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

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)

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)

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)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought. New preface and new footnotes to 1954 edition, with a supplementary 180-item annotated bibliography by author. Calculus, probability, statistics, and Boolean algebra are recommended.

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 article explores the intersection of philosophy and statistics by examining the philosophical assumptions underlying modern mathematical statistics from ontological and epistemological perspectives. Statistics holds interest for philosophers engaged with the problem of induction, as its mathematical apparatus serves as models for philosophical ideas. For instance, the much-discussed concepts of the uniformity of nature and natural kinds correspond to probability models and statistical models, which are fundamental to various statistical methods. Similarly, Dennett’s concept of a real pattern (...) echoes the spirit of various information criteria (such as AIC) used to determine the optimal level of complexity for maximizing a model’s predictive ability. Furthermore, the recent developments in machine learning models, such as deep learning, imply that these machines possess their own 'ontology,' which is potentially more complex and efficient at understanding the world than ours. This leads to a Quinean problem of radical translation between human and machine ontologies. We suggest that this issue is key to the successful application of AI technologies in our society. The other focus of this article is epistemology, where Bayesian and classical statistics are compared to internalist and externalist epistemologies, respectively. This comparison elucidates how and in what sense the statistical methods adopted in each camp are considered to justify scientific hypotheses and also sheds light on their epistemic problems. We conclude with a plea for more research and interdisciplinary dialogues between statistics and the philosophy of various traditions. (shrink)

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)

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)

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.

Los estudios de ciencia, tecnología y sociedad revelan las interrelaciones entre la ciencia y la tecnología como procesos sociales. Este artículo persigue como objetivo: valorar la significación social de un entorno virtual en la enseñanza aprendizaje de la Estadística descriptiva en la carrera de Medicina. El diagnóstico preliminar mediante de la observación, la encuesta y el análisis documental, mostró que existen insuficiencias en el uso de las tecnologías de la información y las comunicaciones en el proceso de enseñanza aprendizaje de (...) la Estadística. Se diseñó un entorno virtual constituido por cinco módulos que incluyen contenidos de Estadística descriptiva, ejercicios, bibliografía y ayuda. Con la validación a partir del criterio de especialistas y la sistematización con la introducción en la práctica, se evaluó el mismo como muy adecuado, fue considerado útil, necesario y aplicable al contexto objeto de estudio, lo que contribuye a la formación científica de los estudiantes desde una posición materialista. Science, technology and society studies reveal the interrelations between science and technology as social processes. This article pursues the following objectives: to assess the social significance of a virtual environment in the teaching and learning of descriptive Statistics in Medicine degree course. The preliminary diagnosis through the observation, opinion poll and documentary analysis, showed that there are insufficiencies in the use of Information and Communication technologies in teaching and learning Statistics. It was designed a virtual environment with five modules that include contents of descriptive Statistics, exercises, bibliography and help. With the validation of specialists and the systematization after putting it in practice, the virtual environment was assessed as adequate, useful, necessary and applicable to the context being studied, which contributes to the scientific training of students from a materialistic position. (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)

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)

I argue that the Bayesian Way of reconstructing Duhem's problem fails to advance a solution to the problem of which of a group of hypotheses ought to be rejected or "blamed" when experiment disagrees with prediction. But scientists do regularly tackle and often enough solve Duhemian problems. When they do, they employ a logic and methodology which may be called error statistics. I discuss the key properties of this approach which enable it to split off the task of testing (...) auxiliary hypotheses from that of appraising a primary hypothesis. By discriminating patterns of error, this approach can at least block, if not also severely test, attempted explanations of an anomaly. I illustrate how this approach directs progress with Duhemian problems and explains how scientists actually grapple with them. (shrink)

Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit also (...) concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth. (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)

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

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)

Morphophonological alternations, such as the voicing alternation that arises in a morphological paradigm due to final-devoicing in Dutch, are notoriously difficult for children to acquire. This has previously been attributed to their unpredictability. In fact, the presence or absence of a voicing alternation is partly predictable if the phonological context of the word is taken into account, and adults have been shown to use this information ( Ernestus and Baayen, 2003 ). This study investigates whether voicing alternations are predictable from (...) the child’s input, and whether children can make use of this information. A corpus study of child-directed speech establishes that the likelihood of a stem-final obstruent alternating is somewhat predictable on the basis of the phonological properties of the stem. In Experiment 1 Dutch 3-year-olds’ production accuracy in a plural-elicitation task is shown to be sensitive to the distributional statistics. However, distributional properties do not play a role in children’s sensitivity to mispronunciations of voicing in a Preferential Looking Task in Experiment 2. (shrink)

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of probability. This article aims to separate the concept of probability which is scientifically based from other concepts that do not have this characteristic. The scientifically based concept of probability is Kolmogorov’s concept of probability models together with the conditions of their applicability. Bayesian (...) class='Hi'>statistics is based on the subjective concept of probability, and as such can only have a heuristic value in searching for the truth, but it cannot and must not replace the truth. The way out of the crisis should take Kolmogorov and Bayesian analysis as elements, each of which has a well-defined and limited use. Only together with qualitative analysis and other types of quantitative analysis, and combined with experiments, they can contribute to reaching correct conclusions. (shrink)

Computational techniques comparing co-occurrences of city names in texts allow the relative longitudes and latitudes of cities to be estimated algorithmically. However, these techniques have not been applied to estimate the provenance of artifacts with unknown origins. Here, we estimate the geographic origin of artifacts from the Indus Valley Civilization, applying methods commonly used in cognitive science to the Indus script. We show that these methods can accurately predict the relative locations of archeological sites on the basis of artifacts of (...) known provenance, and we further apply these techniques to determine the most probable excavation sites of four sealings of unknown provenance. These findings suggest that inscription statistics reflect historical interactions among locations in the Indus Valley region, and they illustrate how computational methods can help localize inscribed archeological artifacts of unknown origin. The success of this method offers opportunities for the cognitive sciences in general and for computational anthropology specifically. (shrink)

Historiography of the development of probability and statistics in the Russian Empire focusses on the contributions of the central figure Pafnutiy Lvovich Chebyshev and his successors. The purpose of this article is to concentrate on an earlier period which culminates with Chebyshev, and specifically on two less-than-well-explored aspects.

I investigate the extent to which perspectival realism agrees with frequentist statistical methodology and philosophy, with an emphasis on J. Neyman’s views. Based on the example of the stopping rule problem, I show how PR can naturally be associated with frequentist statistics in general. I also show that there are some aspects of Neyman’s thought that seem to confirm PR and others that disconfirm it. I argue that epistemic PR is consistent with Neyman’s frequentism to a satisfactory degree and (...) that on the grounds of Neyman’s frequentist methodology one is dealing with genuine and non-trivial perspectives. I also argue that universality and normativity of PR are weakened when analysed from the point of view of Neyman’s statistical methodology. (shrink)

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham’s Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.

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)

Much of the criticism of Stevens's criterion for permissible statistics as applied to measurement data results from a lack of clarity in Stevens's position. In this paper set-theoretical notions have been used to clarify that position. We define a sig-function as a function defined on numerical assignments. If A and R are empirical and numerical relational systems, respectively, then a sig-function F is constant on A with respect to R if, and only if, the value of F is the (...) same for all numerical assignments for A with respect to R. Using these notions we prove rigorously certain generalizations of Stevens's results. (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.

Small things loom large as a distinct category in social and cultural analysis. However, the social construction and effects of this idiom of scale commonly remain vague and underexplored. Bringing the literature on quantification in conversation with the literature on scale-making, this article offers a theoretically-informed analysis of how smallness consolidates as a publicly salient social attribute, and how it feeds collective narratives. The empirical focus is on American Jewry – an ethnoreligious minority group whose leaders and experts have invested (...) in its quantification, including its representation as a small population. Drawing on a variety of texts and images, as well as on interviews and fieldwork, I show that American Jewish research bodies and public figures engage in a myriad of comparative arithmetic exercises and spectacles of scale to assert the smallness of the population. Deploying smallness as a generative narrative tool allows them to engage with the ambivalences implicated in the American-Jewish post-Holocaust, minority, and diasporic experience. In particular, exercises around notions of numerical negligibility, disproportional success, and numerical inferiority elicit protean narratives around endangerment, power, and a questioned diasporic future. The broader theoretical intervention of this article is to offer scalemaking as a valuable prism for understanding the narrative potency and poignancy of arithmetically-based constructs such as smallness. Instead of emphasizing the assumed epistemological strengths of numbers, this article considers the narrative work that statistics do when they lend themselves to multimodal scaling. It argues that through scaling, statistics are infused with perspective, relevance and meaning, descriptively and prescriptively. (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.

Discusses how statistics have changed the field of science in the twentieth century, focusing on the theories and ideas of famous scientists and thinkers.

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)

While cultural sociology has recently made a comeback in research on social inequality both in the context of poverty studies and studies of immigrant integration, it has rarely investigated how particular constructions of the problem of socioeconomic mobility are themselves culturally situated. The article addresses this neglect by investigating the problematization of disadvantaged lives within the relational framework of Bourdieu’s cultural theory of the state. Here, the state exercises symbolic violence by transforming one arbitrary cultural standpoint in social space into (...) a universal standard, or a taken-for-granted “doxa,” against which other cultural positions can only come off as deficient. The article extends this perspective by addressing the role of official statistics in this process. Taking Germany’s official monitoring of the socioeconomic integration of immigrants as its case and drawing from document analysis, interviews, ethnographic observation, and data from the German General Social Survey, the article shows how such statistical instruments of the welfare state in fact tacitly universalize a model of the good life particular to civil servants, the very constructors of the monitors, as a benchmark for immigrant integration. (shrink)