Philosophy of Statistics

The book gathers contributions from philosophers of medicine, pharmacologists, philosophers of biology and (formal) epistemologists around topics such as causal inference, evidential standards and study design, as well as the interplay between ethical, social, and financial dimensions in strategic behaviour underpinning methodological choices, evidential standards, and policies related to drug approval, monitoring and regulation. Authors include: Rani Anjum, Jeffrey Aronson, Marta Bertolaso, Giovanni Boniolo, Gustavo Cevolani, Brendan Clarke, Roberto Festa, Sven Ove Hansson, Bennett Holman, Jürgen Landes,  Mael Lemoine, Ulrich Mansmann, Klaus Ruthenberg, Miriam Solomon, David Teira, and Jon Williamson.

Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of Philosophy of Statistics by encouraging numerous experts to communicate with one another without feeling ���restricted��� by their disciplines or thinking ���piecemeal��� in their treatment of issues. A second goal of this book is to present work in the field without bias toward any particular statistical paradigm. Broadly speaking, ...

One way of explaining Rudolf Carnap’s mature philosophical view is by drawing an analogy between his technical projects — like his work on inductive logic — with a certain kind of conceptual engineering. After all, there are many mathematical similarities between Carnap’s work in inductive logic and a number of results from contemporary confirmation theory, statistics and mathematical probability theory. However, in stressing these similarities, the conceptual dependence of Carnap’s inductive logic on his work on semantics is downplayed. Yet it is precisely the conceptual resources made available to Carnap from his work on
semantics which allows him to understand his work on inductive logic as a kind of conceptual engineering project. The aim of this paper is to elucidate this engineering analogy in light of Carnap’s mature views through the lens of both inductive logic and semantics.

The paper shows how error statistical theory can be deployed to grasp the deeper epistemic logic of the peer-review process. The intent is to provide the readers with a novel lens through which to make sense of the practices of academic publishing.

Medical research makes intensive use of statistics in order to support its claims. In this paper we make explicit an epistemological tension between the conduct of clinical trials and their interpretation: statistical evidence is sometimes discarded on the basis of an (often) underlined Bayesian reasoning. We suggest that acknowledging the potentiality of Bayesian statistics might contribute to clarify and improve comprehension of medical research. Nevertheless, despite Bayesianism may provide a better account for scientific inference with respect to the standard frequentist approach , Bayesian statistics is rarely adopted in clinical research. The main reason lies in the supposed subjective elements characterizing this perspective. Hence, we discuss this objection presenting the so-called Reference analysis, a formal method which has been developed in the context of objective Bayesian statistics in order to define priors which have a minimal or null impact on posterior probabilities. Furthermore, according to this method only available data are relevant sources of information, so that it resists the most common criticisms against Bayesianism.

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

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability assigned to a hypothesis is typically interpreted as the probability that the hypothesis is true. I argue that solving the interpretive problem requires coming up with a new semantics for Bayesian inference. I present and contrast two solutions to the interpretive problem, both of which involve giving a new interpretation of probability. I argue that both of these new interpretations of Bayesian inference have the same advantages that the standard interpretation has, but that they have the added benefit of being applicable in a wider set of circumstances. I furthermore show that the two new interpretations are inter-translatable and I explore the conditions under which they are co-extensive with the standard Bayesian interpretation. Finally, I argue that the solutions to the interpretive problem support the claim that there is pervasive pragmatic encroachment on whether a given Bayesian probability assignment is rational.

Scientists will often trust a hypothesis for predictive purposes even if they believe that the hypothesis is false. Moreover, it is clear that trust -- like belief -- comes in degrees and ought to be updated in response to evidence. I argue that degrees of trust and degrees of belief are governed by different updating norms and that they are therefore two fundamentally distinct epistemic attitudes, neither one of which may be reduced to the other. Interestingly, there is less reason to think that binary (all-or-nothing) trust differs from binary (all-or-nothing) belief, so the discussion highlights a potentially fundamental difference between formal and traditional epistemology. Finally, I show that the distinction between degrees of trust and degrees of belief has important consequences for decision theory because it is trust -- not belief -- that in general ought to guide action.

Barnes and Sheppard (2009) assume that an anti-monist and anti-reductionist economic geography is desirable and that this desirability is so obvious that no argument needs to be advanced in its support. This commentary challenges this assumption and suggests that a monist and reductionist economic geography organized around the idea of truth-seeking is neither unthinkable nor unpalatable. In order to flesh out this idea, the commentary builds on recent work in the philosophy of scientific induction to show why one of its less publicized advances – error statistical theory – holds far more promise for the future development of economic geography than Barnes and Sheppard's vague and nebulous 'engaged pluralism'.

I present a new proof of the Likelihood Principle that avoids two responses to a well-known proof due to Birnbaum ([1962]). I also respond to arguments that Birnbaum’s proof is fallacious, which if correct would apply to this new proof as well. On the other hand, I urge caution in interpreting proofs of the Likelihood Principle as arguments against the use of frequentist statistical methods.

I give a pedagogical derivation of the Cramér-Rao Bound, which gives a lower bound on the variance of estimators used in statistical point estimation, commonly used to give numerical estimates of the systematic uncertainties in a measurement.

Independent India confronted the vacuum generated by the fading away of the Gandhian charkha , a potent symbol of an anti-colonial sociotechnical imaginary. This paper argues that the technological imaginary that followed ,while not being collectively operationalized enough, was crucial in filling up the vacuum. This was a particularly technological understanding of statistics in the vision of the pioneer of statistical planning in India- P.C. Mahalanobis.

In spite of the ample amount of self-relfexivity he practiced about the fundamental implications of statistical planning as an important component of nation-building, there has hardly been any effort to do proper justice to the ideas of Mahalanobis as a philosopher of consequence. Mahalanobis was engaged with a more well-known philosopher-statistician: the maverick scientist Norbert Wiener. Greg Adamson admirably wrote about the interaction between Wiener and Mahalanobis and provided extremely fleeting speculations about Wiener’s views on the nature of industrialization in India.

While the archives do not retain a proper historical record of the influence that Norbert Wiener had on Mahalanobis , one cannot restrict the search for an imaginary to empirical evidence alone. It is worthwhile to speculatively employ Wiener’s cybernetic worldview to elucidate the technological imaginary that empowered the statistical machinery driving a fledgling Indian state. Mahalanobis makes a pertinent remark in this context:

“statistics is not a branch of mathematics but is a technology which is essentially concerned with the contingent world of reality … as distinguished from a world of abstraction” (Rudra, 176)

Statistics individuates as a technology that is exclusive to the state even as it embodies an acknowledgement of the limits of state control (of the contingency of reality). The cybernetic perspective allows one to recast critical readings of Mahalanobis’s use of anthropometry as enabling casteism even as it speaks to the Indian political leadership’s manifest desire for an alternative view of industrialization that considered both the value of the dignity of the individual human body as well as the task of turning a large population into a productive labour force.



Selected References:

A. Rudra, Prasanta Chandra Mahalanobis: A biography. Delhi: Oxford University Press, 1996.

G. Adamson, "Norbert Wiener and Prasanta Chandra Mahalanobis," 2012 IEEE Conference on Technology and Society in Asia (T&SA), Singapore, 2012, pp. 1-5

Video: https://www.youtube.com/watch?v=nAoCMeGA_Uc

The value or utility of statistical inference has not been well-understood among researchers in the humanities. To clarify, the approaches and methodologies of the humanities are primarily interpretative. With appropriate emphasis on interpretation, I argue that a good starting point  for effective statistics education in the humanities is in highlighting controversy that continues to exist, such as investigating when statistical inferences are valid, and how to interpret results from statistical methods. Specifically, I present one way of defining a genuine principle of evidence, as well as reasons why principles of evidence are far-reaching. The import of evidence as a concept is accepted in the humanities, and the humanities are similar to sciences in that both involve the analysis and interpretation of evidence.

This paper discusses the outstanding problem of replicability of empirical data in the context of recent work on meta-analysis, especially within the field of evidence-based medicine. Specifically, it deals with the methodologi-cal issue of how to determine the degrees of heterogeneity between different collected studies. After critically reviewing the standard measures used to quantify meta-analytical heterogeneity, we argue that they should be revised in such a way to take into account the statistical power of the individual studies. We thus propose some new measures of heterogeneity. Subsequently, we apply them to reassess concrete case-studies from clinical research, thereby showing explicitly how the relevant values of heterogeneity diverge from those obtained with the original measures.

Undoubtedly, whether to accept the likelihood principle or not has been, and still is, one of the most crucial issues for philosophical debates on statistics, though interests in it are waning from statistical debates due to general preferences for more practical issues of statistics. The principle says all you need in parameter analyses of a statistical model is found in likelihood for the data obtained. Bayesians and likelihoodists have traditionally regarded this principle as fundamental, declining any forms of statistics which violate it. Frequentism, on the other hand, try to reject this principle, upholding error probability as a more crucial factor for statistical analyses. But arguments made so far on the likelihood principle still seem to stay on those as to what principle we prefer to choose in statistical analyses. The validity of this principle seems to have never been explored fully enough through the arguments on either side. In this paper, I briefly review how these arguments have been made and show some difficulty in maintaining the principle. I think this has some impact upon statistical practices as well.

This paper argues that common intuitions regarding a) the specialness of "use-novel" data for confirmation, and b) that this specialness implies the "no-double-counting rule", which says that data used in "constructing" (calibrating) a model cannot also play a role in confirming the model's predictions, are too crude. The intuitions in question are pertinent in all the sciences, but we appeal to a climate science case study to illustrate what is at stake. Our strategy is to analyse the intuitive claims in light of prominent accounts of confirmation of model predictions. We show that, on the Bayesian account of confirmation, and also on the standard Classical hypothesis-testing account, claims a) and b) are not generally true, but for some select cases, it is possible to distinguish data used for calibration from use-novel data, where only the latter confirm. The more specialised Classical model-selection methods, on the other hand, uphold a nuanced version of claim a), but this comes apart from b), which must be rejected in favour of a more refined account of the relationship between calibration and confirmation. Thus, depending on the framework of confirmation, either the scope or the simplicity of the intuitive position must be revised.

"Dutch Book" arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to "classical" statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices (like fixed-level null hypothesis significance testing), partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists "don’t bet." This paper examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”-type mathematical results with principles actually endorsed by practicing experimentalists.

Wheeler, Gregory and Williamson, Jon (2011) Evidential probability and objective Bayesian epistemology. In: Philosophy of statistics. Handbook of the Philosophy of Science . Elsevier, pp. 307-331. ... The full text of this publication is not available from this repository.

Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of Philosophy of Statistics by encouraging numerous experts to communicate with one another without feeling ���restricted��� by their disciplines or thinking ���piecemeal��� in their treatment of issues. A second goal of this book is to present work in the field without bias toward any particular statistical paradigm. Broadly speaking, ...

Alan H��jek discusses many interesting features and applications of the notion of conditional probability. In addition to this discussion, he also gives arguments for some specific philosophical views on the nature of conditional probability. In general I agree with most of his points, and in particular with his arguments that Kolmogorov's ���ratio analysis��� of conditional probability is not correct. However, he suggests three more points that I would like to contest���that there is a single correct analysis of conditional probability across ...