This paper puts forward the hypothesis that the distinctive features of quantum statistics are exclusively determined by the nature of the properties it describes. In particular, all statistically relevant properties of identical quantum particles in many-particle systems are conjectured to be irreducible, ‘inherent’ properties only belonging to the whole system. This allows one to explain quantum statistics without endorsing the ‘Received View’ that particles are non-individuals, or postulating that quantum systems obey peculiar probability distributions, or assuming that there (...) are primitive restrictions on the range of states accessible to such systems. With this, the need for an unambiguously metaphysical explanation of certain physical facts is acknowledged and satisfied. (shrink)

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us caapble of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach.

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.

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is (...) outlined and endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a (...) straightforward decision problem based around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)

Many biologists, especially in ecology and evolution, analyze their data by estimating fits to a set of candidate models and selecting the best model according to the Akaike Information Criterion (AIC) or the Bayesian Information Criteria (BIC). When the candidate models represent alternative hypotheses, biologists may want to limit the chance of a false positive to a specified level. Existing model selection methodology, however, allows for only indirect control over error rates by setting a threshold for the difference in AIC (...) scores. We present a novel theoretical framework for parametric Neyman-Pearson (NP) model selection using information criteria that does not require a pre-data null and applies to three or more non-nested models simultaneously. We apply the theoretical framework to the Error Control for Information Criteria (ECIC) procedure introduced by Cullan et al. (J Appl Stat 47: 2565–2581, 2019), and we show it shares many of the desirable properties of AIC-type methods, including false positive and negative rates that converge to zero asymptotically. We discuss implications for the compatibility of evidentialist and severity-based approach to evidence in philosophy of science. (shrink)

During the twentieth century statistical methods have transformed research in the experimental and social sciences. Qualitative evidence has largely been replaced by quantitative results and the tools of statistical inference have helped foster a new ideal of objectivity in scientific knowledge. The paper will investigate this transformation by considering the genesis of analysis of variance and experimental design, statistical methods nowadays taught in every elementary course of statistics for the experimental and social sciences. These methods were developed by the (...) mathematician and geneticist R. A. Fisher during the 1920s, while he was working at Rothamsted Experimental Station, where agricultural research was in turn reshaped by Fisher’s methods. Analysis of variance and experimental design required new practices and instruments in field and laboratory research, and imposed a redistribution of expertise among statisticians, experimental scientists and the farm staff. On the other hand the use of statistical methods in agricultural science called for a systematization of information management and made computing an activity integral to the experimental research done at Rothamsted, permanently integrating the statisticians’ tools and expertise into the station research programme. Fisher’s statistical methods did not remain confined within agricultural research and by the end of the 1950s they had come to stay in psychology, sociology, education, chemistry, medicine, engineering, economics, quality control, just to mention a few of the disciplines which adopted them. (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)

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)

1. Deductive and Inductive Inference. Within the traditional treatments of scientific method, e.g., in and, it was customary to divide scientific inference into two parts: deductive and inductive. Deductive inference was taken to mean the activity of deducing theorems from postulates and definitions, whereas inductive inference represented the activity of constructing a general statement from a set of particular “facts.” Deductive inference was relegated to the mathematical sciences, and inductive inference to the empirical sciences. As a consequence, the whole of (...) science was split into two quite distinct parts: deductive science was conceived to start with precise axioms, postulates, and definitions, and its method consisted in drawing inferences from these “givens” in such a way that if the original assumptions are taken as true, then the theorems must be taken as true also. The obligation behind this “must” of the mathematical sciences was an obligation based on strict rules of deductive inference; in the earlier analyses, it was supposed that these rules were all aspects of the general theory of the syllogism, as it was described in an almost complete form in but in later work the rules have been formalized in more general terms. Inductive inference, on the other hand, was supposed to start with observed facts; these facts, or “data,” were presumably given by the senses, and described particular aspects of the external world. If the facts were given in a certain way, then the empirical scientist could “infer” a generalized description; this generalization had the characteristic that if it were granted as true, then all the facts could be deduced as consequences. The inductive process admittedly does not lead to unique generalizations, and the philosopher of science searched for other defining characteristics of good inference, such as “simplicity” and “convenience.” These empirical generalizations were taken to be “descriptions of the phenomenal world of the scientist”; a further inductive step might be taken by constructing a set of very general principles out of the more specialized generalizations within specific research problems. These “higher” inductive inferences were regarded as “theories,” which could be studied by themselves within the method of deductive inference. The scientist was then described as “checking” theory by determining whether or not the predicted consequences deduced from theory actually hold in the phenomenal world. (shrink)

Philosophy of statistics meets modal epistemology: Severity and sensitivity In this paper I take up a challenge raised by Gardiner and Zaharatos (2022) to link severity in philosophy of statistics and sensitivity in modal epistemology. Severity is based on using the error probabilities of statistical methods, not to ensure they rarely fail in a series of use, but to capture their capability to probe mistakes in the case at hand. A claim C is severely tested by passing a (...) test that it (probably) would have failed if it were false. Analogously, a judgement that p is sensitive iff were p false, the agent would not have judged that p. Severe testing is a sensitivity account in the epistemologist’s sense, but with important qualifications. Notably, I will argue that severity avoids a difficulty long thought to bedevil sensitivity accounts: their inability to rule out skeptical challenges to claims regarded as warranted by evidence. This problem has led many to appeal instead to the notion of safety: a claim is safe if it could not easily be false. I compare the severity solution to the appeal to safety. I argue that severity reaches the safety theorist’s destination by a different route: a severely warranted claim could “not easily be false”, since overturning C would require discounting the network of tests that established its warrant. Rather than setting aside skeptical challenges as irrelevant, severity shows—through auditing assumptions and error-probing—that they collapse under severe scrutiny. (shrink)

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

Statistics and probability enabled students to better understand, process, and evaluate massive amounts of quantitative data that existed and had a probabilistic sense in uncertain situations. The research article aimed to elucidate the performance and self-efficacy as predictors of students' achievement in the statistics and probability courses. The study utilized a descriptive-predictive research method and was conducted at Sto. Tomas National High School, involving a sample of 263 grade 11 senior high school students. The gathered data were analyzed (...) using descriptive measures and multiple regression analysis. The study's results revealed that the performance in General Mathematics was very satisfactory, while self-efficacy was high. Moreover, the level of achievement in Statistics and Probability was very satisfactory. It was also revealed that both General Mathematics performance and self-efficacy had a positive and significant relationship with Statistics and Probability achievement. Through regression analysis, it was discovered that General Mathematics performance was the strongest predictor that influenced achievement in Statistics and Probability. The study identified a significant predictive model for Statistics and Probability achievement. These findings could provide valuable guidance to teachers in enhancing the achievement of senior high school students in Statistics and Probability. (shrink)

Statistics at the college level is one of the most technical subjects that needs to have good mental health so that the students can perform well. This study focused on the investigation of the level of anxiety and mental health of college students in learning statistics. A total of 120 engineering students participated in the survey selected as complete enumeration. Data collection was done through a modified students' statistics anxiety questionnaire and level of mental health. Descriptive measures (...) were computed to describe the data, and regression and correlation analysis to explain its relationship. Results depicted that engineering students have moderate anxiety and they have moderate mental health in learning statistics. This suggests that these students are somewhat anxious but still have a positive learning experience. The correlation and regression analysis revealed that the level of anxiety and mental health of students are negatively but weakly associated, however not statistically significant. This implies that students' anxiety level has somehow adversely affected the mental health of students but its likelihood is negligible. The study strongly suggests that statistics teachers must manage the class well and apply teaching strategies that boost student confidence as well as improve academic achievement. Moreover, teachers should be trained to recognize signs of anxiety and mental health issues and equipped with strategies to support student learning and well-being needs. (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)

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)

Humans are fast and accurate in categorizing complex natural images. It is, however, unclear what features of visual information are exploited by brain to perceive the images with such speed and accuracy. It has been shown that low-level contrast statistics of natural scenes can explain the variance of amplitude of event-related potentials (ERP) in response to rapidly presented images. In this study, we investigated the effect of these statistics on frequency content of ERPs. We recorded ERPs from human (...) subjects, while they viewed natural images each presented for 70 ms. Our results showed that Weibull contrast statistics, as a biologically plausible model, explained the variance of ERPs the best, compared to other image statistics that we assessed. Our time-frequency analysis revealed a significant correlation between these statistics and ERPs’ power within theta frequency band (~3-7 Hz). This is interesting, as theta band is believed to be involved in context updating and semantic encoding. This correlation became significant at ~110 ms after stimulus onset, and peaked at 138 ms. Our results show that not only the amplitude but also the frequency of neural responses can be modulated with low-level contrast statistics of natural images and highlights their potential role in scene perception. (shrink)

It was shown in the early seventies that, in Local Quantum Theory (that is the most general formulation of Quantum Field Theory, if we leave out only the unknown scenario of Quantum Gravity) the notion of Statistics can be grounded solely on the local observable quantities (without assuming neither the commutation relations nor even the existence of unobservable charged field operators); one finds that only the well known (para)statistics of Bose/Fermi type are allowed by the key principle of (...) local commutativity of observables. In this frame it was possible to formulate and prove the Spin and Statistics Theorem purely on the basis of First Principles.In a subsequent stage it has been possible to prove the existence of a unique, canonical algebra of local field operators obeying ordinary Bose/Fermi commutation relations at spacelike separations.In this general guise the Spin–Statistics Theorem applies to Theories (on the four dimensional Minkowski space) where only massive particles with finite mass degeneracy can occur. Here we describe the underlying simple basic ideas, and briefly mention the subsequent generalisations; eventually we comment on the possible validity of the Spin–Statistics Theorem in presence of massless particles, or of violations of locality as expected in Quantum Gravity. (shrink)

Quantum theories constructed on the noncommutative spacetime called the Groenewold–Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.

A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers (...) a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia. (shrink)

An argument to the effect that non-relativistic quantum particles can be understood as individual objects in spite of the empirical evidence seemingly lending support to the opposite conclusion. Ways to understand quantum indistinguishability and quantum statistics in terms of individuals are indicated.

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)

Statistics education at all levels includes data collected on human subjects. Thus, statistics educators have a responsibility to educate their students about the ethical aspects related to the collection of those data. The changing statistics education landscape has seen instruction moving from being formula-based to being focused on statistical reasoning. The widely implemented Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report has paved the way for instructors to present introductory statistics to students in (...) a way that is both approachable and engaging. However, with technological advancement and the increase in availability of real-world datasets, it is necessary that instruction also integrate the ethical aspects around data sources, such as privacy, how the data were obtained and whether participants consent to the use of their data. In this article, we propose incorporating ethics into established curricula and integrating ethics into undergraduate-level introductory statistics courses based on recommendations in the GAISE Report. We provide a few examples of how to prompt students to constructively think about their ethical responsibilities when working with data. (shrink)

This paper examines the subversive role of statistics paleontology at the end of the 19th and the beginning of the 20th centuries. In particular, I will focus on German paleontology and its relationship with statistics. I argue that in paleontology, the quantitative method was questioned and strongly limited by the first decade of the 20th century because, as its opponents noted, when the fossil record is treated statistically, it was found to generate results openly in conflict with the (...) Darwinian theory of evolution. Essentially, statistics questions the gradual mode of evolution and the role of natural selection. The main objections to statistics were addressed during the meetings at the Kaiserlich-Königliche Geologische Reichsanstalt in Vienna in the 1880s. After having introduced the statistical treatment of the fossil record, I will use the works of Charles Léo Lesquereux, Joachim Barrande, and Henry Shaler Williams to compare the objections raised in Vienna with how the statistical treatment of the data worked in practice. Furthermore, I will discuss the criticisms of Melchior Neumayr, one of the leading German opponents of statistical paleontology, to show why, and to what extent, statistics were questioned in Vienna. The final part of this paper considers what paleontologists can derive from a statistical notion of data: the necessity of opening a discussion about the completeness and nature of the paleontological data. The Vienna discussion about which method paleontologists should follow offers an interesting case study in order to understand the epistemic tensions within paleontology surrounding Darwin’s theory as well as the variety of non-Darwinian alternatives that emerged from the statistical treatment of the fossil record at the end of the 19th century. (shrink)

For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic (...) logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see [2]). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences. (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)

Through his S–R model of statistical relevance, Wesley Salmon offers a solution to the scientific explanation of objectively improbable events.

Large language models are increasingly present in higher education worldwide, yet debates in many institutions still concentrate mainly on fear, integrity concerns, and possible harm to student learning. This paper is a conceptual and argumentative contribution grounded in an extensive review of recent international and African literature on mathematics, statistics, and computational learning. It aims to clarify how large language models can strengthen quantitative learning when supported by responsible policy, ethical guidance, and sound pedagogy. The reviewed literature indicates that (...) these systems can support stepwise reasoning in mathematics, deepen statistical understanding, enhance programming competence, strengthen writing and reporting skills, and improve student motivation, especially where traditional feedback is limited. The paper argues that meaningful benefit depends on AI literacy, prompting competence, guided use, verification practices, and strong human oversight. It further contends that African higher education requires curriculum reform, assessment redesign, and institutional readiness to integrate AI tools responsibly, while also attending to access, equity, and infrastructural realities. The paper concludes that large language models should not only be viewed as threats. When planned carefully, they can support learning quality, widen participation, and strengthen competence in quantitative disciplines that are critical for development in Nigeria and across Africa. (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)

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.

Statistics play a critical role in biological and clinical research. To promote logically consistent representation and classification of statistical entities, we have developed the Ontology of Biological and Clinical Statistics (OBCS). OBCS extends the Ontology of Biomedical Investigations (OBI), an OBO Foundry ontology supported by some 20 communities. Currently, OBCS contains 686 terms, including 381 classes imported from OBI and 147 classes specific to OBCS. The goal of this paper is to present OBCS for community critique and to (...) describe a number of use cases designed to illustrate its potential applications. The OBCS project and source code are available at http://obcs.googlecode.com. (shrink)

This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.

The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth in a specific way – as (...) a way of epistemically explaining the legal suspicion towards statistical evidence. Still, we do not think of this as a satisfactory vindication of the reluctance to rely on statistical evidence. Knowledge – and Sensitivity, and indeed epistemology in general – are of little, if any, legal value. Instead, we tell an incentive-based story vindicating the suspicion towards statistical evidence. We conclude by showing that the epistemological story and the incentive-based story are closely and interestingly related, and by offering initial thoughts about the role of statistical evidence in morality. (shrink)

Many biologists, especially in ecology and evolution, analyze their data by estimating fits to a set of candidate models and selecting the best model according to the Akaike Information Criterion (AIC) or the Bayesian Information Criteria (BIC). When the candidate models represent alternative hypotheses, biologists may want to limit the chance of a false positive to a specified level. Existing model selection methodology, however, allows for only indirect control over error rates by setting a threshold for the difference in AIC (...) scores. We present a novel theoretical framework for parametric Neyman-Pearson (NP) model selection using information criteria that does not require a pre-data null and applies to three or more non-nested models simultaneously. We apply the theoretical framework to the Error Control for Information Criteria (ECIC) procedure introduced by Cullan et al. (J Appl Stat 47: 2565–2581, 2019), and we show it shares many of the desirable properties of AIC-type methods, including false positive and negative rates that converge to zero asymptotically. We discuss implications for the compatibility of evidentialist and severity-based approach to evidence in philosophy of science. (shrink)

Two experiments were conducted to examine adult learners' ability to extract multiple statistics in simultaneously presented visual and auditory input. Experiment 1 used a cross‐situational learning paradigm to test whether English speakers were able to use co‐occurrences to learn word‐to‐object mappings and concurrently form object categories based on the commonalities across training stimuli. Experiment 2 replicated the first experiment and further examined whether speakers of Mandarin, a language in which final syllables of object names are more predictive of category (...) membership than English, were able to learn words and form object categories when trained with the same type of structures. The results indicate that both groups of learners successfully extracted multiple levels of co‐occurrence and used them to learn words and object categories simultaneously. However, marked individual differences in performance were also found, suggesting possible interference and competition in processing the two concurrent streams of regularities. (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)

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (shrink)

The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot (...) be fundamental. However, if probabilities are epistemic, how can they play a role, as they seem to do, in laws, explanation, and prediction? 2) Many physicists use the notion of typicality instead of the one of probability when discussing statistical mechanics. What is the connection between the two notions? 3) How can one extend Boltzmann’s analysis to the quantum domain, where some theories are indeterministic? 4) Boltzmann’s explanation fundamentally involves cosmology: for the explanation to go through the Big Bang needs to have had extremely low entropy. Does the fact that the Big Bang was a low entropy state imply that it was, in some sense, “highly improbable” and requires an explanation? 5) What exactly is the connection between statistical and classical mechanics? Is the one of theory reduction or there is no such thing? 6) Statistical mechanics has two main formulation: one due to Botzmann and the other due to Gibbs. What is the connection between the two formulations. (shrink)

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)