ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination (...) of the possible posteriors. Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. _1_ Introduction _2_ Alternative Updating Policies _3_ Modelling the Situation for Normal Updating _4_ Tracking: A Criterion for Updating Policies _5_ Tracking: Precise Formulation and Relation to Convexity _6_ The Spanning Criterion _7_ Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria _8_ Policies that Violate the Spanning and Tracking Criteria Appendix Appendix. (shrink)

For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of (...) the possible posteriors. Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. 1 Introduction2 Alternative Updating Policies3 Modelling the Situation for Normal Updating4 Tracking: A Criterion for Updating Policies5 Tracking: Precise Formulation and Relation to Convexity6 The Spanning Criterion7 Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria8 Policies that Violate the Spanning and Tracking Criteria AppendixAppendix. (shrink)

This article provides unified axiomatic foundations for the most common optimality criteria in statistical decision theory. It considers a decision maker who faces a number of possible models of the world (possibly corresponding to true parameter values). Every model generates objective probabilities, and von Neumann–Morgenstern expected utility applies where these obtain, but no probabilities of models are given. This is the classic problem captured by Wald’s (Statistical decision functions, 1950) device of risk functions. In an Anscombe–Aumann environment, I (...) characterize Bayesianism (as a backdrop), the statistical minimax principle, the Hurwicz criterion, minimax regret, and the “Pareto” preference ordering that rationalizes admissibility. Two interesting findings are that c-independence is not crucial in characterizing the minimax principle and that the axiom which picks minimax regret over maximin utility is von Neumann–Morgenstern independence. (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)

Even after multiple cycles of ABET accreditation, many engineering programs are unsure of how much curriculum content is needed to meet the requirements of ABET’s Criterion 3.f (an understanding of professional and ethical responsibility). This study represents the first scholarly attempt to assess the impact of curriculum reform following the introduction of ABET Criterion 3.f. This study sought to determine how much professional and ethical responsibility curriculum content was used between 1995 and 2005, as well as how, when, (...) why, and to what effect changes in the amount of content occurred. Subsequently, the study sought to evaluate if different amounts of curriculum content generated differing student outcomes. The amount of curriculum content used by each of the participating programs was identified during semi-structured interviews with program administrators and a review of ABET Self-Study documents. Quantitative methods were applied to determine if a relationship existed between the curriculum content and performance on a nationally administered, engineering-specific standardized examination. The findings indicate a statistical relationship, but a lack of structure between the amount of required content in the curriculum and performance on the examination. Additional findings were also generated regarding the way that programs interpret the Criterion 3.f feedback generated during accreditation visits. The primary impact of this study is that it dispels the myth that more courses or course time on professionalism and ethics will necessarily lead to positive engineering education outcomes. Much of the impetus to add more curriculum content results from a lack of conclusive feedback during ABET accreditation visits. (shrink)

The study aimed at identifying the intermediate role of the criterion of emphasis on students and beneficiaries in the relationship between adopting the criterion of partnership and resources and achieving the satisfaction of the society. The study used the analytical descriptive method. The study was conducted on university leadership in Al-Azhar, Islamic and Al-Aqsa Universities. The sample of the study consisted of (200) individuals, 182 of whom responded, and the questionnaire was used in collecting the data. The study (...) reached a number of results, the most important of which were: The level of adoption by the Palestinian universities of the criterion of partnership and resources came to a large extent. The level of adoption by the Palestinian universities of the criterion of emphasis on the beneficiary students was very high. The criterion of partnership and resources to achieve the satisfaction of the community surrounding the Palestinian universities, the existence of a statistically significant impact of the adoption of the criterion of partnership and resources to strengthen the focus on students benefiting in Palestinian universities, The focus on the students benefiting from the satisfaction of the community surrounding the Palestinian universities, the existence of a statistically significant impact on the adoption of the criterion of partnership and resources to achieve the satisfaction of the community surrounding the Palestinian universities, The study presented a number of recommendations, most important of which are: Increase interest in the resource and partnership criterion through enhancing the university's resources and developing internal and external partnerships to serve the university and the society. Increase the focus on students and beneficiaries by providing an appropriate educational environment and academic programs that meet the needs of the labor market. Through the strengthening of existing community service centers and the establishment of new community centers, strengthening the partnership of industrial companies and promoting scientific research for the benefit of universities and society. -/- . (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)

Jun Otsuka’s excellent book, Thinking about Statistics - the Philosophical Foundations (Otsuka 2023) is mostly organized around the idea that different statistical approaches can be illuminated by linking them to different ideas in general epistemology. Otsuka connects Bayesianism to internalism and foundationalism, frequentism to reliabilism, and the Akaike Information Criterion in model selection theory to instrumentalism. This useful mapping doesn’t cover all the interesting ideas he presents. His discussions of causal inference and machine learning are philosophically insightful, as (...) is his idea that statisticians embrace an assumption that is similar to Hume’s Principle of the Uniformity of Nature. I discuss these topics in what follows, sometimes disagreeing with details while at other times adding ideas that complement those presented in the book. (shrink)

Classification in statistics is usually used to solve the problems of identifying to which set of categories, such as subpopulations, new observation belongs, based on a training set of data containing information whose category membership is known. The article aims to use the Gaussian Mixture Model to model the daily closing price index over the period of 1/1/2013 to 16/8/2020 in the Kingdom of Saudi Arabia. The daily closing price index over the period declined, which might be the effect of (...) corona virus, and the mean of the study period is about 7866.965. The closing price is the last regular deal that took place during the continuous trading period. If there are no transactions on the stock during the day, the closing price is the previous day’s closing price. The closing auction period comes after the continuous trading period, during which investors can enter by buying and selling the stocks at this period. The experimental results show that the best mixture model is E with three components according to the BIC criterion. The expectation-maximization algorithm converged in 2 repetitions. The data source is from Tadawul KSA. (shrink)

This Article explores the success of the new science of statistics in establishing order within the pandemonium of industrial revolution in the nineteenth century. This success was based on the fact that the expanding circulation of both men and goods that characterized capitalism constituted the ontological foundation of statistics as well. In this respect, one can say that statistics turned variety and multiplicity into the basis of system, if not of uniformity. The study focuses on the 1850 federal census of (...) the United States and, more specifically, on the new taxonomy adopted in the census’s manufacturing schedule for enumerating industrial activity. This taxonomy was organized around a single, universal threshold of capital investment applied to each enterprise, a criterion that replaced various systems applied in previous censuses, all of which were based on an a priori definition of what actually constituted production. The innovation of 1850 resulted in a far more extensive account of manufacturing and was consequently perceived to be a most effective means of measuring the dramatic expansion of the economy. In fact, this was accomplished by making money the rule of measure, and so redefining the essence of industry to be financial rather than material. Profit-making consequently achieved a scientific, and even neutral, status. As such, statistics can be said to have made an epistemological contribution to the legitimization of the new capitalist order. (shrink)

The paper deals with a method of hierarchization of alternatives in a multicriteria environment by means of statistical nonparametric procedures. For each criterion, alternatives are disposed on an ordinal scale. After that a procedure similar to ANOVA is activated on the data. The differences relating to the average ranks of each action are used to build the hierarchical algorithm. The concept of outranking, in a probabilistic meaning, is reached in this way. Thereafter, we arrive at the concept of (...) dominance using pairwise comparisons. A case study is presented which implements the methodological suggestion. (shrink)

Identifying wordlike units in language is typically done by applying a battery of criteria, though how to weight these criteria with respect to one another is currently unknown. We address this question by investigating whether certain criteria are also used as cues for learning an artificial language—if they are, then perhaps they can be relied on more as trustworthy top‐down diagnostics. The two criteria for grammatical wordhood that we consider are a unit's free mobility and its internal immutability. These criteria (...) also map to two cognitive mechanisms that could underlie successful statistical learning: learners might orient themselves around the low transitional probabilities at unit boundaries, or they might seek chunks with high internal transitional probabilities. We find that each criterion has its own facilitatory effect, and learning is best where they both align. This supports the battery‐of‐criteria approach to diagnosing wordhood, and also suggests that the mechanism behind statistical learning may not be a question of either/or; perhaps the two mechanisms do not compete, but mutually reinforce one another. (shrink)

DOI: 10.1080/00031305.2018.1564697 When the editors of Basic and Applied Social Psychology effectively banned the use of null hypothesis significance testing (NHST) from articles published in their journal, it set off a fire-storm of discussions both supporting the decision and defending the utility of NHST in scientific research. At the heart of NHST is the p-value which is the probability of obtaining an effect equal to or more extreme than the one observed in the sample data, given the null hypothesis and (...) other model assumptions. Although this is conceptually different from the probability of the null hypothesis being true, given the sample, p-values nonetheless can provide evidential information, toward making an inference about a parameter. Applying a 10,000-case simulation described in this article, the authors found that p-values’ inferential signals to either reject or not reject a null hypothesis about the mean (α = 0.05) were consistent for almost 70% of the cases with the parameter’s true location for the sampled-from population. Success increases if a hybrid decision criterion, minimum effect size plus p-value (MESP), is used. Here, rejecting the null also requires the difference of the observed statistic from the exact null to be meaningfully large or practically significant, in the researcher’s judgment and experience. The simulation compares performances of several methods: from p-value and/or effect size-based, to confidence-interval based, under various conditions of true location of the mean, test power, and comparative sizes of the meaningful distance and population variability. For any inference procedure that outputs a binary indicator, like flagging whether a p-value is significant, the output of one single experiment is not sufficient evidence for a definitive conclusion. Yet, if a tool like MESP generates a relatively reliable signal and is used knowledgeably as part of a research process, it can provide useful information. (shrink)

By the end of the 19th century, the Prussian censuses registered regularly the nationality of the population according to a standard criterion: the mother tongue. The background to this institutionalization could be mapped out in terms of the early creation of the statistical office, the reform of the bureaucracy, and the political challenge following the annexation of the western part of the former Polish state. However, this paper gives a different account of that goes beyond a state-level history (...) of a statistical institution. At the beginning of the 19th century, nationality was already registered in some localities. The purpose was to measure the use of German in schools and churches and hence the effectiveness of the Germanization of the Poles. Although the statistical office was in existence, it had little influence on these local practices, and their heterogeneity prevailed for decades. This situation was modified by the centralization of the census in the 1860s in the hands of the statistical office, and the emergence of a demographic approach. This change occurred in the context of discussions with local authorities regarding their use of language statistics. The census has to be seen therefore as an integration on multiple levels of statistical practices. (shrink)

This paper addresses the problem that Bayesian statistical inference cannot accommodate theory change, and proposes a framework for dealing with such changes. It first presents a scheme for generating predictions from observations by means of hypotheses. An example shows how the hypotheses represent the theoretical structure underlying the scheme. This is followed by an example of a change of hypotheses. The paper then presents a general framework for hypotheses change, and proposes the minimization of the distance between hypotheses as (...) a rationality criterion. Finally the paper discusses the import of this for Bayesian statistical inference. (shrink)

We address Northcott’s criticism of Pearson’s correlation coefficient ‘r’ in measuring causal strength by replacing Pearson’s linear regressions by nonparametric nonlinear kernel regressions. Although new proof shows that Suppes’ intuitive causality condition is neither necessary nor sufficient, we resurrect Suppes’ probabilistic causality theory by using nonlinear tools. We use asymmetric generalized partial correlation coefficients from Vinod [2014] as our third criterion in addition to two more criteria. We aggregate the three criteria into one unanimity index, UI in [-100; 100], (...) quantifying causal strengths associated with causal paths: Xi -> Xj, Xj -> Xi, and Xi Xj. (shrink)

The general definition of mental disorder stated in the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders seems to identify a mental disorder with a harmful dysfunction. However, the presence of distress or disability, which may be bracketed as the presence of harm, is taken to be merely usual, and thus not a necessary requirement: a mental disorder can be diagnosed as such even if there is no harm at all. In this paper, we focus on (...) the harm requirement. First, we clarify what it means to say that the harm requirement is not necessary for defining the general concept of mental disorder. In this respect, we briefly examine the two components of harm, distress and disability, and then trace a distinction between mental disorder tokens and mental disorder types. Second, we argue that the decision not to regard the harm requirement as a necessary criterion for mental disorder is tenable for a number of practical and theoretical reasons, some pertaining to conceptual issues surrounding the two components of harm and others pertaining to the problem of false negatives and the status of psychiatry vis-à-vis somatic medicine. However, we believe that the harm requirement can be maintained among the specific diagnostic criteria of certain individual mental disorders. More precisely, we argue that insofar as the harm requirement is needed among the specific diagnostic criteria of certain individual mental disorders, it should be unpacked and clarified. (shrink)

Much of the criticism of Stevens's criterion for permissible statistics as applied to measurement data results from a lack of clarity in Stevens's position. In this paper set-theoretical notions have been used to clarify that position. We define a sig-function as a function defined on numerical assignments. If A and R are empirical and numerical relational systems, respectively, then a sig-function F is constant on A with respect to R if, and only if, the value of F is the (...) same for all numerical assignments for A with respect to R. Using these notions we prove rigorously certain generalizations of Stevens's results. (shrink)

The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodness-of-fit (...) as the primary criterion for ‘best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. ‡I am grateful to Deborah Mayo and Clark Glymour for many valuable suggestions and comments on an earlier draft of the paper; estimating the Ptolemaic model was the result of Glymour's prompting and encouragement. †To contact the author, please write to: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, problems arise for using safety as a condition on knowledge: safety is not necessary for knowledge and cannot always explain the Gettier cases and cases of statistical evidence it is meant to address. In this paper, I argue for a new modal condition designed to capture the non-accidental relationship between facts and evidence required (...) for knowledge: causal safety. I argue that possible errors in belief can be captured by accounting for deviations in causal relationships and that there is a natural way to characterize which causal errors are relevant in an epistemic situation. Using this, I develop a causal analogue to safety, where one’s belief in p is causally safe if it is true in all causally relevant worlds where one believes p. Causal safety, I argue, can better explain the cases safety is meant to address and can avoid the arguments raised against the necessity of safety. (shrink)

A theory of true observation is developed as a generalization of the method of inter-observer agreement that scientists use to determine the objectivity and reliability of observations. A true observation is defined as a statement included in a set of statements in which there is statistical dependence and perfect agreement between the statements made by a universe of experimentally independent persons. Meaningfulness--the existence of an objective referent--for each form of statement included in the set is inferred from statistical (...) dependence, correct meaning within the universe of observers from the absence of disagreement. In this theory truth is inferred from a spatio-temporal pattern of statements as behavior rather than from the traditional correspondence between observation and object or logical relationships among statements. (shrink)

For the case of statistical theories, the criteria of explanation, prediction, and testability can all be viewed as particular instances of a more general evaluation scheme. Using the ideas of a gain matrix and expected gain from statistical decision theory, these three criteria can be compared in terms of the elements in their associated gain matrices. This analysis leads to (1) further understanding of the interrelationship between the current criteria, (2) the proposal of an ordering for the criteria, (...) and (3) the suggestion of a new criterion. (shrink)

It is shown here that the microcanonical ensemble for a system of noninteracting bosons and fermions contains a subensemble of state vectors for which all particles of the system are distinguishable. This “IQC” (inner quantum-classical) subensemble is therefore fully classical, except for a rather extreme quantization of particle momentum and position, which appears as the natural price that must be paid for distinguishability. The contribution of the IQC subensemble to the entropy is readily calculated, and the criterion for this (...) to be a good approximation to the exact entropy is a logarithmically strengthened form of the usual criterion for the validity of classical statistics in terms of the thermal de Broglie wavelength and the average volume per particle. Thus, it becomes possible to derive the Maxwell-Boltzmann distribution directly from the ensemble in the classical limit, using fully classical reasoning about the distinguishability of particles. The entropy is additive—theN! factor of the Boltzmann count cancels out in the course of the calculation, and the “N! paradox” is thereby resolved. The method of “correct Boltzmann counting” and the lowest term of the Wigner-Kirkwood series for the partition function are seen to be partly based on the IQC subensemble, and their partly nonclassical nature is clarified. The clear separation in the full ensemble of classical and nonclassical components makes it possible to derive the classical statistics of indistinguishable particles from their quantum statistics in a controlled, explicit way. This is particularly important for nonequilibrium theory. The treatment of molecular collisions along too-literally classical lines turns out to require exorbitantly high temperatures, although there are suggestions of indirect ways in which classical nonequilibrium theory might be justified at ordinary temperatures. The applicability of exact classical ergodic and mixing theory to systems at ordinary temperatures is called into question, although the general idea of coarse-graining is confirmed. The concepts on which the IQC idea is based are shown to give rise to a series development of thermostatistical quantities, starting with the distinguishable-particle approximation. (shrink)

Despite its widespread use in science, the Neyman-Pearson Theory of Statistics (NPT) has been rejected as inadequate by most philosophers of induction and statistics. They base their rejection largely upon what the author refers to as after-trial criticisms of NPT. Such criticisms attempt to show that NPT fails to provide an adequate analysis of specific inferences after the trial is made, and the data is known. In this paper, the key types of after-trial criticisms are considered and it is argued (...) that each fails to demonstrate the inadequacy of NPT because each is based on judging NPT on the grounds of a criterion that is fundamentally alien to NPT. As such, each may be seen to either misconstrue the aims of NPT, or to beg the question against it. (shrink)

Generics exhibit genericity, and though a theory of generics is closely connected to a theory of genericity, the two are distinct. They raise a host of interesting linguistic and philosophical issues, both separately and in their interaction. This chapter begins with a fairly manifest phenomenon one can observe in natural language. There is a range of sentences that, speaking intuitively, one can use to talk about kinds. It argues that there's no simple statistical criterion that systematically captures the (...) patterns of the truth and falsity of generics. Generics seem to not just be substantially independent of statistical facts in the world and at the time with respect to which they are evaluated. The chapter points‐out a likely form of context dependence in generics, and argues that on a quantificational approach to generics, the restrictor of the generic quantifier must be determined at least in part by the predicate at issue. (shrink)

Currently there is hardly any connection between philosophy of science and Artificial Intelligence research. We argue that both fields can benefit from each other. As an example of this mutual benefit we discuss the relation between Inductive-Statistical Reasoning and Default Logic. One of the main topics in AI research is the study of common-sense reasoning with incomplete information. Default logic is especially developed to formalise this type of reasoning. We show that there is a striking resemblance between inductive-statistical (...) reasoning and default logic. A central theme in the logical positivist study of inductive-statistical reasoning such as Hempels Criterion of Maximal Specificity turns out to be equally important in default logic. We also discuss to what extent the relevance of the results of Logical Positivism to AI research could contribute to a reevaluation of Logical Positivism in general. (shrink)

In this article we describe our approach to understanding wrongdoing in medical research and practice, which involves the statistical analysis of coded data from a large set of published cases. We focus on understanding the environmental factors that predict the kind and the severity of wrongdoing in medicine. Through review of empirical and theoretical literature, consultation with experts, the application of criminological theory, and ongoing analysis of our first 60 cases, we hypothesize that 10 contextual features of the medical (...) environment (including financial rewards, oversight failures, and patients belonging to vulnerable groups) may contribute to professional wrongdoing. We define each variable, examine data supporting our hypothesis, and present a brief case synopsis from our study that illustrates the potential influence of the variable. Finally, we discuss limitations of the resulting framework and directions for future research. (shrink)

Statistical criteria of fairness are formal measures of how an algorithm performs that aim to help us determine whether an algorithm would be fair to use in decision-making. In this paper, I introduce a new version of the criterion known as “Equalized Odds,” argue that it is a requirement of procedural fairness, and show that it is immune to a number of objections to the standard version.

The correspondence between Richard von Mises and George Pólya of 1919/20 contains reflections on two well-known articles by von Mises on the foundations of probability in the Mathematische Zeitschrift of 1919, and one paper from the Physikalische Zeitschrift of 1918. The topics touched on in the correspondence are: the proof of the central limit theorem of probability theory, von Mises' notion of randomness, and a statistical criterion for integer-valuedness of physical data. The investigation will hint at both the (...) fruitfulness and the limits of several of von Mises' notions such as ``collective'', ``distribution'' and ``complex adjuncts'' (characteristic functions) for further developments in probability theory and in ``directional statistics''. By pointing to the selectiveness of Pólya's criticism, the historical analysis shows the differing expectations of the two men with respect to the further development of the theory of probability and its applications. The paper thus gives a glimpse of the provisional state of the theory around 1920, before others such as P. Lévy (1886–1971) and A. N. Kolmogorov (1903–1987) stepped in and created a new paradigm for probability theory. (shrink)

Is there some general reason to expect organisms that have beliefs to have false beliefs? And after you observe that an organism occasionally occupies a given neural state that you think encodes a perceptual belief, how do you evaluate hypotheses about the semantic content that that state has, where some of those hypotheses attribute beliefs that are sometimes false while others attribute beliefs that are always true? To address the first of these questions, we discuss evolution by natural selection and (...) show how organisms that are risk-prone in the beliefs they form can be fitter than organisms that are risk-free. To address the second question, we discuss a problem that is widely recognized in statistics – the problem of over-fitting – and one influential device for addressing that problem, the Akaike Information Criterion (AIC). We then use AIC to solve epistemological versions of the disjunction and distality problems, which are two key problems concerning what it is for a belief state to have one semantic content rather than another. (shrink)

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.

Proper linear models are those in which predictor variables are given weights such that the resulting linear composite optimally predicts some criterion of interest; examples of proper linear models are standard regression analysis, discriminant function analysis, and ridge regression analysis. Research summarized in P. Meehl's book on clinical vs statistical prediction and research stimulated in part by that book indicate that when a numerical criterion variable is to be predicted from numerical predictor variables, proper linear models outperform (...) clinical intuition. Improper linear models are those in which the weights of the predictor variables are obtained by some nonoptimal method. The present article presents evidence that even such improper linear models are superior to clinical intuition when predicting a numerical criterion from numerical predictors. In fact, unit weighting is quite robust for making such predictions. The application of unit weights to decide what bullet the Denver Police Department should use is described; some technical, psychological, and ethical resistances to using linear models in making social decisions are considered; and arguments that could weaken these resistances are presented. (shrink)

The Akaike Information Criterion can be a valuable tool of scientific inference. This statistic, or any other statistical method for that matter, cannot, however, be the whole of scientific methodology. In this paper some of the limitations of Akaikean statistical methods are discussed. It is argued that the full import of empirical evidence is realized only by adopting a richer ideal of empirical success than predictive accuracy, and that the ability of a theory to turn phenomena into (...) accurate, agreeing measurements of causally relevant parameters contributes to the evidential support of the theory. This is illustrated by Newton's argument from orbital phenomena to the inverse-square law of gravitation. (shrink)

This paper develops a novel competition criterion for evaluating institutional schemes. Roughly, this criterion says that one institutional scheme is normatively superior to another to the extent that the former would engender more widespread political competition than the latter. I show that this criterion should be endorsed by both global egalitarians and their statist rivals, as it follows from their common commitment to the moral equality of all persons. I illustrate the normative import of the competition (...) class='Hi'>criterion by exploring its potential implications for the scope of egalitarian principles of distributive justice. In particular, I highlight the challenges it raises for global egalitarians' efforts to justify extending the scope of egalitarian justice beyond the state. (shrink)

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the Pauli exclusion principle, (...) the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory. (shrink)

The Akaike Information Criterion can be a valuable tool of scientific inference. This statistic, or any other statistical method for that matter, cannot, however, be the whole of scientific methodology. In this paper some of the limitations of Akaikean statistical methods are discussed. It is argued that the full import of empirical evidence is realized only by adopting a richer ideal of empirical success than predictive accuracy, and that the ability of a theory to turn phenomena into (...) accurate, agreeing measurements of causally relevant parameters contributes to the evidential support of the theory. This is illustrated by Newton's argument from orbital phenomena to the inverse-square law of gravitation. (shrink)

In Philosophical Problems of Statistical Inference, Seidenfeld argues that the Neyman-Pearson (NP) theory of confidence intervals is inadequate for a theory of inductive inference because, for a given situation, the 'best' NP confidence interval, [CIλ], sometimes yields intervals which are trivial (i.e., tautologous). I argue that (1) Seidenfeld's criticism of trivial intervals is based upon illegitimately interpreting confidence levels as measures of final precision; (2) for the situation which Seidenfeld considers, the 'best' NP confidence interval is not [CIλ] as (...) Seidenfeld suggests, but rather a one-sided interval [CI0]; and since [CI0] never yields trivial intervals, NP theory escapes Seidenfeld's criticism entirely; (3) Seidenfeld's criterion of non-triviality is inadequate, for it leads him to judge an alternative confidence interval, [CI alt. ], superior to [CIλ] although [CI alt. ] results in counterintuitive inferences. I conclude that Seidenfeld has not shown that the NP theory of confidence intervals is inadequate for a theory of inductive inference. (shrink)

The study of cultural evolution has taken on an increasingly interdisciplinary and diverse approach in explicating phenomena of cultural transmission and adoptions. Inspired by this computational movement, this study uses Bayesian networks analysis, combining both the frequentist and the Hamiltonian Markov chain Monte Carlo (MCMC) approach, to investigate the highly representative elements in the cultural evolution of a Vietnamese city’s architecture in the early 20th century. With a focus on the façade design of 68 old houses in Hanoi’s Old Quarter (...) (based on 78 data lines extracted from 248 photos), the study argues that it is plausible to look at the aesthetics, architecture, and designs of the house façade to find traces of cultural evolution in Vietnam, which went through more than six decades of French colonization and centuries of sociocultural influence from China. The in-depth technical analysis, though refuting the presumed model on the probabilistic dependency among the variables, yields several results, the most notable of which is the strong influence of Buddhism over the decorations of the house façade. Particularly, in the top 5 networks with the best Bayesian Information Criterion (BIC) scores and p<0.05, the variable for decorations (DC) always has a direct probabilistic dependency on the variable B for Buddhism. The paper then checks the robustness of these models using Hamiltonian MCMC method and find the posterior distributions of the models’ coefficients all satisfy the technical requirement. Finally, this study suggests integrating Bayesian statistics in the social sciences in general and for the study of cultural evolution and architectural transformation in particular. (shrink)

A general criterion for the theory of belief revision is that when we revise a state of belief by a sentence A, as much of the old information as possible should be retained in the revised state of belief. The motivating idea in this paper is that if a belief B is irrelevant to A, then B should still be believed in the revised state. The problem is that the traditional definition of statistical relevance suffers from some serious (...) shortcomings and cannot be used as a tool for defining belief revision processes. In particular, the traditional definition violates the requirement that if A is irrelevant to C and B is irrelevant to C, then A&B is irrelevant to C. In order to circumvent these drawbacks, I develop an amended notion of relevance which has the desired properties. On the basis of the new definition, I outline how it can be used to simplify a construction of a belief revision method. (shrink)

A generalized reality criterion which attributes physical properties to statistical ensembles is used in order to deduce an inequality which is violated by quantum mechanics in realistic conditions. This new form of the Einstein-Podolsky-Rosen paradox is developed exclusively from the reality criterion and from separability without any use of the previously introduced restrictive assumptions about the probabilistic scheme.

Taking multidimensional ethics scale approach, this article describes an empirical survey of top managers’ moral decision-making patterns and their change from 1994 to 2004 during morally problematic situations in the Finnish context. The survey questionnaire consisted of four moral dilemmas and a multidimensional scale with six ethical dimensions: justice, deontology, relativism, utilitarianism, egoism and female ethics. The managers evaluated their decision-making in the problems using the multidimensional ethics scale. Altogether 880 questionnaires were analysed statistically. It is concluded that relying on (...) the utilitarian principles is a core ethical evaluation criterion amongst top business managers in Finland. This study proves that managers’ moral decision-making patterns change over time. According to the results of this research, managers’ moral decision-making became more multidimensional during the study period. The change is explained by the inclusion of female ethics items in the scale which allows managers to show more diversity in their decision- making, the change in the Finnish economic context from depression to economic prosperity and growth during the study period, which is conducive to the spread of post materialist values, such as the importance of social relations and the increasing public discussion of the importance ethical issues in business. (shrink)

This article describes abductions as special patterns of inference to the best explanation whose structure determines a particularly promising abductive conjecture and thus serves as an abductive search strategy. A classification of different patterns of abduction is provided which intends to be as complete as possible. An important distinction is that between selective abductions, which choose an optimal candidate from given multitude of possible explanations, and creative abductions, which introduce new theoretical models or concepts. While selective abduction has dominated the (...) literature, creative abductions are rarely discussed, although they are essential in science. The article introduces several kinds of creative abductions, such as theoretical model abduction, common cause abduction and statistical factor analysis, and illustrates them by various real case examples. It is suggested to demarcate scientifically fruitful abductions from purely speculative abductions by the criterion of causal unification. (shrink)

In what follows I will discuss an example of the Duhem-Quine problem in which Pr(H A), Pr(A H), and Pr(OI +H& ?A) (where H is the hypothesis, A the auxiliary assumptions, and O the observational prediction) can be construed objectively; however, only some of those quantities are relevant to the analysis that I provide. The example involves medical diagnosis. The goal is to test the hypothesis that someone has tuberculosis; the auxiliary assumptions describe the er- ror characteristics of the test (...) procedure. Although it can make sense to talk about the objective probability that someone (randomly drawn from a given population) has tuberculosis and it also can make sense to talk about the objective probability that a test procedure has a certain set of error characteristics, neither of these quantities will enter into the analysis. The analysis proceeds entirely via likelihoods, what one needs to consider is just the probability of the observations conditional on four conjunctions of the form (?H & +A).' It is a special feature of the example that all four of these conjunctions are simple statistical hypotheses in the technical sense that each unambigu-ously confers a probability on the observations.'o After describing how the likelihood concept applies to the example concerning medical diagnosis, I will show how similar patterns can arise in the context of a second inferential framework-that of H. Akaike's criterion of model selection;" this time the example will involve phylogenetic inference. (shrink)

Wittgenstein offers three objections to the idea of aesthetics as a branch of psychology: (i) Statistical data about people’s preferences have no normative force. (ii) Artistic value is not instrumental value, a capacity to produce independently identifiable – and scientifically measurable – psychological effects. (iii) While psychological investigations may bring to light the causes of aesthetic preferences, they fail to provide reasons for them. According to Wittgenstein, aesthetic explanations (unlike scientific explanations) are poignant synoptic representations of aspects of a (...) work, and the criterion of success of an aesthetic explanation is that it satisfies the addressee. He repeatedly remarked that they resemble philosophical explanations, which also try to dispel puzzlement or confusion. The difference, however, is that whereas in philosophy we deal with general conceptual problems, aesthetic explanations typically concern individual responses to particular works of art. (shrink)

The present paper studies a specific way of addressing the question whether the laws involving the basic constituents of nature are statistical. While most German physicists, above all Planck, treated the issues of determinism and causality within a Kantian framework, the tradition which I call Vienna Indeterminism began from Mach’s reinterpretation of causality as functional dependence. This severed the bond between causality and realism because one could no longer avail oneself of a priori categories as a criterion for (...) empirical reality. Hence, an independent reality criterion had to be sought, a problem which all three physicists to be studied solved in different ways that were mainly conditioned by their different concepts of probability. In order to prevent a dissipation of intuited facts, Mach had to resort to a principle of unique determination as his reality criterion, especially when discussing the Principle of Least Action. Giving theories more independence, Boltzmann understood atomism as property reduction to precisely defined theoretical entities and their interactions. While this served as a relative reality criterion, he also advocated a constructivist one because atomism was already implied by our finitary reasoning power. Finally, Exner contemplated the idea that all apparently deterministic laws are only a macroscopic limit of an irreducible indeterminism, because by adopting the frequency interpretation, observable collectives could be considered as the real basic entities. (shrink)

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error (...) probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies. Introduction and overview 1.1 Behavioristic and inferential rationales for Neyman–Pearson (N–P) tests 1.2 Severity rationale: induction as severe testing 1.3 Severity as a meta-statistical concept: three required restrictions on the N–P paradigm Error statistical tests from the severity perspective 2.1 N–P test T(): type I, II error probabilities and power 2.2 Specifying test T() using p-values Neyman's post-data use of power 3.1 Neyman: does failure to reject H warrant confirming H? Severe testing as a basic concept for an adequate post-data inference 4.1 The severity interpretation of acceptance (SIA) for test T() 4.2 The fallacy of acceptance (i.e., an insignificant difference): Ms Rosy 4.3 Severity and power Fallacy of rejection: statistical vs. substantive significance 5.1 Taking a rejection of H0 as evidence for a substantive claim or theory 5.2 A statistically significant difference from H0 may fail to indicate a substantively important magnitude 5.3 Principle for the severity interpretation of a rejection (SIR) 5.4 Comparing significant results with different sample sizes in T(): large n problem 5.5 General testing rules for T(), using the severe testing concept The severe testing concept and confidence intervals 6.1 Dualities between one and two-sided intervals and tests 6.2 Avoiding shortcomings of confidence intervals Beyond the N–P paradigm: pure significance, and misspecification tests Concluding comments: have we shown severity to be a basic concept in a N–P philosophy of induction? (shrink)

One conception of underdetermination is that it corresponds to the impossibility of reliable inquiry. In other words, underdetermination is defined to be the situation where, given a set of background assumptions and a space of hypotheses, it is logically impossible for any hypothesis selection method to meet a given reliability standard. From this perspective, underdetermination in a given subject of inquiry is a matter of interplay between background assumptions and reliability or success criteria. In this paper I discuss underdetermination in (...) causal inference along this line. In particular I will analyze several success criteria that can be applied to causal inference from statistical regularities. The criteria center on the notions of consistency in mathematical statistics. For each criterion I present its epistemic implication in terms of simple conditions under which the criterion cannot possibly be met. I then investigate which of the familiar principles and their variants in the literature, if adopted as background assumptions, are sufficient to overcome different levels of underdetermination induced by the success criteria. “亚决定性”是知识论和科学哲学中一个重要的概念。对这个概念的一种阐释是把它对应于可靠探索的不可能性。就是说，在一个（经验）问题中，给定一些公设和一些供选择的理论或假说，如果逻辑上不可能找到一种理论选择 的方法能满足一定的可靠或成功标准，那么相对于这个标准就存在亚决定性。从这个观点看，亚决定性总是相对于一个问题设定，尤其是公设和成功标准而言的。本文从这个角度对近来的统计因果推理研究作一番梳理。首先，基 于数理统计中的一致性概念，我会讨论和分析一系列可应用于因果推理的成功标准。对每一个标准，我会用一个相对简单的条件来刻画它对应的亚决定性。然后我对文献里一部分重要的结果作一个综述，以澄清什么样的公设可以 消除什么样的亚决定性。. (shrink)

In this paper, we derive necessary and sufficient conditions on team based tasks in order for a selection criterion applied to individuals to produce optimal teams. We assume only that individuals have types and that a team’s performance depends on its size and the type composition of its members. We first derive the selection principle which states that if a selection criterion exists, it must rank types by homogeneous team performance, the performance of a team consisting only of (...) that type. We then prove that a selection criterion exists if and only if replacing the team’s lowest ranked type, as measured by homogeneous team performance, with a higher ranked type increases team performance. Finally, we show that the replace the lowest ranked property rules out most common types of team complementarities, including benefits to diverse types and types that fill structural holes. (shrink)

Algorithmic predictions are promising for insurance companies to develop personalized risk models for determining premiums. In this context, issues of fairness, discrimination, and social injustice might arise: Algorithms for estimating the risk based on personal data may be biased towards specific social groups, leading to systematic disadvantages for those groups. Personalized premiums may thus lead to discrimination and social injustice. It is well known from many application fields that such biases occur frequently and naturally when prediction models are applied to (...) people unless special efforts are made to avoid them. Insurance is no exception. In this paper, we provide a thorough analysis of algorithmic fairness in the case of insurance premiums. We ask what “fairness” might mean in this context and how the fairness of a premium system can be measured. For this, we apply the established fairness frameworks of the fair machine learning literature to the case of insurance premiums and show which of the existing fairness criteria can be applied to assess the fairness of insurance premiums. We argue that two of the often-discussed group fairness criteria, independence (also called statistical parity or demographic parity) and separation (also known as equalized odds), are not normatively appropriate for insurance premiums. Instead, we propose the sufficiency criterion (also known as well-calibration) as a morally defensible alternative that allows us to test for systematic biases in premiums towards certain groups based on the risk they bring to the pool. In addition, we clarify the connection between group fairness and different degrees of personalization. Our findings enable insurers to assess the fairness properties of their risk models, helping them avoid reputation damage resulting from potentially unfair and discriminatory premium systems. (shrink)