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

Numerous philosophers, among them Carl G. Hempel and Wesley C. Salmon, have attempted to explicate the notion of explanatory relevance in terms of the statistical relevance of various properties of an individual to the explanandum property itself (or what is here called narrow statistical relevance). This approach seems plausible if one assumes that to explain an occurrence is to show that it was to be expected or to exhibit its degree of expectability and the factors (...) which influence its expectability. But considerations of narrow statistical relevance do not provide an adequate basis for explanatory classification, and the aforementioned views of explanation are accordingly mistaken. Explanatory classification must provide at least a partial account of the nature of a thing, and such an account will generally go beyond what is required as a basis for correct expectation. (shrink)

In Salmon's discussion of his account of statistical relevance and statistical explanation there is a peculiarity in the selection of examples. Where he wishes to show that statistical accounts are reasonably treated as explanatory, he draws examples from the social sciences, such as juvenile delinquency. But when he explains the concept of 'causal' relevance, the examples are selected from the natural sciences. This conceals difficulties with salmon's account of causality in the face of multiple causes (...) such as are characteristic of the social sciences. Salmon's account is shown not to escape difficulties associated with Simon's earlier approach. (shrink)

This paper argues that a notion of statistical explanation, based on Salmon’s statistical relevance model, can help us better understand deep neural networks. It is proved that homogeneous partitions, the core notion of Salmon’s model, are equivalent to minimal sufficient statistics, an important notion from statistical inference. This establishes a link to deep neural networks via the so-called Information Bottleneck method, an information-theoretic framework, according to which deep neural networks implicitly solve an optimization problem that generalizes (...) minimal sufficient statistics. The resulting notion of statistical explanation is general, mathematical, and subcausal. (shrink)

In this paper I critically examine the Generality Problem and argue that it does not succeed as an objection to reliabilism. Although those who urge the Generality Problem are correct in claiming that any process token can be given indefinitely many descriptions that pick out indefinitely many process types, they are mistaken in thinking that reliabilists have no principled way to distinguish between relevant and irrelevant process types.

Indicative conditionals and tendency causal claims are closely related (e.g., Frosch and Byrne, 2012), but despite these connections, they are usually studied separately. A unifying framework could consist in their dependence on probabilistic factors such as high conditional probability and statistical relevance (e.g., Adams, 1975; Eells, 1991; Douven, 2008, 2015). This paper presents a comparative empirical study on differences between judgments on tendency causal claims and indicative conditionals, how these judgments are driven by probabilistic factors, and how these (...) factors differ in their predictive power for both causal and conditional claims. (shrink)

Explanation is a central concept in human psychology. Drawing upon philosophical theories of explanation, psychologists have recently begun to examine the relationship between explanation, probability and causality. Our study advances this growing literature in the intersection of psychology and philosophy of science by systematically investigating how judgments of explanatory power are affected by the prior credibility of a potential explanation, the causal framing used to describe the explanation, the generalizability of the explanation, and its statistical relevance for the (...) evidence. Collectively, the results of our five experiments support the hypothesis that the prior credibility of a causal explanation plays a central role in explanatory reasoning: first, because of the presence of strong main effects on judgments of explanatory power, and second, because of the gate-keeping role it has for other factors. Highly credible explanations were not susceptible to causal framing effects. Instead, highly credible hypotheses were sensitive to the effects of factors which are usually considered relevant from a normative point of view: the generalizability of an explanation, and its statistical relevance for the evidence. These results advance current literature in the philosophy and psychology of explanation in three ways. First, they yield a more nuanced understanding of the determinants of judgments of explanatory power, and the interaction between these factors. Second, they illuminate the close relationship between prior beliefs and explanatory power. Third, they clarify the relationship between abductive and probabilistic reasoning. (shrink)

In discussions of the power of causal explanations, one often finds a commitment to two premises. The first is that, all else being equal, a causal explanation is powerful to the extent that it cites the full causal history of why the effect occurred. The second is that, all else being equal, causal explanations are powerful to the extent that the occurrence of a cause allows us to predict the occurrence of its effect. This article proves a representation theorem showing (...) that there is a unique family of functions measuring a causal explanation’s power that satisfies these two premises. (shrink)

Matthen (Philos Sci 76(4):464–487, 2009) argues that explanations of evolutionary change that appeal to natural selection are statistically abstractive explanations, explanations that ignore some possible explanatory partitions that in fact impact the outcome. This recognition highlights a difficulty with making selective analyses fully rigorous. Natural selection is not about the details of what happens to any particular organism, nor, by extension, to the details of what happens in any particular population. Since selective accounts focus on tendencies, those factors that impact (...) the actual outcomes but do not impact the tendencies must be excluded. So, in order to properly exclude the factors irrelevant to selection, the relevant factors must be identified, and physical processes, environments, and populations individuated on the basis of being relevantly similar for the purposes of selective accounts. Natural selection, on this view, becomes in part a measure of the robustness of particular kinds of outcomes given variations over some kinds of inputs. (shrink)

While philosophers have studied probability and induction, statistics has not received the kind of philosophical attention mathematics and physics have. Despite increasing use of statistics in science, statistical advances have been little noted in the philosophy of science literature. This paper shows the relevance of statistics to both theoretical and applied problems of philosophy. It begins by discussing the relevance of statistics to the problem of induction and then discusses the reasoning that leads to causal generalizations and (...) how statistics elucidates the structure of science as it is actually practiced. In addition to being relevant for building an adequate theory of scientific inference, it is argued that statistics provides a link between philosophy, science and public policy. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In order to explain why falling barometers don't cause rain, a "no-eclipsing" requirement needs to be added to the regularity account of causation. This refinement of the regularity account allows us to see how conclusions about deterministic causes can be based on statistical premises, and thus indicates a criticism of Wesley Salmon 's "statistical relevance" account of causation. The refinement also casts some light on the problem of backwards causation.

In this paper I will evaluate whether some knowledge states that are interpretatively derived from statistical mechanical probabilities could be somehow relevant in actual practices, as famously rejected by Albert (2000). On one side, I follow Frigg (2010a) in rejecting the causal relevance of knowledge states as a mere byproduct of misinterpreting this theoretical field. On the other side, I will argue against Uffink (2011) that probability-represented epistemic states cannot be explanatorily relevant, because (i) probabilities cannot faithfully represent (...) significant epistemic states, and (ii) those states cannot satisfactorily account for why an agent should theoretically believe or expect something. (shrink)

Statistical evidence is pervasive in medicine. In this chapter we will focus on the reliability of randomized clinical trials (RCTs) conducted to test the safety and efficacy of medical treatments. RCTs are scientific experiments and, as such, we expect them to be replicable: if we repeat the same experiment time and again, we should obtain the same outcome (Norton 2015). The statistical design of the test should guarantee that the observed outcome is not a random event, but rather (...) a real effect of the treatments administered. However, for more than a decade now, we have been discussing a replicability crisis across different experimental disciplines including medicine: the outcomes of trials published in very prestigious journals often disappear when the experiment is repeated (see, e.g., Lehrer 2010, Begley and Ellis 2012, Horton 2015). -/- There are different accounts of the reason for this replicability crisis, ranging from scientific fraud to lack of institutional incentives to double-check someone else’s results. In this chapter we will use the replicability crisis as a thread to introduce some central issues in the design of scientific experiments in medicine. First, in section 1, we will see how replicability and statistical significance are connected: we can only make sense of the p-value of a trial outcome within a series of replications of the test. But in order to conduct these replications properly, we need to agree on the proper design of the experiment we are going to repeat. In particular, we need to prevent the preferences of the experimenters from biasing the outcome of the experiment. If there is such a bias, when the experiment is replicated by a third party, the observed outcome will vanish. In section 2, we will argue that trialists need to agree on the debiasing procedures and the statistical quality controls that feature in the trial protocol, if they want the outcome to be replicable. In section 3, we will make two complementary points. On the one hand, replicability per se is not everything: we need trial outcomes that are not only statistically significant but also clinically relevant. On the other hand, trials are not everything: the experts analyzing the evidence can improve the reliability of statistical evidence, although they sometimes fail; we need to further study how they make their decisions. In section 4, we will use a controversy about the overprescription of statins to show how non-replicable effects are obtained in trials and how experts may fail at detecting such flaws, if the commercial interests are big enough. (shrink)

The advance of science and human knowledge is impeded by misunderstandings of various statistics, insufficient reporting of findings, and the use of numerous standardized and non-standardized presentations of essentially identical information. Communication with journalists and the public is hindered by the failure to present statistics that are easy for non-scientists to interpret as well as by use of the word significant, which in scientific English does not carry the meaning of "important" or "large." This article promotes a new standard method (...) for reporting two-group and two-variable statistics that can enhance the presentation of relevant information, increase understanding of findings, and replace the current presentations of two-group ANOVA, t-tests, correlations, chi-squares, and z-tests of proportions. A brief call to highly restrict the publication of risk ratios, odds ratios, and relative increase in risk percentages is also made, since these statistics appear to provide no useful scientific information regarding the magnitude of findings. (shrink)

Statistical evidence is crucial throughout disparate impact’s three-stage analysis: during (1) the plaintiff’s prima facie demonstration of a policy’s disparate impact; (2) the defendant’s job-related business necessity defense of the discriminatory policy; and (3) the plaintiff’s demonstration of an alternative policy without the same discriminatory impact. The circuit courts are split on a vital question about the “practical significance” of statistics at Stage 1: Are “small” impacts legally insignificant? For example, is an employment policy that causes a one percent (...) disparate impact an appropriate policy for redress through disparate impact litigation? This circuit split calls for a comprehensive analysis of practical significance testing across disparate impact’s stages. Importantly, courts and commentators use “practical significance” ambiguously between two aspects of practical significance: the magnitude of an effect and confidence in statistical evidence. For example, at Stage 1 courts might ask whether statistical evidence supports a disparate impact (a confidence inquiry) and whether such an impact is large enough to be legally relevant (a magnitude inquiry). Disparate impact’s texts, purposes, and controlling interpretations are consistent with confidence inquires at all three stages, but not magnitude inquiries. Specifically, magnitude inquiries are inappropriate at Stages 1 and 3—there is no discriminatory impact or reduction too small or subtle for the purposes of the disparate impact analysis. Magnitude inquiries are appropriate at Stage 2, when an employer defends a discriminatory policy on the basis of its job-related business necessity. (shrink)

Statistics in public life .................................................................................................... .....5 Things and numbers............................................................................................. ...................8 Representative samples............................................................................................. ..........8 Averages: meaning and relevance .....................................................................................9 Correlations........................................................................................ ................................10 Applied statistics .................................................................................................... ................13 Relative risks .................................................................................................... ..................14 Relative risk versus absolute risk.....................................................................................16 Problems of classification and confounding factors....................................................17 Epidemiological research............................................................................................ ..........19 Publication bias................................................................................................ ..................20 Statistical significance versus scientific relevance................................................................24 Relative risk again............................................................................................... ...............24 P-values............................................................................................ ...................................25 Confidence intervals .................................................................................................... .....26 Correlation is not causation .............................................................................................26 An infamous episode .................................................................................................... ....27 Terror, utopianism and power .............................................................................................29 Faith and science .................................................................................................... ...........29 Fear and power: the precautionary principle.................................................................30 Utopian salvation........................................................................................... ....................32....

Quantitative researchers often discuss research ethics as if specific ethical problems can be reduced to abstract normative logics (e.g., virtue ethics, utilitarianism, deontology). Such approaches overlook how values are embedded in every aspect of quantitative methods, including ‘observations,’ ‘facts,’ and notions of ‘objectivity.’ We describe how quantitative research practices, concepts, discourses, and their objects/subjects of study have always been value-laden, from the invention of statistics and probability in the 1600s to their subsequent adoption as a logic made to appear as (...) if it exists prior to, and separate from, ethics and values. This logic, which was embraced in the Academy of Management from the 1960s, casts management researchers as ethical agents who ought to know about a reality conceptualized as naturally existing in the image of statistics and probability (replete with ‘constructs’), while overlooking that S&P logic and practices, which researchers made for themselves, have an appreciable role in making the world appear this way. We introduce a different way to conceptualize reality and ethics, wherein the process of scientific inquiry itself requires an examination of its own practices and commitments. Instead of resorting to decontextualized notions of ‘rigor’ and its ‘best practices,’ quantitative researchers can adopt more purposeful ways to reason about the ethics and relevance of their methods and their science. We end by considering implications for addressing ‘post truth’ and ‘alternative facts’ problems as collective concerns, wherein it is actually the pluralistic nature of description that makes defending a collectively valuable version of reality so important and urgent. (shrink)

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)

Multivariate pattern analysis can reveal new information from neuroimaging data to illuminate human cognition and its disturbances. Here, we develop a methodological approach, based on multivariate statistical/machine learning and time series analysis, to discern cognitive processing stages from functional magnetic resonance imaging (fMRI) blood oxygenation level dependent (BOLD) time series. We apply this method to data recorded from a group of healthy adults whilst performing a virtual reality version of the delayed win-shift radial arm maze (RAM) task. This task (...) has been frequently used to study working memory and decision making in rodents. Using linear classifiers and multivariate test statistics in conjunction with time series bootstraps, we show that different cognitive stages of the task, as defined by the experimenter, namely, the encoding/retrieval, choice, reward and delay stages, can be statistically discriminated from the BOLD time series in brain areas relevant for decision making and working memory. Discrimination of these task stages was significantly reduced during poor behavioral performance in dorsolateral prefrontal cortex (DLPFC), but not in the primary visual cortex (V1). Experimenter-defined dissection of time series into class labels based on task structure was confirmed by an unsupervised, bottom-up approach based on Hidden Markov Models. Furthermore, we show that different groupings of recorded time points into cognitive event classes can be used to test hypotheses about the specific cognitive role of a given brain region during task execution. We found that whilst the DLPFC strongly differentiated between task stages associated with different memory loads, but not between different visual-spatial aspects, the reverse was true for V1. Our methodology illustrates how different aspects of cognitive information processing during one and the same task can be separated and attributed to specific brain regions based on information contained in multivariate patterns of voxel activity. (shrink)

Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in (...) data analysis. (shrink)

Biomarkers are widely used not only as prognostic or diagnostic indicators, or as surrogate markers of disease in clinical trials, but also to formulate theories of pathogenesis. We identify two problems in the use of biomarkers in mechanistic studies. The first problem arises in the case of multifactorial diseases, where different combinations of multiple causes result in patient heterogeneity. The second problem arises when a pathogenic mediator is difficult to measure. This is the case of the oxidative stress (OS) theory (...) of disease, where the causal components are reactive oxygen species (ROS) that have very short half-lives. In this case, it is usual to measure the traces left by the reaction of ROS with biological molecules, rather than the ROS themselves. Borrowing from the philosophical theories of signs, we look at the different facets of biomarkers and discuss their different value and meaning in multifactorial diseases and system medicine to inform their use in patient stratification in personalized medicine. (shrink)

The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals (...) and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model.This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods. (shrink)

Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of (...) false positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness. (shrink)

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has (...) been revived for a new generation of readers. (shrink)

The purpose of this paper is to provide a systematic appraisal of the covering law and statistical relevance theories of statistical explanation advanced by Carl G. Hempel and by Wesley C. Salmon, respectively. The analysis is intended to show that the difference between these accounts is inprinciple analogous to the distinction between truth and confirmation, where Hempel's analysis applies to what is taken to be the case and Salmon's analysis applies to what is the case. Specifically, it (...) is argued (a) that statistical explanations exhibit the nomic expectability of their explanandum events, which in some cases may be strong but in other cases will not be; (b) that the statistical relevance criterion is more fundamental than the requirement of maximal specificity and should therefore displace it; and, (c) that if statistical explanations are to be envisioned as inductive arguments at all, then only in a qualified sense since, in particular, the requirement of high inductive probability between explanans and explanandum must be abandoned. (shrink)

The main point of the paper is to show how popular probabilistic measures of incremental confirmation and statistical relevance with qualitatively different features can be embedded smoothly in generalized parametric families. In particular, I will show that the probability difference, log probability ratio, log likelihood ratio, odds difference, so-called improbability difference, and Gaifman’s measures of confirmation can all be subsumed within a convenient biparametric continuum. One intermediate step of this project may have interest on its own, as it (...) provides a unified representation of graded belief of which both probabilities and odds are special cases. (shrink)

Setting optimal significance levels that minimize Type I and Type II errors allows for more transparent and well‐considered statistical decision making compared to the traditional α = 0.05 significance level. We use the optimal α approach to re‐assess conclusions reached by three recently published tests of the pace‐of‐life syndrome hypothesis, which attempts to unify occurrences of different physiological, behavioral, and life history characteristics under one theory, over different scales of biological organization. While some of the conclusions reached using optimal (...) α were consistent to those previously reported using the traditional α = 0.05 threshold, opposing conclusions were also frequently reached. The optimal α approach reduced probabilities of Type I and Type II errors, and ensured statistical significance was associated with biological relevance. Biologists should seriously consider their choice of α when conducting null hypothesis significance tests, as there are serious disadvantages with consistent reliance on the traditional but arbitrary α = 0.05 significance level. (shrink)

With his new riddle of induction, Goodman raised a problem for enumerative induction which many have taken to show that only some ‘natural’ properties can be used for making inductive inferences. Arguably, however, (i) enumerative induction is not a method that scientists use for making inductive inferences in the first place. Moreover, it seems at first sight that (ii) Goodman’s problem does not affect the method that scientists actually use for making such inferences—namely, classical statistics. Taken together, this would indicate (...) that (iii) ‘naturalness’ is not such a relevant concept for the problem of induction, after all. I have no objections against (i) and (iii). But, contrary to (ii), I argue that classical statistics does face a version of Goodman’s problem, which I call the statistical riddle of induction. Given that his problem merely is an instance of the more general problem of underdetermination, this is hardly surprising. Perhaps more importantly, I also show how my riddle can be used for exposing a common fallacy in probabilistic reasoning, without relying on Bayesian assumptions. (shrink)

As a contribution to current debates on the ‘social life of methods’, in this article we present an ethnomethodological study of the role of understanding within statistical practice. After reviewing the empirical turn in the methods literature and the challenges to the qualitative-quantitative divide it has given rise to, we argue such case studies are relevant because they enable us to see different ways in which ‘methods’, here quantitative methods, come to have a social life – by embodying and (...) exhibiting understanding they ‘make the social structures of everyday activities observable’ ( Garfinkel, 1967 : 75), thereby putting society on display. Exhibited understandings rest on distinctive lines of practical social and cultural inquiry – ethnographic ‘forays’ into the worlds of the producers and users of statistics – which are central to good statistical work but are not themselves quantitative. In highlighting these non-statistical forms of social and cultural inquiry at work in statistical practice, our case study is an addition to understandings of statistics and usefully points to ways in which studies of the social life of methods might be further developed from here. (shrink)

While the effects of pattern learning on language processing are well known, the way in which pattern learning shapes exploratory behavior has long gone unnoticed. We report on the way in which individual differences in statistical pattern learning affect performance in the domain of language along multiple dimensions. Analyzing data from healthy monolingual adults' performance on a serial reaction time task and a self‐paced reading task, we show how individual differences in statistical pattern learning are reflected in readers' (...) knowledge of linguistic co‐occurrence patterns and in their exploration and exploitation of content‐specific and task‐general information. First, we investigated the extent to which an individual's pattern learning correlates with his or her sensitivity to systematic morphological and syntactic co‐occurrences, as evidenced while reading authentic sentences. We found that the stream of morphological and syntactic information has a more pronounced effect on the reading speed of, as we will label them, content‐sensitive learners in that the more probable the co‐occurrence pattern, the faster their reading of that pattern will be. Next, we investigated how differences in pattern learning are reflected in the ways in which individuals approach the reading task itself and adapt to it. Casting this relation in terms of exploration/exploitation strategies, known from Reinforcement Learning, we conclude that content‐sensitive learners are also more likely to initially probe (explore) a wider range of directly relevant patterns, which they can later use (exploit) to optimize their reading performance further. By affecting exploratory behavior, pattern learning influences the information that is gathered and becomes available for exploitation, thereby increasing the effect pattern learning has on language cognition. (shrink)

The article focuses on exploring the directions for implementing innovative analytical-statistical technologies as a tool for monitoring and detecting corruption in the state. To achieve this goal, the author clarifies the content of key concepts, defines the essence of innovative analytical-statistical technologies, and analyzes the applications of these technologies as elements of the state’s anti-corruption policy. It is determined that modern analytical-statistical technologies are integral to information technologies, which have emerged as a separate branch of production known (...) as the information industry. Information technologies, including analytical-statistical ones, are realized through information systems, which combine technical tools (computers, communication devices and channels, peripherals, input/output devices, etc.) with software applications that facilitate the functioning of the technical components and analytical aspects, including the mathematical component (statistics). The use of analytical-statistical technologies as a tool to counter corruption at the state level is driven by the specificity of the corruption identification process. The application of relevant technologies is possible when perceiving corruption as a form of fraud. Therefore, the search for corruption in modern society requires a comprehensive approach, utilizing mathematical, analytical, and psychophysical research methods. This approach enables not only the identification but also the prediction of probable instances of abuse. Five directions for implementing innovative analytical-statistical technologies in anti-corruption activities are identified: 1) automation of data collection and processing; 2) automation of communication and office processes; 3) automation of direct management processes; 4) automation of decision-making processes and development; 5) development of expert systems. It is noted that analytical-statistical technologies find the most implementation in four of the identified directions: data collection/processing, direct management, decision support, and expert support. (shrink)

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

What is it for the verdict of a criminal trial to be just? It is widely agreed that a Guilty verdict is just only if the defendant did the relevant deed, and only if his rights were not violated in the process of apprehending, charging, and convicting him. I argue that more is required: he must be found Guilty because he is guilty, and not solely for other reasons. The conviction must be based on the guilt. I argue that many (...) rules of evidence and procedural rules designed to protect a defendant's rights also encourage fulfillment of this basing condition and that the condition helps to explain how an erroneous conviction involving no misconduct can nevertheless be a moral wrong. I argue that the condition also gives an explanation (among others) of why a naked statistic is insufficient for a just conviction. (shrink)

The unity of this study rests on the notion that both statistics and emergence are intimately connected with randomness. A statistical law discovers an ideal frequency from which the actual frequency diverges only randomly i.e. the divergence is not contained in a law. Statistics and randomness, thus, mutually define each other. Emergence is related on the one hand, to regularly recurring events and, on the other hand, to the non-ordered events on one level which may be contained in a (...) higher order law. A discussion of the three linked notions naturally turns to the relations between the sciences and to the relations between the events which are their objects; thus the apparent oddness of a considered subtitle—‘Towards an adequate Weltanschauung’ —is eliminated, for an adequate Weltanschauung for the contemporary philosopher will have to include a position on the interconnexions between sciences. Perhaps the philosopher of science will readily grant this but recent thrusts in the philosophy of art, as well as the clear tendencies of the human sciences indicate that an understanding of these questions is increasingly important. It must be clear, for instance, that no serious comprehensive study of artistic meaning after Langer can afford to neglect utterly the nature of the shift from biological regularity to artistic pattern. I have passed from the unity on the side of the object to a corresponding unity on the side of the subject. For how is one to go about the discovery of the relevant interconnexions. So an earlier title refers to the concrete logic of discovery which itself is discovered not merely—perhaps not at all—by the verbal objectification of a theory but by the actual operations of the discoverer who is reflecting critically on himself. This view on the nature of philosophic enquiry, from which belief as present within the scientific community and essential to the proper development of science, is excluded, guides the form of the expression which continually points away from itself to the crucial experiments which the reader must himself perform. Indicative of this elusiveness is a reference to Goedel which is little more than an indication that at this point in the argument it would be valuable to do some work on the theorem. One may be inclined to cavil at this mode of expression; nevertheless it may be suggested that if philosophy does differ significantly from science it is possible that its proper mode of expression will likewise differ from that of science, and that this mode requires more investigation than it has yet received. Perhaps Wittgenstein is not aphorism at all. (shrink)

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way that they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a (...) probabilistic one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his concept of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concepts that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover. (shrink)

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both (...) logically and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (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.

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

I am very grateful to both Edward Erwin and Peter Fonagy for their thoughtful and engaging comments. I do not have space to deal fully with all the issues they raise, but I will try to clarify some key points at which perhaps I implied more than I intended, or failed to be clear. Erwin states that I claim the following principle is a method for inferring causes: “if X is causally relevant to the occurrence of Y, then the incidence (...) of Ys in the class of Xs and Ys will be different compared with the incidence of Ys in the class of non-Xs and Ys” (Erwin 2012, 217). This is not so. The method I attribute to Grünbaum is given in what follows the principle in the quotation given on p. 199, namely, “To validate a .. (shrink)

Can the evidence provided by software systems meet the standard of proof for civil or criminal cases, and is it individualized evidence? Or, to the contrary, do software systems exclusively provide bare statistical evidence? In this paper, we argue that there are cases in which evidence in the form of probabilities computed by software systems is not bare statistical evidence, and is thus able to meet the standard of proof. First, based on the case of State v. Loomis, (...) we investigate recidivism predictions provided by software systems used in the courtroom. Here, we raise problems for software systems that provide predictions that are based on bare statistical evidence. Second, by examining the case of People v. Chubbs, we argue that the statistical evidence provided by software systems in cold hit DNA cases may in some cases suffice for individualized evidence, on a view on which individualized evidence is evidence that normically supports the relevant proposition (Smith, in Mind 127:1193–1218, 2018). (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)

Recent philosophical studies of probabilistic causation and statistical explanation have opened up the possibility of unifying philosophical approaches with causal modeling as practiced in the social and biological sciences. This unification rests upon the statistical tools employed, the principle of common cause, the irreducibility of causation to statistics, and the idea of causal process as a suitable framework for understanding causal relationships. These four areas of contact are discussed with emphasis on the relevant aspects of causal modeling.

I discuss the philosophical significance of the statistical model selection criteria, in particular their relevance for philosophical of underdetermination. I present an easily comprehensible account of their simplest possible application and contrast it with their application to curve-fitting problems. I embed philosophers' earlier discussion concerning the situations in which the criteria yield implausible results into a more general framework. Among other things, I discuss a difficulty which is related to the so-called subfamily problem, and I show that it (...) has analogies in all legitimate applications of the model selection criteria, and that an analogy of Goodman's new riddle of induction can be formulated in only some of their applications. (shrink)