Bell’s theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an assumption called Statistical Independence. Violations of Statistical Independence are commonly interpreted as correlations between the measurement settings and the hidden variables. Such correlations have been discarded as “fine-tuning” or a “conspiracy”. We here point out that the common interpretation is at best (...) physically ambiguous and at worst incorrect. The problem with the common interpretation is that Statistical Independence might be violated because of a non-trivial measure in state space, a possibility we propose to call “supermeasured”. We use Invariant Set Theory as an example of a supermeasured theory that violates the Statistical Independence assumption in Bell’s theorem without requiring correlations between hidden variables and measurement settings. (shrink)

There is little empirical evidence showing a direct link between a capacity for statistical learning (SL) and proficiency with natural language. Moreover, discussion of the role of SL in language acquisition has seldom focused on literacy development. Our study addressed these issues by investigating the relationship between SL and reading ability in typically developing children and healthy adults. We tested SL using visually presented stimuli within a triplet learning paradigm and examined reading ability by administering the Wide Range Achievement (...) Test (WRAT-4; Wilkinson & Robertson, 2006). A total of 38 typically developing children (mean age of 9;5 years, range 6;4–12;5) and 37 healthy adults (mean age of 21 years, range 18–34) were assessed. In children, SL was significantly related to reading ability. Importantly, this relationship was independent of grade and also age. The adult data, too, revealed that SL was significantly related to reading ability. A regression analysis of the combined child and adult data revealed that SL accounted for a unique amount of variance in reading ability, after age and attention had been taken into consideration. For the first time, this study provides empirical evidence that a capacity for more effective SL is related to higher reading ability in the general population. (shrink)

Of the many proposals for inferring genetic regulatory structure from microarray measurements of mRNA transcript hybridization, several aim to estimate regulatory structure from the associations of gene expression levels measured in repeated samples. The repeated samples may be from a single experimental condition, or from several distinct experimental conditions; they may be “equilibrium” measurements or time series; the associations may be estimated by correlation coefficients or by conditional frequencies (for discretized measurements) or by some other statistic. This paper describes two (...) elementary statistical difficulties for all such procedures, no matter whether based on Bayesian updating, conditional independence testing, or other machine learning procedures such as simulated annealing or neural net pruning. One difficulty obtains if large numbers of cells are aggregated in a measurement of expression levels from a common population of cells; the other obtains if small numbers of cells are aggregated or if samples are separately aggregated over different populations of cells. (shrink)

Causation is a macroscopic phenomenon. The temporal asymmetry displayed by causation must somehow emerge along with other asymmetric macroscopic phenomena like entropy increase and the arrow of radiation. I shall approach this issue by considering ‘causal inference’ techniques that allow causal relations to be inferred from sets of observed correlations. I shall show that these techniques are best explained by a reduction of causation to structures of equations with probabilistically independent exogenous terms. This exogenous probabilistic independence imposes a recursive (...) order on these equations and a consequent distinction between dependent and independent variables that lines up with the temporal asymmetry of causation. (shrink)

The projection latticesP(ℳ1),P(ℳ2) of two von Neumann subalgebras ℳ1, ℳ2 of the von Neumann algebra ℳ are defined to be logically independent if A ∧ B≠0 for any 0≠AεP(ℳ1), 0≠BP(ℳ2). After motivating this notion in independence, it is shown thatP(ℳ1),P(ℳ2) are logically independent if ℳ1 is a subfactor in a finite factor ℳ andP(ℳ1),P(ℳ2 commute. Also, logical independence is related to the statistical independence conditions called C*-independence W*-independence, and strict locality. Logical independence ofP(ℳ1,P(ℳ2 (...) turns out to be equivalent to the C*-independence of (ℳ1,ℳ2) for mutually commuting ℳ1,ℳ2 and it is shown that if (ℳ1,ℳ2) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(ℳ1,P(ℳ2 are logically independent in the following cases: ℳ is a finite-dimensional full-matrix algebra and ℳ1,ℳ2 are C*-independent; (ℳ1,ℳ2) is a W*-independent pair; ℳ1,ℳ2 have the property of strict locality. (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)

The statistical aspects of quantum explanation are intrinsic to quantum physics; individual quantum events are created in the interactions associated with observation and are not describable by predictive theory. The superposition principle shows the essential difference between quantum and non-quantum physics, and the principle is exemplified in the classic single-photon two-slit interference experiment. Recently Mandel and Pfleegor have done an experiment somewhat similar to the optical single-photon experiment but with two independently operated lasers; interference is obtained even with beam (...) intensity so small that only one photon is in the apparatus at a time. The result can be understood in terms of the superposition of states; or, in terms of the Uncertainty Principle, which is found to forbid the determination of which of the two lasers is the source of a given photon (if conditions for interference are to obtain). The Mandel-Pfleegor experiment gives a physical argument against the continuous localization of a photon that is assumed in the hidden variable theories and therefore gives further support for the generally accepted view that an observed entity (observed state) is created in the observation event. This aspect of quantum physics implies a subjectivism on the level of individual quantum-level occurrences, since there is in quantum theory no basis for asserting the existence of the event independently of observation of it. Extension of this subjectivism to large scale, non-quantum phenomena falls within the principles of quantum theory; counter considerations that argue against such an extension are noted. (shrink)

To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but (...) we show that if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation. (shrink)

Of the many proposals for inferring genetic regulatory structure from microarray measurements of mRNA transcript hybridization, several aim to estimate regulatory structure from the associations of gene expression levels measured in repeated samples. The repeated samples may be from a single experimental condition, or from several distinct experimental conditions; they may be “equilibrium” measurements or time series; the associations may be estimated by correlation coefficients or by conditional frequencies (for discretized measurements) or by some other statistic. This paper describes two (...) elementary statistical difficulties for all such procedures, no matter whether based on Bayesian updating, conditional independence testing, or other machine learning procedures such as simulated annealing or neural net pruning. One difficulty obtains if large numbers of cells are aggregated in a measurement of expression levels from a common population of cells; the other obtains if small numbers of cells are aggregated or if samples are separately aggregated over different populations of cells. (shrink)

We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.

Christopher Boorse’s bio-statistical theory of health and disease argues that the central discipline on which theoretical medicine relies is physiology. His theory has been much discussed but little has been said about its focus on physiology or, conversely, about the role that other biomedical disciplines may play in establishing a theoretical concept of health. Since at least the 1950s, epidemiology has gained in strength and legitimacy as an independent medical science that contributes to our knowledge of health and disease. (...) Indeed, it not only provides important information about disease distribution and aetiology, but the risk-factor approach it employs seems to challenge BST’s binary conception of health and disease. The objective of the article is to show, firstly, how important information deriving from descriptive and analytical epidemiology forms part of our contemporary medical concepts of health and disease, and secondly, that these elements are not taken into account by BST in a satisfactory way. The article’s central contention, therefore, is that if the project of defining the theoretical concept of health is to be maintained, more importance should be accorded to the contribution made by epidemiology—alongside physiology—in defining health. (shrink)

A fundamental question in visual neuroscience is: Why are the response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input, and it proceeds by modeling statistical regularities in ecologically valid visual input (natural images). A seminal model was linear sparse coding, which is equivalent to independent component analysis (ICA), and provided a very good description of the receptive fields of simple cells. Further models based on modeling (...) residual dependencies of the ‘‘independent” components have later been introduced. These models lead to emergence of further properties of visual neurons: the complex cell receptive fields, the spatial organization of the cells, and some surround suppression and Gestalt effects. So far, these models have concentrated on the response properties of neurons, but they hold great potential to model various forms of inference and learning. (shrink)

Assumptions of stochastic independence are crucial to statistical models in science. Under what circumstances is it reasonable to suppose that two events are independent? When they are not causally or logically connected, so the standard story goes. But scientific models frequently treat causally dependent events as stochastically independent, raising the question whether there are kinds of causal connection that do not undermine stochastic independence. This paper provides one piece of an answer to this question, treating the simple (...) case of two tossed coins with and without a midair collision. (shrink)

The laws of social development are objective in content and, in contrast to the laws of nature, are manifested and function only through the activity of human beings. The development of all spheres of human activity, in turn, cannot be conceived of as independent of the will, consciousness, moods and beliefs, propensities and preferences of human beings, nor as independent of the effectiveness of forms of social organization, etc. The social specificity of laws of social development in turn defines another (...) feature of these laws, namely, their statistical nature. History and social practice persuasively demonstrate that the laws of social development in turn defines another feature of these laws, namely, their statistical nature. History and social practice persuasively demonstrate that the laws of social development, functioning either in all socioeconomic formations or in only some of them , or laws operating within only one of these formations are of a statistical nature. Even when the conditions of life of societies within a particular socioeconomic formation are the same, the results of the operation of any law of social development are never absolutely identical. This is graphically evident in an analysis of the operation of the law of surplus value, the laws of class struggle, or the law of social revolution, especially its operation under the conditions of the contemporary world revolutionary process. We need only point out the variety of nuances in the ultimate results of the operation of the law of social revolution after the Second World War, when socialist countries and countries with a socialist orientation emerged. (shrink)

This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts (...) on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students. Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual. (shrink)

This paper argues that cosmopolitan law has been more successfully achieved not by appeal to a supra-state authority or community, but by the development of features of existing treaty law. Specifically, it shows how the International Criminal Court's jurisdiction over serious human rights violations has been extended to the citizens and territories of non-member states – and even to otherwise immune state officials – not by challenging the sovereignty of non-member states directly, but on the basis of member states’ own (...) territorial sovereignty and the universal jurisdiction which they delegate to the Court and to the United Nations Security Council. In light of this, the authors argue that cosmopolitanism is better conceived not as invoking an independent sense of global community that supersedes and constrains state sovereignty, but as an immanent, contingent and creative development of statist criminal law itself, rooted in its principles of state sovereignty. (shrink)

The use of artificial intelligence (AI) to aid legal decision making has become prominent. This paper investigates the use of AI in a critical issue in employment law, the determination of a worker’s status—employee vs. independent contractor—in two common law countries (the U.S. and Canada). This legal question has been a contentious labor issue insofar as independent contractors are not eligible for the same benefits as employees. It has become an important societal issue due to the ubiquity of the gig (...) economy and the recent disruptions in employment arrangements. To address this problem, we collected, annotated, and structured the data for all Canadian and Californian court cases related to this legal question between 2002 and 2021, resulting in 538 Canadian cases and 217 U.S. cases. In contrast to legal literature focusing on complex and correlated characteristics of the employment relationship, our statistical analyses of the data show very strong correlations between the worker’s status and a small subset of quantifiable characteristics of the employment relationship. In fact, despite the variety of situations in the case law, we show that simple, off-the-shelf AI models classify the cases with an out-of-sample accuracy of more than 90%. Interestingly, the analysis of misclassified cases reveals consistent misclassification patterns by most algorithms. Legal analyses of these cases led us to identify how equity is ensured by judges in ambiguous situations. Finally, our findings have practical implications for access to legal advice and justice. We deployed our AI model via the open-access platform, https://MyOpenCourt.org/, to help users answer employment legal questions. This platform has already assisted many Canadian users, and we hope it will help democratize access to legal advice to large crowds. (shrink)

Statistical learning is often taken to lie at the heart of many cognitive tasks, including the acquisition of language. One particular task in which probabilistic models have achieved considerable success is the segmentation of speech into words. However, these models have mostly been tested against English data, and as a result little is known about how a statistical learning mechanism copes with input regularities that arise from the structural properties of different languages. This study focuses on statistical (...) word segmentation in Arabic, a Semitic language in which words are built around consonantal roots. We hypothesize that segmentation in such languages is facilitated by tracking consonant distributions independently from intervening vowels. Previous studies have shown that human learners can track consonant probabilities across intervening vowels in artificial languages, but it is unknown to what extent this ability would be beneficial in the segmentation of natural language. We assessed the performance of a Bayesian segmentation model on English and Arabic, comparing consonant-only representations with full representations. In addition, we examined to what extent structurally different proto-lexicons reflect adult language. The results suggest that for a child learning a Semitic language, separating consonants from vowels is beneficial for segmentation. These findings indicate that probabilistic models require appropriate linguistic representations in order to effectively meet the challenges of language acquisition. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, and Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects (...) can be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave- functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave- function in this interpretation is best regarded as ψ-ontic and incomplete.

According to Lange,?Really Statistical explanations? constitute an important kind of non-causalscientific explanation. However, Roski has argued that all alleged RS explanations are either causalexplanations or not explanations at all. In so arguing, Roski has invoked Kahneman?s interpretation of onealleged RS explanation. I employ Roski?s arguments as an opportunity to elaborate and defend RS explanations. Iargue that?RS explanations? genuinely explain rather than deny the presuppositions of why-questions. I argue thatthe RS model is not excessively permissive in allowing some explanations to (...) work purely statistically rather than bydescribing causal relations. I argue that Roski?s view that some?RS explanations? operate by describing causalrelations fails to capture the kind of explanatory insight that RS explanations provide. I elaborate the notion of a?characteristically statistical phenomenon? that figures in the RS model and thereby explain how an RS explanationreveals that its explanandum is independent of any causal facts or specific chances, but rather depends only on ageneric sort of arrangement of chances. Finally, I argue that Roski misinterprets Kahneman, who actually holds thatthe explanation he discusses is a non-causal explanation that nicely fits the RS model. RS explanations constitutean important kind of non-causal scientific explanation. (shrink)

An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with a given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can emerge. However, the concept does not allow philosophically crucial free will decisions. The quantum world and its conjugate evolve independently, and one can replace fixed final states on each side just with a common matching one. This change allows for external manipulations done in (...) the quantum world and its conjugate, which do not otherwise alter the basic quantum dynamics. In a big bang/big crunch universe, the expanding part can be attributed to the quantum world and the contracting one to the conjugate one. The obtained bi-linear picture has several noteworthy consequences. (shrink)

An important appeal of strategy-proofness is the robustness that it implies. Under a strategy-proof voting rule, every individual has an optimal strategy independently of the behavior of all other voters, namely truth-telling. In particular, optimal play is robust with respect to the beliefs voters may have about the type and the behavior of the other voters. Following Blin and Satterthwaite (Economet J Economet Soc 45(4):881–888, 1977), we call this logically weaker property “belief-independence.” In this paper, we give a number (...) of examples of voting rules that are belief-independent but not strategy-proof. However, we also show that belief-independence implies strategy-proofness under a few natural additional conditions. The notion of belief-independence naturally leads to a the strengthening of strategy-proofness to “robust” strategy-proofness which requires that no voter whose true preference may come from a restricted domain can benefit by submitting any unrestricted preference ordering given any unrestricted preference profile for all other voters. There are examples of strategy-proof voting rules (on a restricted domain) that are not robustly strategy-proof, but under natural additional conditions the two properties are shown to be equivalent. (shrink)

Unsatisfied with stringent statistical theories of information such as Dretske's unity theory, Millikan (2001, 2004, 2007) and Shea (2007) have independently introduced ?soft? statistical notions of information. I argue here that these soft statistical notions do not present viable alternative senses of information to that proposed by Dretske. Furthermore, what appears to be the primary motivation for ?soft? information can be undercut.

One approach to validating simulation models is to formally compare model outputs with independent data. We consider such model validation from the point of view of Frequentist statistics. A range of estimates and tests of goodness of fit have been advanced. We review these approaches, and demonstrate that some of the tests suffer from difficulties in interpretation because they rely on the null hypothesisHypothesis that the model is similar to the observationsObservations. This reliance creates two unpleasant possibilities, namely, a model (...) could be spuriously validated when dataData are too few, or inappropriately rejected when data are too many. Finally, these tests do not allow a principled declaration of what a reasonable level of difference would be considering the purposes to which the model will be put. We consider equivalence tests, and demonstrate that they do not suffer from the previously identified shortcomings. We provide two case studies to illustrate the claims of the chapter. (shrink)

Although the subjective expected utility (SEU) theory is more than 60 years old, it was recently discovered by Hartmann (Econometrica 88(1):203–205, 2020, https://doi.org/10.3982/ECTA17428) that one of the original seven postulates is redundant, i.e., it is implied by the other six postulates. In this brief communication, we show that this redundant axiom is the only one that is implied by the other axioms, thereby establishing that the remaining six postulates form an independent axiomatic system. This result further streamlines the preference assumptions (...) underlying the SEU theory. (shrink)

Madole & Harden argue that the Mendelian reshuffling of genes and genomes is analogous to randomised controlled trials. We are not convinced by their arguments. First, their recipe for meeting the demands on randomised experiments is inherently inconsistent. Second, disequilibrium across chromosomes conflicts with their assumption of statistical independence. Third, the genome-wide association study (GWAS) method has many pitfalls, including low repeatability.

Relying on some auxiliary assumptions, usually considered mild, Bell’s theorem proves that no local theory can reproduce all the predictions of quantum mechanics. In this work, we introduce a fully local, superdeterministic model that by explicitly violating ‘settings independence’—one of these auxiliary assumptions, requiring statistical independence between measurement settings and systems to be measured—is able to reproduce all the predictions of quantum mechanics. Moreover, we show that contrary to widespread expectations, our model can break settings independence (...) without an initial state that is too complex to handle, without visibly losing all explanatory power, and without outright nullifying all of experimental science. Still, we argue that our model is unnecessarily complicated and does not offer true advantages over its non-local competitors. We conclude that while our model does not appear to be a viable contender to its non-local counterparts, it provides the ideal framework to advance the debate over violations of statistical independence via the superdeterministic route. (shrink)

In order to extract the regularities underlying a continuous sensory input, the individual elements constituting the stream have to be encoded and their transitional probabilities (TPs) should be learned. This suggests that variance in statistical learning (SL) performance reflects efficiency in encoding representations as well as efficiency in detecting their statistical properties. These processes have been taken to be independent and temporally modular, where first, elements in the stream are encoded into internal representations, and then the co‐occurrences between (...) them are computed and registered. Here, we entertain a novel hypothesis that one unifying construct—the rate of information in the sensory input—explains learning performance. This theoretical approach merges processes related to encoding of events and those related to learning their regularities into a single computational principle. We present data from two large‐scale experiments with over 800 participants tested in support for this hypothesis, showing that rate of information in a visual stream clearly predicts SL performance, and that similar rate of information values leads to similar SL performance. We discuss the implications for SL theory and its relation to regularity learning. (shrink)

The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can (...) be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle. (shrink)

There are two motivations commonly ascribed to historical actors for taking up statistics: to reduce complicated data to a mean value (e.g., Quetelet), and to take account of diversity (e.g., Galton). Different motivations will, it is assumed, lead to different methodological decisions in the practice of the statistical sciences. Karl Pearson and W. F. R. Weldon are generally seen as following directly in Galton’s footsteps. I argue for two related theses in light of this standard interpretation, based on a (...) reading of several sources in which Weldon, independently of Pearson, reflects on his own motivations. First, while Pearson does approach statistics from this "Galtonian" perspective, he is, consistent with his positivist philosophy of science, utilizing statistics to simplify the highly variable data of biology. Weldon, on the other hand, is brought to statistics by a rich empiricism and a desire to preserve the diversity of biological data. Secondly, we have here a counterexample to the claim that divergence in motivation will lead to a corresponding separation in methodology. Pearson and Weldon, despite embracing biometry for different reasons, settled on precisely the same set of statistical tools for the investigation of evolution. (shrink)

PurposeThis study investigated whether the ability to utilize statistical regularities from fluent speech and map potential words to meaning at 18-months predicts vocabulary at 18- and again at 24-months.MethodEighteen-month-olds were exposed to an artificial language with statistical regularities within the speech stream, then participated in an object-label learning task. Learning was measured using a modified looking-while-listening eye-tracking design. Parents completed vocabulary questionnaires when their child was 18-and 24-months old.ResultsAbility to learn the object-label pairing for words after exposure to (...) the artificial language predicted productive vocabulary at 24-months and amount of vocabulary change from 18- to 24 months, independent of non-verbal cognitive ability, socio-economic status and/or object-label association performance.ConclusionEighteen-month-olds’ ability to use statistical information derived from fluent speech to identify words within the stream of speech and then to map the “words” to meaning directly predicts vocabulary size at 24-months and vocabulary change from 18 to 24 months. The findings support the hypothesis that statistical word segmentation is one of the important aspects of word learning and vocabulary acquisition in toddlers. (shrink)

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It (...) is shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (shrink)

Normic laws have the form "if A, then normally B." They are omnipresent in everyday life and non-physical 'life' sciences such as biology, psychology, social sciences, and humanities. They differ significantly from ceteris-paribus laws in physics. While several authors have doubted that normic laws are genuine laws at all, others have argued that normic laws express a certain kind of prototypical normality which is independent of statistical majority. This paper presents a foundation for normic laws which is based on (...) generalized evolution theory and explains their omnipresence, lawlikeness, and reliability. It is argued that the fact that normic laws are a product of evolution must establish a systematic connection between prototypical and statistical normality. (shrink)

This theoretical note proposes a two-dimensional cognitive architecture for dual-process theories of reasoning and decision making. Evans (2007b, 2008a, 2009) distinguishes between two types of dual-processing models: parallel-competitive , in which both types of processes operate in parallel, and default-interventionist , in which heuristic processes precede the analytic processes. I suggest that this temporal dimension should be enhanced with a functional distinction between interactionist architecture, in which either type of process influences the content and valence of the other, and independent (...) architecture, in which they do not. Override architecture is a special case of the latter, which postulates statistical interaction, but no interaction of valence and content. I show that this added dimensional distinction casts doubt on two assumptions of statistical modelling that Evans makes: independence and linearity. However, Evans' (2007b) point, that statistical modelling is underspecified vis- -vis the verbal theory, is given further support. The functional dimension is crucial to interpreting the statistical model, as well as to theoretical understanding of the cognitive architecture and its educational applications. (shrink)

Let an unbiased coin be used to form an ω-sequence S of independent tosses. Let N be the positive integers. The finite initial segment of length n ∈ N is denoted by Sn (thus, S1 holds exactly the first toss). For n ∈ N , let Hn be the proportion of heads that show up in Sn.

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector potential (...) that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)

In this paper, we provide two novel expected utility theorems by suitably adjusting the independence and continuity axioms. Our first theorem characterizes expected utility preferences using weak versions of the independence axiom (with varying mixture weights) and a new weak continuity axiom. Our second theorem characterizes these preferences using weaker versions of the independence axiom (with mixture weights fixed at 1/2) and a strong topological continuity axiom. We provide useful examples to illustrate the tightness of these characterizations.

Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support for this approach. In our work, a geometric approach to quantum indistinguishability is introduced which allows the treatment of singlevaluedness of wave functions in a global, model independent way.

Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.

Two key ideas of scientific explanation - explanations as causal information and explanation as unification - have frequently been set into mutual opposition. This paper proposes a "dialectical solution" to this conflict, by arguing that causal explanations are preferable to non-causal explanations because they lead to a higher degree of unification at the level of the explanation of statistical regularities. The core axioms of the theory of causal nets are justified because they give the best if not the only (...) unifying explanation of two statistical phenomena: screening off and linking up. Alternative explanation attempts are discussed and it is shown why they don't work. It is demonstrated that not the core of TC but extended versions of TC have empirical content, by means of which they can generate independently testable predictions. (shrink)

Two key ideas of scientific explanation−explanation as causal information and explanation as unification-have frequently been set into mutual opposition. This paper proposes a “dialectical solution” to this conflict, by arguing that causal explanations are preferable to non-causal ones, because they lead to a higherdegree of unification at the level of explaining statistical regularities. The core axioms of the theory of causal nets (TC) are justified because they offer the best if not the only unifying explanation of two statistical (...) phenomena: screening off and linking up. Alternative explanations of the two phenomena are discussed and it isshown why they don’t work. It is demonstrated that although the core axioms of TC are empirically vacuous, extended versions of TC have empirical content by means of which they can generate independently testable predictions.Con frecuencia se han planteado como contrapuestas dos ideas clave en la explicacion cientifica (explicacion como informacion causal y explicacion como unificacion). El presente articulo propone una “solucion dialectica” argumentando que las explicaciones causales son preferibles a las no-causales porque aquellas comportan un mayor grado de unificacion en la explicacion de regularidades estadisticas. Los axiomas centrales de la teoria de redes causales (TC) estan justificados porque ofrecen la mejor, si no la unica, explicacion unificada de dos fenomenos estadisticos: neutralizacion (screening off) y vinculacion (linking up). Se discuten las explicaciones alternativas de estos dos fenomenos y se razona por que no funcionan. Se demuestra ademas que aunque los axiomas centrales de TC son empiricamente vacuos, las versiones extendidas de TC tienen un contenido empirico gracias al cual pueden generar predicciones independientemente contrastables. (shrink)

Humans have the ability to learn surprisingly complicated statistical information in a variety of modalities and situations, often based on relatively little input. These statistical learning (SL) skills appear to underlie many kinds of learning, but despite their ubiquity, we still do not fully understand precisely what SL is and what individual differences on SL tasks reflect. Here, we present experimental work suggesting that at least some individual differences arise from stimulus-specific variation in perceptual fluency: the ability to (...) rapidly or efficiently code and remember the stimuli that SL occurs over. Experiment 1 demonstrates that participants show improved SL when the stimuli are simple and familiar; Experiment 2 shows that this improvement is not evident for simple but unfamiliar stimuli; and Experiment 3 shows that for the same stimuli (Chinese characters), SL is higher for people who are familiar with them (Chinese speakers) than those who are not (English speakers matched on age and education level). Overall, our findings indicate that performance on a standard SL task varies substantially within the same (visual) modality as a function of whether the stimuli involved are familiar or not, independent of stimulus complexity. Moreover, test–retest correlations of performance in an SL task using stimuli of the same level of familiarity (but distinct items) are stronger than correlations across the same task with stimuli of different levels of familiarity. Finally, we demonstrate that SL performance is predicted by an independent measure of stimulus-specific perceptual fluency that contains no SL component at all. Our results suggest that a key component of SL performance may be related to stimulus-specific processing and familiarity. (shrink)

The social and cognitive science replication crisis is partly due to the limitations of commonly used statistical tools. Inferential statistics require that unsystematic measurement variation is independent of system history, and weak relative to systematic or causal sources of variation. However, contemporary systems research underscores the dynamic, adaptive nature of social, cognitive, and behavioral systems. Variation in human activity includes the influences of intrinsic dynamics intertwined with changing contextual circumstances. Conventional inferential techniques presume milder forms of variability, such as (...) unsystematic measurement error, as in a Gaussian distribution. Inferential statistics indicate an elementary Newtonian cause-effect metaphor for change that is inconsistent with known principles of change in complex systems. Pattern formation in self-organizing systems and quantum probability are used to illustrate theoretical metaphors that instantiate alternative notions of change in complex systems. Inferential statistics and related techniques are crucial scientific resources. However, in the social and behavioral sciences, they must be practiced in conjunction with an appropriate general systems framework that accommodates intrinsic fluctuations and contextual adaptation. (shrink)

Inferential statistical tests-such as analysis of variance, t-tests, chi-square and Wilcoxin signed ranks-now constitute a principal class of methods for the testing of scientific hypotheses. In this paper I will consider the role of one statistical concept (statistical power) and two statistical principles or assumptions (homogeneity of variance and the independence of random error), in the reliable application of selected statistical methods. I defend a tacit but widely-deployed naturalistic principle of explanation (E): Philosophers should (...) not treat as inexplicable or basic those correlational facts that scientists themselves do not treat as irreducible. In light of (E), I contend that the conformity of epistemically reliable statistical tests to these concepts and assumptions entails at least the following modest or austere realist commitment: (C) The populations under study have a stable theoretical or unobserved structure that metaphysically grounds the observed values; the objects therefore have a fixed value independent of our efforts to measure them. (C) provides the best explanation for the correlation between the joint use of statistical assumptions and statistical tests, on the one hand, and methodological success on the other. (shrink)

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model that incorporates varying degrees of prior belief in class-conditional independence, learns whether (...) or not independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments—designed using optimal experimental design principles—were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks. (shrink)

Word recognition is the Petri dish of the cognitive sciences. The processes hypothesized to govern naming, identifying and evaluating words have shaped this field since its origin in the 1970s. Techniques to measure lexical processing are not just the back-bone of the typical experimental psychology laboratory, but are now routinely used by cognitive neuroscientists to study brain processing and increasingly by social and clinical psychologists (Eder, Hommel, and De Houwer 2007). Models developed to explain lexical processing have also aspired to (...) be statements about the nature of human cognition (e.g., connectionist models, Plaut, McClelland, Seidenberg, and Patterson 1996). Words were convenient objects to study for cognitive psychologists because they are welldefined and their nature as alphabetic strings was a good fit to analysis with the computer programming languages of the 1970s and 1980s which excelled at string manipulation. But are words actually the privileged unit of mental representation and processing that all of this scientific attention makes them out to be? Like a growing number of other language researchers, our answer is no (see, e.g., (Bybee and Hopper 2001; Wray 2002). We propose that the mental representations for lexical structures form a continuum, from word combinations which have fossilized into single units (nightclub) to those that both exist as independent units and yet have bonds, varying in tightness, with the words with which they frequently co-occur (Harris 1998). The first line of support for this view is the simple observation that fluent speakers easily recognize the familiarity and cohesive quality of word combinations in their language. Examples in English include common noun compounds (last year, brand new), verb phrases (cut down, get a hold of, faced with) and other multi-word expressions such as common sayings and references to cultural concepts (saved by the bell, speed of light; Jackendoff 1995).. (shrink)

It is generally accepted that, around the turn of the century, GIBBS and EINSTEIN independently developed two equivalent formulations of statistical mechanics. GIBBS version is taken as genuine and rigorous, while EINSTEINs, despite some features which are characteristic of him, is usually considered a not totally satisfactory attempt.It will be shown in the present work that such a picture is oversimplified and requires further nuancing. In fact, there are significant differences, with important implications which have not been sufficiently examined, (...) between the two formulations. Several issues relating to the impact of the two versions will also be addressed. (shrink)