Philosophy of Statistics

This article concerns the psychology of the paradoxical Two Envelope Problem. The goal is to find instructive variants of the envelope switching problem that are capable of clear-cut resolution, while still retaining paradoxical features. By relocating the original problem into different contexts involving commutes and playing cards the reader is presented with a succession of resolved paradoxes that reduce the confusion arising from the parent paradox. The goal is to reduce confusion by understanding how we sometimes misread mathematical statements; or, (...) to completely avoid confusion, either by reforming language, or adopting an unambiguous notation for switching problems. This article also suggests that an illusion close in character to the figure/ground illusion hampers our understanding of switching problems in general and helps account for the intense confusion that switching problems sometimes generate. (shrink)

A common line of reasoning that argues against teleological conjectures in physics, cosmology, and especially evolutionary biology, resorts to statistical concepts based on notions of randomness, unpredictability or chance. A conceptual relationship between the aleatory uncertainty of a process and its inherent lack of goal-directedness is often taken for granted. This relies on a misunderstanding of the real significance of stochastic concepts importing a popular semantics into scientific considerations, which leads to unwarranted conclusions. We felt it necessary to clarify terms (...) and concepts involving stochastic processes and why there is no mutual exclusivity between randomness in the physical world and conjectures involving teleological arguments in physics and evolution envisaging a goal-driven and conscious universe. (shrink)

Ex ante predicted outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. But error rates have error rates. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat tails, regardless of (...) the probability distribution used. A mere .01% branching error rate about the STD (itself an error rate), and .01% branching error rate about that error rate, etc. (recursing all the way) results in explosive (and infinite) moments higher than 1. Missing any degree of regress leads to the underestimation of small probabilities and concave payoffs (a standard example of which is Fukushima). The paper states the conditions under which higher order rates of uncertainty (expressed in spreads of counterfactuals) alters the shapes the of final distribution and shows which a priori beliefs about conterfactuals are needed to accept the reliability of conventional probabilistic methods (thin tails or mildly fat tails). (shrink)

Personalized medicine relies on two points: 1) causal knowledge about the possible effects of X in a given statistical population; 2) assignment of the given individual to a suitable reference class. Regarding point 1, standard approaches to causal inference are generally considered to be characterized by a trade-off between how confidently one can establish causality in any given study (internal validity) and extrapolating such knowledge to specific target groups (external validity). Regarding point 2, it is uncertain which reference class leads (...) to the most reliable inferences. -/- Instead, pharmacovigilance focuses on both elements of the individual prediction at the same time, that is, the establishment of the possible causal link between a given drug and an observed adverse event, and the identification of possible subgroups, where such links may arise. We develop an epistemic framework that exploits the joint contribution of different dimensions of evidence and allows one to deal with the reference class problem not only by relying on statistical data about covariances, but also by drawing on causal knowledge. That is, the probability that a given individual will face a given side effect, will probabilistically depend on his characteristics and the plausible causal models in which such features become relevant. The evaluation of the causal models is grounded on the available evidence and theory. (shrink)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases suggests (...) standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

While practitioners think highly of randomized studies, some philosophers argue that there is no epistemic reason to randomize. Here I show that their arguments do not entail their conclusion. Moreover, I provide novel reasons for randomizing in the context of interventional studies. The overall discussion provides a unified framework for assessing baseline balance, one that holds for interventional and observational studies alike. The upshot: practitioners’ strong preference for randomized studies can be defended in some cases, while still offering a nuanced (...) approach to evidence-appraisal, one where not all non-randomized studies are treated equally. (shrink)

This book investigates the interplay between two new and influential subdisciplines in the philosophy of science and philosophy: contemporary scientific metaphysics and the philosophy of information. Scientific metaphysics embodies various scientific realisms and has a partial intellectual heritage in some forms of neo-positivism, but is far more attuned than the latter to statistical science, theory defeasibility, scale variability, and pluralist ontological and explanatory commitments, and is averse to a-priori conceptual analysis. The philosophy of information is the combination of what has (...) been called the informational turn in philosophy and ontology, with the informational turn in logic. The book explores the intersecting theoretical commitments and metaphysical basis of both. It applies scientific metaphysics to the philosophy of information, and also correspondingly proposes a new informational interpretation of scientific metaphysics. These are applied to numerous outstanding ontological, philosophical, and theoretical problems in the philosophy of information, scientific realism, cognitive science, theories of semantic information, and informational logic. The book investigates known and new problems, and advances debates and insights in the philosophy of information. It will be of interest to philosophers of information and science, metaphysicians, and cognitive scientists. (shrink)

The origins of testing scientific models with statistical techniques go back to 18th century mathematics. However, the modern theory of statistical testing was primarily developed through the work of Sir R.A. Fisher, Jerzy Neyman, and Egon Pearson in the inter-war period. Some of Fisher's papers on testing were published in economics journals (Fisher, 1923, 1935) and exerted a notable influence on the discipline. The development of econometrics and the rise of quantitative economic models in the mid-20th century made statistical significance (...) testing a commonplace, albeit controversial tool within economics. -/- In the debate about significance testing, methodological controversies intertwine with epistemological issues and sociological developments. Our aim in this chapter is to expound these connections and to show how the use of, and the debate about, significance testing in economics differs from other social sciences, such as psychology. (shrink)

A prominent pillar of Bayesian philosophy is that, relative to just a few constraints, priors “wash out” in the limit. Bayesians often appeal to such asymptotic results as a defense against charges of excessive subjectivity. But, as Seidenfeld and coauthors observe, what happens in the short run is often of greater interest than what happens in the limit. They use this point as one motivation for investigating the counterintuitive short run phenomenon of dilation since, it is alleged, “dilation contrasts with (...) the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962)” (Herron et al., 1994). A partition dilates an event if, relative to every cell of the partition, uncertainty concerning that event increases. The measure of uncertainty relevant for dilation, however, is not the same measure that is relevant in the context of results concerning whether priors wash out or “opinions merge.” Here, we explicitly investigate the short run behavior of the metric relevant to merging of opinions. As with dilation, it is possible for uncertainty (as gauged by this metric) to increase relative to every cell of a partition. We call this phenomenon distention. It turns out that dilation and distention are orthogonal phenomena. (shrink)

One is occasionally reminded of Foucault's proclamation in a 1970 interview that "perhaps, one day this century will be known as Deleuzian." Less often is one compelled to update and restart with a supplementary counter-proclamation of the mathematician, David Lindley: "the twenty-first century would be a Bayesian era..." The verb tenses of both are conspicuous. // To critically attend to what is today often feared and demonized, but also revered, deployed, and commonly referred to as algorithm(s), one cannot avoid the (...) mathematical and philosophical legacies of probability. // But attending to these probabilistic or Bayesian legacies must include an undeniable theological legacy in which they remain entangled. // We are not, today, discovering quirky theological metaphors in contemporary technics. It's the other way around. The technologies are mere metaphors of past theologies. (shrink)

"Correlation is not causation" is one of the mantras of the sciences—a cautionary warning especially to fields like epidemiology and pharmacology where the seduction of compelling correlations naturally leads to causal hypotheses. The standard view from the epistemology of causation is that to tell whether one correlated variable is causing the other, one needs to intervene on the system—the best sort of intervention being a trial that is both randomized and controlled. In this paper, we argue that some purely correlational (...) data contains information that allows us to draw causal inferences: statistical noise. Methods for extracting causal knowledge from noise provide us with an alternative to randomized controlled trials that allows us to reach causal conclusions from purely correlational data. (shrink)

The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the alternative—Bayesian statistics—that many have suggested as a replacement. The Frequentist approach and the Bayesian approach offer radically different perspectives on evidence and inference with the Frequentist approach prioritising error control and the Bayesian approach offering a formal method for quantifying the relative strength of evidence for hypotheses. (...) We suggest that rather than mere statistical reform, what is needed is a better understanding of the different modes of statistical inference and a better understanding of how statistical inference relates to scientific inference. (shrink)

From 1950 to 1952, statisticians W.G. Cochran, C.F. Mosteller, and J.W. Tukey reviewed A.C. Kinsey and colleagues’ methodology. Neither the history-and-philosophy of science literature nor contemporary theories of interdisciplinarity seem to offer a conceptual model that fits this forced interaction, which was characterized by significant power asymmetries and disagreements on multiple levels. The statisticians initially attempted to exclude all non-technical matters from their evaluation, but their political and personal investments interfered with this agenda. In the face of McCarthy’s witch hunts, (...) negotiations with Kinsey and his funding institutions became integral to the review group’s work. This paper analyzes the heavy burden of emotional and affective labor in this collaboration, the conflicts caused by competing visions of objectivity, and the uses of statistical knowledge to gain and sustain authority. Kinsey’s refusal to adopt the recommended probability sample damaged his already precarious position even further and marked him as a biased researcher who put his personal agenda above methodological rigor. Kinsey’s uncooperative demeanor can be explained by distrust resulting from numerous adverse reactions to his work and by fear of having his sexuality exposed. This case study illustrates that the very concept of valid numbers can become an arena for power struggles and that quantification alone does not guarantee productive exchanges across disciplines. It calls for a deeper conceptual analysis of the prerequisites for successful scientific collaborations. (shrink)

For computer simulation models to usefully inform climate risk management, uncertainties in model projections must be explored and characterized. Because doing so requires running the model many ti...

A prevalent narrative locates the discovery of the statistical phenomenon of regression to the mean in the work of Francis Galton. It is claimed that after 1885, Galton came to explain the fact that offspring deviated less from the mean value of the population than their parents did as a population-level statistical phenomenon and not as the result of the processes of inheritance. Arguing against this claim, we show that Galton did not explain regression towards mediocrity statistically, and did not (...) give up on his ideas regarding an inheritance process that caused offspring to revert to the mean. While the common narrative focuses almost exclusively on Galton’s statistics, our arguments emphasize the anthropological and biological questions that Galton addressed. Galton used regression towards mediocrity to support the claim that some biological types were more stable than others and hence were resistant to evolutionary change. This view had implications concerning both natural selection and eugenics. The statistical explanation attributed to Galton appeared later, during the biometrician-mutationist debate in the early 1900s. It was in the context of this debate and specifically by the biometricians, that the development of the statistical explanation was originally attributed to Galton. (shrink)

In this work, we explore the epistemic import of the value-ladenness of Neyman-Pearson’s Theory of Testing Hypotheses by reconstructing and extending Daniel Steel’s argument for the legitimate influence of pragmatic values on scientific inference. We focus on how to properly understand N-P’s pragmatic value-ladenness and the epistemic reliability of N-P. We develop an account of the twofold influence of pragmatic values on N-P’s epistemic reliability and replicability. We refer to these two distinguished aspects as “direct” and “indirect”. We discuss the (...) replicability of experiments in terms of the indirect aspect and the replicability of outcomes in terms of the direct aspect. We argue that the influence of pragmatic values is beneficial to N-P’s epistemic reliability and replicability indirectly. We show that while the direct influence of pragmatic values can be beneficial, its negative effects on reliability and replicability are also unavoidable in some cases, with the direct and indirect aspects possibly being incongruent. (shrink)

Evidence-based medicine frequently uses statistical hypothesis testing. In this paradigm, data can only disconfirm a research hypothesis’ competitors: One tests the negation of a statistical hypothesis that is supposed to correspond to the research hypothesis. In practice, these hypotheses are often misaligned. For instance, directional research hypotheses are often paired with non-directional statistical hypotheses. Prima facie, one cannot gain proper evidence for one’s research hypothesis employing a misaligned statistical hypothesis. This paper sheds lights on the nature of and the reasons (...) for such misalignments and it provides a thorough analysis of whether they pose a threat to evidence-based medicine. The upshots are that the misalignments are often hidden for clinicians and that although some cases of misalignments can be partially counterbalanced, the overall threat is non-negligible. The counterbalances either lead to methodological inadequacy, loss of statistical power, or involve a lack of information that could be crucial for decision making. This result casts doubt on various findings of medical studies in addition to issues associated with under-powered studies or the replication crisis. (shrink)

A worldview that does not involve religion or science seems to be incomplete. However, a worldview that includes both religion and science may arouse concern of incompatibility. This paper looks at the particular religion, Christianity, and proceeds to develop a worldview in which Christianity and Science are compatible with each other. The worldview may make use of some ideas of Christianity and may involve some author’s own ideas on Christianity. It is thought that Christianity and Science are in harmony in (...) the sense that science can support beliefs in Christianity and in turn beliefs in Christianity can support science. To avoid future unnecessary conflicts between science and religion, it is suggested that a core faith Christianity worldview should be taken. However, this does not mean that certain parts of scripture are abandoned. (shrink)

The history of statistics is filled with many controversies, in which the prime focus has been the difference in the “interpretation of probability” between Fre- quentist and Bayesian theories. Many philosophical arguments have been elabo- rated to examine the problems of both theories based on this dichotomized view of statistics, including the well-known stopping-rule problem and the catch-all hy- pothesis problem. However, there are also several “hybrid” approaches in theory, practice, and philosophical analysis. This poses many fundamental questions. This paper (...) reviews three cases and argues that the interpretation problem of probabil- ity is insufficient to begin a philosophical analysis of the current issues in the field of statistics. A novel viewpoint is proposed to examine the relationship between the stopping-rule problem and the catch-all hypothesis problem. (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)

Ian Hacking (born in 1936, Vancouver, British Columbia) is most well-known for his work in the philosophy of the natural and social sciences, but his contributions to philosophy are broad, spanning many areas and traditions. In his detailed case studies of the development of probabilistic and statistical reasoning, Hacking pioneered the naturalistic approach in the philosophy of science. Hacking’s research on social constructionism, transient mental illnesses, and the looping effect of the human kinds make use of historical materials to shed (...) light on how developments in the social, medical, and behavioural sciences have shaped our contemporary conceptions of identity and agency. Hacking’s other contributions to philosophy include his work on the philosophy of mathematics (Hacking, 2014), philosophy of statistics, philosophy of logic, inductive logic (Hacking, 1965, 1979, 2001) and natural kinds (Hacking, 1991, 2007a). (shrink)

My aim in this paper is to show how the problem of inflated effect sizes corrupts the severity measure of evidence. This has never been done. In fact, the Winner’s Curse is barely mentioned in the philosophical literature. Since the severity score is the predominant measure of evidence for frequentist tests in the philosophical literature, it is important to underscore its flaws. It is also crucial to bring the philosophical literature up to speed with the limits of classical testing. The (...) Winner’s Curse is one of them. The problem is that when a significant result is obtained by using an underpowered test, the severity score becomes particularly high for large discrepancies from the null-hypothesis. This means that such discrepancies are very well supported by the evidence according to that measure. However, it is now well documented that significant tests with low power display inflated effect sizes. They systematically show departures from the null hypothesis H0 that are much greater than they really are. From an epistemological point of view this means that a significant result produced by an underpowered test does not provide evidence for large discrepancies from H0. Therefore, the severity score is an inadequate measure of evidence. Given that we are now aware of the phenomenon of inflated effect sizes, it would be irresponsible to rely on the severity score to measure the strength of the evidence against the null. Instead, one must take appropriate measures to try and avoid using underpowered tests by setting a threshold for the sample size or by replicating the results of the experiment. (shrink)

Scientists often adjust their significance threshold during null hypothesis significance testing in order to take into account multiple testing and multiple comparisons. This alpha adjustment has become particularly relevant in the context of the replication crisis in science. The present article considers the conditions in which this alpha adjustment is appropriate and the conditions in which it is inappropriate. A distinction is drawn between three types of multiple testing: disjunction testing, conjunction testing, and individual testing. It is argued that alpha (...) adjustment is only appropriate in the case of disjunction testing, in which at least one test result must be significant in order to reject the associated joint null hypothesis. Alpha adjustment is inappropriate in the case of conjunction testing, in which all relevant results must be significant in order to reject the joint null hypothesis. Alpha adjustment is also inappropriate in the case of individual testing, in which each individual result must be significant in order to reject each associated individual null hypothesis. The conditions under which each of these three types of multiple testing is warranted are examined. It is concluded that researchers should not automatically assume that alpha adjustment is necessary during multiple testing. Illustrations are provided in relation to joint studywise hypotheses and joint multiway ANOVAwise hypotheses. (shrink)

The popular science of phrenology is known for its preoccupation with geniuses and criminals, but this article shows that phrenologists also introduced ideas about the ‘average’ person. Popular phrenologists in the US and the UK examined the heads of their clients to give an indication of their character. Based on the publications of phrenologists and on a large collection of standardized charts with clients’ scores, this article analyses their definition of what they considered to be the ‘average’. It can be (...) concluded that phrenologists were some of the first to teach individuals to see their identity in relation to an imagined statistical community. (shrink)

The social sciences face a problem of sample non-representation, where the majority of samples consist of undergraduate students from Euro-American institutions. The problem has been identified for decades with little trend of improvement. In this paper, I trace the history of sampling theory. The dominant framework, called the design-based approach, takes random sampling as the gold standard. The idea is that a sampling procedure that is maximally uninformative prevents samplers from introducing arbitrary bias, thus preserving sample representation. I show how (...) this framework, while good in theory, faces many challenges in application. Instead, I advocate for an alternative framework, called the model-based approach to sampling, where representative samples are those balanced in composition, however they were drawn. I argue that the model-based framework is more appropriate in the social sciences because it allows for systematic assessment of imperfect samples and methodical improvement in resource-limited scientific contexts. I end with practical proposals of improving sample quality in the social sciences. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

How we can reliably draw inferences from data, evidence and/or experience has been and continues to be a pressing question in everyday life, the sciences, politics and a number of branches in philosophy (traditional epistemology, social epistemology, formal epistemology, logic and philosophy of the sciences). In a world in which we can now longer fully rely on our experiences, interlocutors, measurement instruments, data collection and storage systems and even news outlets to draw reliable inferences, the issue becomes even more pressing. (...) While we were working on this question using a formal epistemology approach Landes and Osimani (2020); De Pretis et al. (2019); Osimani and Landes (2020); Osimani (2020), we realised that the width of current active interests in the notion of reliability was much broader than we initially thought. Given the breadth of approaches and angles present in philosophy (even in this journal Schubert 2012; Avigad 2021; Claveau and Grenier 2019; Kummerfeld and Danks 2014; Landes 2021; Trpin et al. 2021; Schippers 2014; Schindler 2011; Kelly et al. 2016; Mayo-Wilson 2014; Olsson and Schubert 2007; Pittard 2017), we thought that it would be beneficial to provide a forum for an open exchange of ideas, in which philosophers working in different paradigms could come together. Our call for expression of interest received a great variety of promised manuscripts, the variety is reflected in the published papers. They range from fields far away from our own interests such as quantum probabilities de Ronde et al. (2021), evolvable software systems Primiero et al. (2021), to topics closer to our own research in the philosophy of medicine Lalumera et al. (2020), psychology Dutilh et al. (2021), traditional epistemology Dunn (2021); Tolly (2021) to finally close shared interests in formal epistemology Romero and Sprenger (2021) even within our own department Merdes et al. (2021). Our job is now to reliably inform you about all the contributions in the papers in this special issue. Unfortunately, that task is beyond our capabilities. What we can and instead do is to summarise the contributed papers to inform your reliable inference to read them all in great detail. (shrink)

A brief idea on statistics and epistemology.

In this essay we examine the relationships between Big Data and cognition, in particular human cognition. The reason for exploring such relationships lies in two aspects. First, because in the domain of cognitive science, many speculate about the benefits that the uses of Big Data analysis techniques can provide to the characterization and understanding of cognition. Secondly, because the scientific and technological sectors that promote data analysis activities, particularly statistics, computer science and data science, naturally accustomed to working with Big (...) Data, have in recent years used the idea of ​​cognition. and its related concepts as terms that seem capable of remedying the deficiencies of the era of symbolic artificial intelligence, as a response to the automation of typically human activities in the process of analyzing data and using its results. of data science, seeking to understand what Big Data really is and to investigate whether the use of cognition models could be applied to the sector. On the other hand, we will analyze the potential of using Big Data to help cognitive science. We also tried to provide a certain didactic character in some points, aiming to help the understanding, by non-specialists, regarding some principles and aspects of the methodology of data science and statistics that will eventually be mentioned in the development of our analysis. (Translated from original). (shrink)

The enduring replication crisis in many scientific disciplines casts doubt on the ability of science to estimate effect sizes accurately, and in a wider sense, to self-correct its findings and to produce reliable knowledge. We investigate the merits of a particular countermeasure—replacing null hypothesis significance testing with Bayesian inference—in the context of the meta-analytic aggregation of effect sizes. In particular, we elaborate on the advantages of this Bayesian reform proposal under conditions of publication bias and other methodological imperfections that are (...) typical of experimental research in the behavioral sciences. Moving to Bayesian statistics would not solve the replication crisis single-handedly. However, the move would eliminate important sources of effect size overestimation for the conditions we study. (shrink)

Fisher criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.” The present article considers the responses to this criticism provided by Pearson and Neyman. Pearson interpreted alpha levels in relation to imaginary replications of the original test. This interpretation is appropriate when test users are sure that their replications will be equivalent to one another. However, by definition, scientific researchers do not possess sufficient knowledge about the relevant (...) and irrelevant aspects of their tests and populations to be sure that their replications will be equivalent to one another. Pearson also interpreted the alpha level as a personal rule that guides researchers’ behavior during hypothesis testing. However, this interpretation fails to acknowledge that the same researcher may use different alpha levels in different testing situations. Addressing this problem, Neyman proposed that the average alpha level adopted by a particular researcher can be viewed as an indicator of that researcher’s typical Type I error rate. Researchers’ average alpha levels may be informative from a metascientific perspective. However, they are not useful from a scientific perspective. Scientists are more concerned with the error rates of specific tests of specific hypotheses, rather than the error rates of their colleagues. It is concluded that neither Neyman nor Pearson adequately rebutted Fisher’s “repeated sampling” criticism. Fisher’s significance testing approach is briefly considered as an alternative to the Neyman-Pearson approach. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

Bài mới xuất bản vào ngày 19-5-2020 với tác giả liên lạc là NCS Nguyễn Minh Hoàng, cán bộ nghiên cứu của Trung tâm ISR, trình bày tiếp cận thống kê Bayesian cho việc nghiên cứu dữ liệu khoa học xã hội. Đây là kết quả của định hướng Nhóm nghiên cứu SDAG được nêu rõ ngay từ ngày 18-5-2019.

Numerous papers have investigated the transitivity principle of ‘better-than.’ A recent argument appeals to the principle of mereological dominance for transitivity. However, writers have not treated mereological dominance in much detail. This paper sets out to evaluate the generality of mereological dominance and its effectiveness in supporting the transitivity principle. I found that the mereological dominance principle is vulnerable to a counterexample based on Simpson’s Paradox. The thesis concludes that the mereological dominance principle should be revised in certain ways.

In the late 19th century, the questionnaire was one means of taking the case study into the multitudes. This article engages with Forrester’s idea of thinking in cases as a means of interrogating questionnaire-based research in early American psychology. Questionnaire research was explicitly framed by psychologists as a practice involving both natural historical and statistical forms of scientific reasoning. At the same time, questionnaire projects failed to successfully enact the latter aspiration in terms of synthesizing masses of collected data into (...) a coherent whole. Difficulties in managing the scores of descriptive information questionnaires generated ensured the continuing presence of individuals in the results of this research, as the individual case was excerpted and discussed alongside a cast of others. As a consequence, questionnaire research embodied an amalgam of case, natural historical, and statistical thinking. Ultimately, large-scale data collection undertaken with questionnaires failed in its aim to construct composite exemplars or ‘types’ of particular kinds of individuals; to produce the singular from the multitudes. (shrink)

It is sometimes claimed that the Bayesian framework automatically implements Ockham’s razor—that conditionalizing on data consistent with both a simple theory and a complex theory more or less inevitably favours the simpler theory. It is shown here that the automatic razor doesn’t in fact cut it for certain mundane curve-fitting problems.

Cancer research is experiencing ‘paradigm instability’, since there are two rival theories of carcinogenesis which confront themselves, namely the somatic mutation theory and the tissue organization field theory. Despite this theoretical uncertainty, a huge quantity of data is available thanks to the improvement of genome sequencing techniques. Some authors think that the development of new statistical tools will be able to overcome the lack of a shared theoretical perspective on cancer by amalgamating as many data as possible. We think instead (...) that a deeper understanding of cancer can be achieved by means of more theoretical work, rather than by merely accumulating more data. To support our thesis, we introduce the analytic view of theory development, which rests on the concept of plausibility, and make clear in what sense plausibility and probability are distinct concepts. Then, the concept of plausibility is used to point out the ineliminable role played by the epistemic subject in the development of statistical tools and in the process of theory assessment. We then move to address a central issue in cancer research, namely the relevance of computational tools developed by bioinformaticists to detect driver mutations in the debate between the two main rival theories of carcinogenesis. Finally, we briefly extend our considerations on the role that plausibility plays in evidence amalgamation from cancer research to the more general issue of the divergences between frequentists and Bayesians in the philosophy of medicine and statistics. We argue that taking into account plausibility-based considerations can lead to clarify some epistemological shortcomings that afflict both these perspectives. (shrink)

Ethically permissible clinical trials must not expose subjects to risks that are unreasonable in relation to anticipated benefits. In the research ethics literature, this moral requirement is typically understood in one of two different ways: as requiring the existence of a state of clinical equipoise, meaning a state of honest, professional disagreement among the community of experts about the preferred treatment; or as requiring an equilibrium between individual and collective ethics. It has been maintained that this second interpretation makes it (...) mandatory to minimize the number of patients receiving the treatment that will eventually be shown to be inferior by the trial. This requirement has led to the development of adaptive trials, i.e., trials in which treatment allocation is determined by data accumulated during interim analysis. Many statisticians argue that in some circumstances—typically with potentially high benefits, as in the much discussed ECMO trial—adaptive design is the only ethically permissible experimental design. Nevertheless, some proponents of clinical equipoise argue that adaptive trials are neither ethically required nor permissible. More specifically, they argue that clinical trials using adaptive designs fail to meet the moral requirement of clinical equipoise, since these trials presuppose an epistemic state that is incompatible with a physician’s duty of care to her subjects. This paper emphasizes that the debate is to a large extent resting on an epistemological confusion. Specifically, I argue that this response conflates two different conceptions of statistical evidence, and that recognizing this distinction elucidates an epistemological framework in which adaptive trials are both consistent with and recommended by the moral requirement of clinical equipoise. (shrink)

The overflow of scientific literature stimulates poor reading habits which can aggravate science's reproducibility crisis. Thus, solving the reproducibility crisis demands not only methodological changes, but also changes in our relationship with the scientific literature, especially our reading habits. Importantly, this does not mean reading more, it means reading better.

We map the recently proposed notions of algorithmic fairness to economic models of Equality of opportunity (EOP)---an extensively studied ideal of fairness in political philosophy. We formally show that through our conceptual mapping, many existing definition of algorithmic fairness, such as predictive value parity and equality of odds, can be interpreted as special cases of EOP. In this respect, our work serves as a unifying moral framework for understanding existing notions of algorithmic fairness. Most importantly, this framework allows us to (...) explicitly spell out the moral assumptions underlying each notion of fairness, and interpret recent fairness impossibility results in a new light. Last but not least and inspired by luck egalitarian models of EOP, we propose a new family of measures for algorithmic fairness. We illustrate our proposal empirically and show that employing a measure of algorithmic (un)fairness when its underlying moral assumptions are not satisfied, can have devastating consequences for the disadvantaged group's welfare. (shrink)

Bayesian confirmation theory is a leading theory to decide the confirmation/refutation of a hypothesis based on probability calculus. While it may be much discussed in philosophy of science, is it actually practiced in terms of hypothesis testing by scientists? Since the assignment of some of the probabilities in the theory is open to debate and the risk of making the wrong decision is unknown, many scientists do not use the theory in hypothesis testing. Instead, they use alternative statistical tests that (...) can measure the risk or the reliability in decision making, circumventing some of the theoretical problems in practice. Therefore, the theory is not very popular in hypothesis testing among scientists at present. However, there are some proponents of Bayesian hypothesis testing, and software packages are made available to accelerate utilization by scientists. Time will tell whether Bayesian confirmation theory can become both a leading theory and a widely practiced method. In addition, this theory can be used to model the belief of scientists when testing hypotheses. (shrink)

John D. Norton’s “Material Theory of Induction” has been one of the most intriguing recent additions to the philosophy of induction. Norton’s account appears to be a notably natural account of actual inductive practices, although his theory has attracted considerable criticism. I detail several novel issues for his theory but argue that supplementing the Material Theory with a theory of direct inference could address these problems. I argue that if this combination is possible, a stronger theory of inductive reasoning emerges, (...) which has a more propitious answer to the Problem of Induction. (shrink)

The goal of this chapter is to show that human behavior is not random but follows principles and laws that result into regular patterns that can be not only observed, but also automatically detected and analyzed. The word “behavior” accounts here for nonverbal behavioral cues (e.g., facial expressions, laughter, gestures, etc.) that people display, typically outside conscious awareness, during social interactions. In particular, the chapter shows that observable behavioral patterns typically account for social and psychological differences that cannot be observed (...) directly. Therefore, the analysis of behavioral patterns is important from a human sciences point of view because it helps to understand how people work. Furthermore, it is becoming increasingly important from a technological point of view because observable behavior can be thought of as the physical, machine detectable trace of social and psychological phenomena. In particular, if it is possible to automatically detect and interpret behavioral patterns, it means that machines can make sense of social and psychological phenomena in the same way as people do. (shrink)

The phenomenon of regression toward the mean is notoriously liable to be overlooked or misunderstood; regression fallacies are easy to commit. But even when regression phenomena are duly recognized, it remains perplexing how they can feature in explanations. This article develops a philosophical account of regression explanations as “statistically autonomous” explanations that cannot be deepened by adducing details about causal histories, even if the explananda as such are embedded in the causal structure of the world. That regression explanations have statistical (...) autonomy was first suggested by Ian Hacking and has recently been defended and elaborated by André Ariew, Yasha Rohwer, and Collin Rice. However, I will argue that these analyses fail to capture what regression’s statistical autonomy consists in and how it sets regression explanations apart from other kinds of explanation. The alternative account I develop also shows what is amiss with a recent denial of regression’s statistical autonomy. Marc Lange has argued that facts that can be explained as regression phenomena can in principle also be explained by citing a conjunction of causal histories. The account of regression explanation developed here shows that his argument is based on a misunderstanding of the nature of statistical autonomy. (shrink)

Simple regression (regression analysis with a single explanatory variable), and multiple regression (regression models with multiple explanatory variables), typically correspond to very different biological questions. The former use regression lines to describe univariate associations. The latter describe the partial, or direct, effects of multiple variables, conditioned on one another. We suspect that the superficial similarity of simple and multiple regression leads to confusion in their interpretation. A clear understanding of these methods is essential, as they underlie a large range of (...) procedures in common use in biology. Beyond simple and multiple regression in their most basic forms, understanding the key principles of these procedures is critical to understanding, and properly applying, many methods, such as mixed models, generalised models, and causal inference using graphs (including path analysis and its extensions). A simple, but careful, look at the distinction between these two analyses is valuable in its own right, and can also be used to clarify widely-held misconceptions about collinearity (correlations among explanatory variables). There is no general sense in which collinearity is a problem. We suspect that the perception of collinearity as a hindrance to analysis stems from misconceptions about interpretation of multiple regression models, and so we pursue discussions about these misconceptions in this light. In particular, collinearity causes multiple regression coefficients to be less precisely estimated than corresponding simple regression coefficients. This should not be interpreted as a problem, as it is perfectly natural that direct effects should be harder to characterise than univariate associations. Purported solutions to the perceived problems of collinearity are detrimental to most biological analyses. (shrink)

Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the usefulness (...) of this measure by employing it to develop an answer to Popper’s Paradox of Ideal Evidence. (shrink)

According to influential accounts of scientific method, such as critical rationalism, scientific knowledge grows by repeatedly testing our best hypotheses. But despite the popularity of hypothesis tests in statistical inference and science in general, their philosophical foundations remain shaky. In particular, the interpretation of non-significant results—those that do not reject the tested hypothesis—poses a major philosophical challenge. To what extent do they corroborate the tested hypothesis, or provide a reason to accept it? Popper sought for measures of corroboration that could (...) adequately answer this question. According to Popper, corroboration is different from probability-raising, and grounded in the predictive success and testability of a hypothesis. As such, corroboration becomes an indicator of the scientific value of a hypothesis and guides our practical preferences over hypotheses that have been subjected to severe tests. This article proves two impossibility results for corroboration measures based on statistical relevance. The generality of these results shows that Popper’s qualitative characterization of corroboration must be misguided. I explore what a more promising and scientifically useful concept of corroboration could look like. (shrink)

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

Dân Trí (25/10/2017) — Lần đầu tiên, có một nhà khoa học người Việt, thực hiện công trình nghiên cứu hoàn toàn 100% tại Việt Nam, đứng tên một mình được công bố tại tạp chí Scientific Data, một tạp chí hàng đầu về khoa học dữ liệu thuộc danh mục xuất bản của Nature Research danh tiếng.