consciousness. First, we discuss previous data supporting a mild Overflow position, according to which transient visual awareness can overflow report. These data are open to two interpretations: (i) observers transiently experience specific visual elements outside attentional focus without encoding them into working memory; (ii) no specific visual elements but only statistical summaries are experienced in such conditions. We present new data showing that under data-limited conditions observers cannot discriminate (...) a simple relation (same versus different) without discriminating the elements themselves and, based on additional computational considerations, we argue that this supports the first interpretation: summary statistics (same/different) are grounded on the transient experience of elements. Second, we examine recent data from a variant of ‘inattention blindness’ and argue that contrary to widespread assumptions, it provides further support for Overflow by highlighting another factor, ‘task relevance’, which affects the ability to conceptualize and report (but not experience) visual element. (shrink)

This article provides a concise summary of Thinking About Statistics: The Philosophical Foundations (Routledge, 2023), with a focus on the book’s exploration of ontological and epistemological topics.

What justifies the use of Bayesian statistics in science? The traditional answer is that Bayesian statistics is simply an instance of orthodox expected utility theory. Thus, Bayesian statistical methods, like principles of utility theory, are justified by norms of individual rationality. In particular, most Bayesians argue that a scientist's credences must satisfy the probability axioms if she adheres to norms of practical and epistemic rationality. We argue that, to justify Bayesian statistics as a tool for science, it (...) is necessary that a scientist's public credences obey the probability axioms. We claim that norms of collective science help justify this restricted view, termed public probabilism. (shrink)

A vast literature has developed probing the law's aversion to statistical/probability evidence in general and its rejection of naked statistical evidence in particular. This literature rests on false premises. At least so far as US law is concerned, there is no general aversion to statistical forms of proof and even naked statistics are admissible and sufficient for a verdict when the evidentiary proffer meets the normal standards of admissibility, the most important of which is reliability. The belief to the (...) contrary rests upon a series of mistakes: most importantly, mismodeling of the structure of legal systems and the nature of common law decision making. Contributing to these mistakes is the common methodology in this literature of relying on weird hypotheticals that mismodel the underlying legal relations and contain impossible epistemological demands. Collectively, these phenomena have distracted attention from issues that actually affect real legal systems. (shrink)

The efficient coding hypothesis posits that sensory systems are tuned to the regularities of their natural input. The statistics of natural image databases have been the topic of many studies, which have revealed biases in the distribution of orientations that are related to neural representations as well as behavior in psychophysical tasks. However, commonly used natural image databases contain images taken with a camera with a planar image sensor and limited field of view. Thus, these images do not incorporate (...) the physical properties of the visual system and its active use reflecting body and eye movements. Here, we investigate quantitatively, whether the active use of the visual system influences image statistics across the visual field by simulating visual behaviors in an avatar in a naturalistic virtual environment. Images with a field of view of 120° were generated during exploration of a virtual forest environment both for a human and cat avatar. The physical properties of the visual system were taken into account by projecting the images onto idealized retinas according to models of the eyes' geometrical optics. Crucially, different active gaze behaviors were simulated to obtain image ensembles that allow investigating the consequences of active visual behaviors on the statistics of the input to the visual system. In the central visual field, the statistics of the virtual images matched photographic images regarding their power spectra and a bias in edge orientations toward cardinal directions. At larger eccentricities, the cardinal bias was superimposed with a gradually increasing radial bias. The strength of this effect depends on the active visual behavior and the physical properties of the eye. There were also significant differences between the upper and lower visual field, which became stronger depending on how the environment was actively sampled. Taken together, the results show that quantitatively relating natural image statistics to neural representations and psychophysical behavior requires not only to take the structure of the environment into account, but also the physical properties of the visual system, and its active use in behavior. (shrink)

Increasingly, clinical research is evaluated on the quality of its statistical analysis. Traditionally, statistical analyses in clinical research have been carried out from a ‘frequentist’ perspective. The presence of an alternative paradigm – the Bayesian paradigm – has been relatively unknown in clinical research until recently. There is currently a growing interest in the use of Bayesian statistics in health care research. This is due both to a growing realization of the limitations of frequentist methods and to the ability (...) of Bayesian methods explicitly to incorporate prior expert knowledge and belief into the analyses. This is in contrast to frequentist methods, where prior experience and beliefs tend to be incorporated into the analyses in an ad hoc fashion. This paper outlines the frequentist and Bayesian paradigms. Acute myocardial infarction mortality data are then analysed from both a Bayesian and a frequentist perspective. In some analyses, the two methods are seen to produce comparable results; in others, they produce different results. It is noted that in this example, there are clinically relevant questions that are more easily addressed from a Bayesian perspective. Finally, areas in clinical research where Bayesian ideas are increasingly common are highlighted. (shrink)

In his book The Austrian Mind (1972) W. M. Johnston observes that between 1861 and 1938 a striking number of Austrian intellectuals committed uicide. He also remarks that prior to 1920 suicide was relatively rare among Hungarian intellectuals, and as a possible explanation he refers to their more intensive political activity. The present paper investigates relations between a society's intellectual life and its general suicidal tendencies. In so doing it takes up a central theme of T. G. Masaryk's Suicide as (...) a Social Mass Phenomenon of Modern Civilization, published in Vienna in 1881. (shrink)

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

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)

The ArgumentMost lay users of statistics think in terms of means (averages), variances or the square of the standard deviation, and Gaussians or bell-shaped curves. Such conventions are entrenched by statistical practice, by deep mathematical theorems from probability, and by theorizing in the various natural and social sciences. I am not claiming that the particular conventions (here, the statistics) we adopt are arbitrary. Entrenchment can be rational without its being as well categorical (excluding all other alternatives), even if (...) that entrenchment claims also to provide for categoricity. 1 provide a detailed description of how a science is “normal” and conventionalized. A characteristic feature of this entrenchment of conventions by practice, theorems, and theorizing, is its highly technical form, the canonizing work enabled by apparently formal and esoteric mathematical means. (shrink)

The last two decades have seen a welcome proliferation of the collection and dissemination of data on social progress, as well as considered public debates rethinking existing standards of measuring the progress of societies. These efforts are to be welcomed. However, they are only a nascent step on a longer road to the improved measurement of social progress. In this paper, I focus on the central role that gender should take in future efforts to measure progress in securing human rights, (...) with a particular focus on anti-poverty rights. I proceed in four parts. First, I argue that measurement of human rights achievements and human rights deficits is entailed by the recognition of human rights, and that adequate measurement of human rights must be genuinely gender-sensitive. Second, I argue that existing systems of information collection currently fail rights holders, especially women, by failing to adequately gather information on the degree to which their rights are secure. If my first two claims are correct, this failure represents a serious injustice, and in particular an injustice for women. Third, I make recommendations regarding changes to existing information collection that would generate gender-sensitive measures of anti-poverty rights. Fourth, I conclude by responding to various objections that have been raised regarding the rise of indicators to track human rights. (shrink)