Philosophy of Statistics

We will flip a fair coin infinitely many times. Al calls the first flip, claiming it will land heads. Betty calls every odd numbered flip, claiming they will all land heads. Carl calls every flip bar none, claiming they will all land heads. Pre-theoretically, it seems that Al's claim is infinitely more likely than Betty's, and that Betty's claim is infinitely more likely than Carl's. But standard, real-valued probability theory says that, while Al's claim is infinitely more likely than Betty's, (...) Betty's claim is exactly as likely as Carl's. I use John Conway's surreal numbers to capture these pre-theoretic judgements about the relative probabilities of Al's, Betty's, and Carl's claims. Surreal-valued probabilities also allow us to calculate precise numerical values for those claims. For instance, we will see that Betty's claim has a probability equal to the reciprocal of the product of the square root of cardinality of the continuum and the fourth root of 2. The article provides a 'user's guide' to surreal-valued probabilities and raises questions for further research. (shrink)

Although probabilistic statements are ubiquitous, probability is still poorly understood. This shows itself, for example, in the mere stipulation of policies like expected utility maximisation and in disagreements about the correct interpretation of probability. In this work, we provide an account of probabilistic predictions that explains when, how, and why they can be useful for decision-making. We demonstrate that a calibration criterion on finite sets of predictions allows one to anticipate the distribution of utilities that a given policy will yield. (...) Based on this, we specify assumptions under which expected utility maximisation is a sensible decision criterion. We also introduce the notion of prediction methods, highlighting the dependence on schemes of abstraction, and argue that all probabilities are outputs of such prediction methods. This helps explain how the calibration criterion can be satisfied and shows that also supposedly objective probabilities are model-dependent. We compare our account of probability with conventional interpretations and show that it recovers key intuitions behind the latter. We, thus, provide a general account of what probabilities are and how they can enable successful decision-making under uncertainty. (shrink)

Recently I proposed “quantum language” (or,“the linguistic Copenhagen interpretation of quantum mechanics”), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes=Kant epistemology. Namely, quantum language is the scientific final goal of dualistic idealism. It has a great power to describe classical systems as well as quantum systems. In this research report, quantum language is seen as a fundamental theory of statistics and reveals the true nature of statistics.

The debate between scientific realism and anti-realism remains at a stalemate, making reconciliation seem hopeless. Yet, important work remains: exploring a common ground, even if only to uncover deeper points of disagreement and, ideally, to benefit both sides of the debate. I propose such a common ground. Specifically, many anti-realists, such as instrumentalists, have yet to seriously engage with Sober's call to justify their preferred version of Ockham's razor through a positive account. Meanwhile, realists face a similar challenge: providing a (...) non-circular explanation of how their version of Ockham's razor connects to truth. The common ground I propose addresses these challenges for both sides; the key is to leverage the idea that everyone values some truths and to draw on insights from scientific fields that study scientific inference—namely, statistics and machine learning. This common ground also isolates a distinctively epistemic root of the irreconcilability in the realism debate. (shrink)

There has long been an impression that reliabilism implies externalism and that frequentist statistics, due to its reliabilist nature, is inherently externalist. I argue, however, that frequentist statistics can plausibly be understood as a form of internalist reliabilism -- internalist in the conventional sense, yet reliabilist in certain unconventional and intriguing ways. Crucially, in developing the thesis that reliabilism does not imply externalism, my aim is not to stretch the meaning of ‘reliabilism’ merely to sever the implication. Instead, it is (...) to gain a deeper understanding of frequentist statistics, which stands as one of the most sustained attempts by scientists to develop an epistemology for their own use. (shrink)

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)

One justification for preregistering research hypotheses, methods, and analyses is that it improves the transparent evaluation of the severity of hypothesis tests. In this article, I consider two cases in which preregistration does not improve this evaluation. First, I argue that, although preregistration can facilitate the transparent evaluation of severity in Mayo’s error statistical philosophy of science, it does not facilitate this evaluation in Popper’s theory-centric approach. To illustrate, I show that associated concerns about Type I error rate inflation are (...) only relevant in the error statistical approach and not in a theory-centric approach. Second, I argue that a preregistered test procedure that allows deviations in its implementation does not provide a more transparent evaluation of Mayoian severity than a non-preregistered procedure. In particular, I argue that sample-based validity-enhancing deviations cause an unknown inflation of the test procedure’s Type I (familywise) error rate and, consequently, an unknown reduction in its capability to license inferences severely. I conclude that preregistration does not improve the transparent evaluation of severity in Popper’s philosophy of science or when deviations are allowed. (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)

I argue for a connection between two debates in the philosophy of probability. On the one hand, there is disagreement about conditional probability. Is it to be defined in terms of unconditional probability, or should we instead take conditional probability as the primitive notion? On the other hand, there is disagreement about how additive probability is. Is it merely finitely additive, or is it additionally countably additive? My thesis is that, if conditional probability is primitive, then it is not countably (...) additive. (shrink)

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

Traditional wisdom dictates that statistical model outputs are estimates, not measurements. Despite this, statistical models are employed as measurement instruments in the social sciences. In this article, I scrutinize the use of a specific model—the logit model—for psychological measurement. Given the adoption of a criterion for measurement that I call comparability, I show that the logit model fails to yield measurements due to properties that follow from its fixed residual variance.

This article reviews and develops an epistemological tradition in philosophy of science, called convergentism, which holds that inference methods should be assessed in terms of their abilities to converge to the truth. This tradition is compared with three competing ones: (1) explanationism, which holds that theory choice should be guided by a theory's overall balance of explanatory virtues, such as simplicity and fit with data; (2) instrumentalism, according to which scientific inference should be driven by the goal of obtaining useful (...) models, rather than true theories; (3) Bayesianism, which features a shift of focus from all-or-nothing beliefs to degrees of belief. (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)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their (...) performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

Ambiguity occurs insofar as a reasoner lacks information about the relevant physical probabilities. There are objections to the application of standard Bayesian inductive logic and decision theory in contexts of significant ambiguity. A variety of alternative frameworks for reasoning under ambiguity have been proposed. Two of the most prominent are Imprecise Bayesianism and Dempster–Shafer theory. We compare these inductive logics with respect to the Ambiguity Dilemma, which is a problem that has been raised for Imprecise Bayesianism. We develop an agent-based (...) model comparison that isolates the difference between the two inductive logics in their updating methods. We find that Dempster–Shafer theory does not avoid the Ambiguity Dilemma. We discuss the implications of this result. (shrink)

We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of agreeing on (...) what data streams are algorithmically random, two Bayesian agents can thus be taken to concur on what global regularities they expect to see in the data. We show that this type of compatibility between priors suffices to ensure that two computable Bayesian agents will reach inter-subjective agreement with increasing information. In other words, it guarantees that their respective probability assignments will almost surely become arbitrarily close to each other as the number of observations increases. Thus, when shared by computable Bayesian learners with different subjective priors, the beliefs about uniformity captured by algorithmic randomness provably lead to merging of opinions. (shrink)

The development of a biological notion of “population” over the first century of the theory of evolution has been commented upon by a number of historians and philosophers of biology. Somewhat less commonly discussed, however, is the parallel development of the statistical concept of a population over precisely the same period, in some cases driven by the same historical actors (such as Francis Galton and R. A. Fisher). We explore here these parallel developments, first from the perspective of a reconstruction (...) of the historical development of each concept, then with the aid of a digital analysis of a corpus of literature drawn from the journals Biometrika and Journal of Genetics, between 1900 and 1960. These twin analyses show both points of interesting overlap between these two historical trends as well as points of important divergence. The biological and statistical notions of “population” seem to be relatively clearly distinguishable over these six decades, in spite of the fact that a number of authors contributed clearly to both traditions. The complex interplay of continuity and discontinuity across these two notions of “population” makes them a particularly interesting case study of scientific conceptual change. (shrink)

Simpson’s paradox (SP) is a statistical phenomenon where the association between two variables reverses, disappears, or emerges, after conditioning on a third variable. It has been proposed (by, e.g., Judea Pearl) that SP should be analyzed using the framework of graphical causal models (i.e., causal DAGs) in which SP is diagnosed as a symptom of confounding bias. This paper contends that this confounding-based analysis cannot fully capture SP: there are cases of SP that cannot be explained away in terms of (...) confounding. Previous works have argued that some cases of SP do not require causal analysis at all. Despite being a logically valid counterexample, we argue that this type of cases poses only a limited challenge to Pearl’s analysis of SP. In our view, a more powerful challenge to Pearl comes from cases of SP that do require causal analysis but can arise without confounding. We demonstrate with examples that accidental associations due to genetic drift, the use of inappropriate aggregate variables as causes, and interactions between units (i.e., inter-unit causation) can all give rise to SP of this type. The discussion is also extended to the amalgamation paradox (of which SP is a special form) which can occur due to the use of non-collapsible association measures, in the absence of confounding. (shrink)

I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many reject this thesis because it appears to permit finding defendants liable solely on the basis of statistical evidence. To the contrary, I argue – by combining Thomson's (1986) causal analysis of legal evidence with formal methods of causal inference – that legal standards of proof can be reduced to probabilities, but that deriving these probabilities involves more than just statistics.

Otsuka (2023) argues for a correspondence between data science and traditional epistemology: Bayesian statistics is internalist; classical (frequentist) statistics is externalist, owing to its reliabilist nature; model selection is pragmatist; and machine learning is a version of virtue epistemology. Where he sees diversity, I see an opportunity for unity. In this article, I argue that classical statistics, model selection, and machine learning share a foundation that is reliabilist in an unconventional sense that aligns with internalism. Hence a unification under internalist (...) reliabilism. (shrink)

When thinking about the debate between frequentists and Bayesians on scientific methodology, it is unproductive and misleading to choose from two dichotomized, oversimplified positions. A spectrum is developed here to make explicit some remarkable options, organized by two dimensions---or two questions. First, ask what kinds of probabilities exist. Only frequencies? Or only degrees of belief? Or both? Then ask what standards should be used to assess inference procedures. Only frequentist standards? Or just Bayesian ones? Or both? Or something else? In (...) combination, there are at least five positions that have been seriously defended in the history and philosophy of statistics. (shrink)

Do imprecise beliefs lead to worse decisions under uncertainty? This BJPS Short Reads article provides an informal introduction to our use of agent-based modelling to investigate this question. We explain the strengths of imprecise probabilities for modelling evidential states. We explain how we used an agent-based model to investigate the relative performance of Imprecise Bayesian reasoners against a standard Bayesian who has precise credences. We found that the very features of Imprecise Bayesianism which give it representational strengths also cause relative (...) underperformance in this decision problem. We explain the practical relevance of this research to applications of Bayesian reasoning in areas like artificial intelligence. (shrink)

The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin (...) by introducing the concept of Type I error rates and distinguishing between statistical errors and theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ misinterpretation of statistical errors and their underestimation of theoretical errors. (shrink)

Methods of machine learning (ML) are gradually complementing and sometimes even replacing methods of classical statistics in science. This raises the question whether ML faces the same methodological problems as classical statistics. This paper sheds light on this question by investigating a long-standing challenge to classical statistics: the reference class problem (RCP). It arises whenever statistical evidence is applied to an individual object, since the individual belongs to several reference classes and evidence might vary across them. Thus, the problem consists (...) in choosing a suitable reference class for the individual. I argue that deep neural networks (DNNs) are able to overcome specific instantiations of the RCP. Whereas the criteria of narrowness, reliability, and homogeneity, that have been proposed to determine a suitable reference class, pose an inextricable tradeoff to classical statistics, DNNs are able to satisfy them in some situations. On the one hand, they can exploit the high dimensionality in big-data settings. I argue that this corresponds to the criteria of narrowness and reliability. On the other hand, ML research indicates that DNNs are generally not susceptible to overfitting. I argue that this property is related to a particular form of homogeneity. Taking both aspects together reveals that there are specific settings in which DNNs can overcome the RCP. (shrink)

We argue that subjective Bayesians face a dilemma: they must offend against the spirit of their permissivism about rational credence or reject the principle that one should avoid accuracy dominance.

A view that emancipates free will by means of quantum indeterminism is frequently rejected based on arguments pointing out its incompatibility with what we know about quantum physics. However, if one carefully examines what classical physical causal determinism and quantum indeterminism are according to physics, it becomes clear what they really imply–and, especially, what they do not imply–for agent-causation theories. Here, we will make necessary conceptual clarifications on some aspects of physical determinism and indeterminism, review some of the major objections (...) against libertarian conjectures, and show that there is no conceptual incompatibility preventing us from taking a ‘quantum-libertarian’ approach to the problem of free will. In particular, we will illustrate the possible role of self-causation (causa sui) as a potential solution to otherwise apparently incompatible or even paradoxical statements concerning free will and quantum indeterminism. (shrink)

The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...) approximations to Solomonoff prediction do not always converge. (shrink)

It is one thing to hold that merely statistical evidence is _sometimes_ insufficient for rational belief, as in typical lottery and profiling cases. It is another thing to hold that merely statistical evidence is _always_ insufficient for rational belief. Indeed, there are cases where statistical evidence plainly does justify belief. This project develops a dispositional account of the normativity of statistical evidence, where the dispositions that ground justifying statistical evidence are connected to the goals (= proper function) of objects. There (...) are strong intuitive motivations for doing this. For we can turn almost any case of _non-justifying_ merely statistical evidence into a case of _justifying_ merely statistical evidence by adding information about the dispositions and goals of the objects involved. The resulting view not only helps us understand when and why merely statistical evidence is normatively significant, but it also helps us understand how statistical evidence relates to more standard forms of evidence (perceptual, testimonial). The emerging view also has surprising applications, as it imposes limitations on the epistemic value of fine-tuning arguments for theism as well as undermines a standard class of case-based arguments for moral encroachment. (shrink)

Acknowledging that many members of the SM3D Portal need reference documents related to Bayesian Mindsponge Framework (BMF) analytics to conduct research projects effectively, we present the essential materials and most up-to-date studies employing the method in this post. By summarizing all the publications and preprints associated with BMF analytics, we also aim to help researchers reduce the time and effort for information seeking, enhance proactive self-learning, and facilitate knowledge exchange and community dialogue through transparency.

Climate scientists often apply statistical tools to a set of different estimates generated by an “ensemble” of models. In this paper, I argue that the resulting inferences are justified in the same way as any other statistical inference: what must be demonstrated is that the statistical model that licenses the inferences accurately represents the probabilistic relationship between data and target. This view of statistical practice is appropriately termed “model-based,” and I examine the use of statistics in climate fingerprinting to show (...) how the difficulties that climate scientists encounter in applying statistics to ensemble-generated data are the practical difficulties of normal statistical practice. The upshot is that whether the application of statistics to ensemble-generated data yields trustworthy results should be expected to vary from case to case. (shrink)

Over the last twenty-five years, climate scientists working on the attribution of climate change to humans have developed increasingly sophisticated statistical models in a process that can be understood as a kind of calibration: the gradual changes to the statistical models employed in attribution studies served as iterative revisions to a measurement(-like) procedure motivated primarily by the aim of neutralizing particularly troublesome sources of error or uncertainty. This practice is in keeping with recent work on the evaluation of models more (...) generally that views models as tools for particular tasks: what drives the process is the desire for models that provide more reliable grounds for inference rather than accuracy to the underlying mechanisms of data-generation. (shrink)

This essay presents a unified account of safety, sensitivity, and severe testing. S’s belief is safe iff, roughly, S could not easily have falsely believed p, and S’s belief is sensitive iff were p false S would not believe p. These two conditions are typically viewed as rivals but, we argue, they instead play symbiotic roles. Safety and sensitivity are both valuable epistemic conditions, and the relevant alternatives framework provides the scaffolding for their mutually supportive roles. The relevant alternatives condition (...) holds that a belief is warranted only if the evidence rules out relevant error possibilities. The safety condition helps categorise relevant from irrelevant possibilities. The sensitivity condition captures ‘ruling out’. Safety, sensitivity, and the relevant alternatives condition are typically presented as conditions on warranted belief or knowledge. But these properties, once generalised, help characterise other epistemic phenomena, including warranted inference, legal verdicts, scientific claims, reaching conclusions, addressing questions, warranted assertion, and the epistemic force of corroborating evidence. We introduce and explain Mayo’s severe testing account of statistical inference. A hypothesis is severely tested to the extent it passes tests that probably would have found errors, were they present. We argue Mayo’s account is fruitfully understood using the resulting relevant alternatives framework. Recasting Mayo’s condition using the conceptual framework of contemporary epistemology helps forge fruitful connections between two research areas—philosophy of statistics and the analysis of knowledge—not currently in sufficient dialogue. The resulting union benefits both research areas. (shrink)

Pluralistische Wissenschaftstheorie ist kein etabliertes Format. Herkömmliche Darstellungen nehmen meist die Perspektive einer einzelnen Ausprägung von Wissenschaft ein, verbunden mit impliziten Wertungen und unbefragten Präferenzen. So belasten Kämpfe um Deutungshoheit notorisch die kooperative Forschung. Werner Kogge entfaltet demgegenüber einen neuen Ansatz: Er zeichnet nach, wie sich aus mehreren historischen Quellen verschiedene Typen wissenschaftlicher Forschung ausprägten, und wie diese Typen heute praktiziert werden. So entsteht ein Bild unterschiedlicher, aber gleichberechtigter Formen wissenschaftlicher Forschungspraxis, ohne hierarchische Staffelung oder eine evolutionäre Entwicklungslinie. Mit dieser (...) Pluralität kommt auch eine neue Form von Interdisziplinarität in den Blick: strukturell, modular und praxisbezogen. (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)

According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such absences ‘the frontiers of science', where background scientific (...) theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science. (shrink)

In his recent book, John Norton has created a theory of inference to the best explanation, within the context of his "material theory of induction". I apply it to the problem of scientific explanations that are false: if we want the theories in our explanations to be true, then why do historians and scientists often say that false theories explained phenomena? I also defend Norton's theory against some possible objections.

As part of a book symposium on Erwin Dekker's Jan Tinbergen (1903–1994) and the Rise of Economic Expertise (2021), William Peden reflects on shared views on the objectivity and nature of statistics between Tinbergen and Keynes underlying the Tinbergen-Keynes debates.

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)

This book provides a new all-round perspective on the life and work of Edgar Zilsel (1891-1944) as a philosopher, historian, and sociologist. He was close to the Vienna Circle and has been hitherto almost exclusively referred to in terms of the so-called “Zilsel thesis” on the origins of modern science. Much beyond this “thesis”, Zilsel’s brilliant work provides original insights on a broad number of topics, ranging from the philosophy of probability and statistics to the concept of “genius”, from the (...) issues of scientific laws and theories to the sociological background of science and philosophy, and to the political analysis of the problems of his time. Praised by Herbert Feigl as an “outstanding brilliant mind”, Zilsel, being as a Social-Democrat of Jewish origins, mostly led a life of hardship marked by emigration and coming to a sudden and tragic end by suicide in 1944. The impossibility of an academic career has hindered the reception of Zilsel’s scientific work for a long time. This volume is a contribution to its late reception, providing new insights especially into his work during his years in Vienna; moreover, it shows the heuristic value of Zilsel’s ideas for future Scholar research – in philosophy, history, and sociology. -/- (ISSN: 0929-6328). (shrink)

Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...) short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

Being a researcher is challenging, especially in the beginning. Early Career Researchers (ECRs) need achievements to secure and expand their careers. In today’s academic landscape, researchers are under many pressures: data collection costs, the expectation of novelty, analytical skill requirements, lengthy publishing process, and the overall competitiveness of the career. Innovative thinking and the ability to turn good ideas into good papers are the keys to success.

"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)

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)

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)

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)

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)