Classical probability models of incentive response are inadequate in where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.

Previous studies of auditory statistical learning have typically presented learners with sequential structural information that is uniformly distributed across the entire exposure corpus. Here we present learners with nonuniform distributions of structural information by altering the organization of trisyllabic nonsense words at midstream. When this structural change was unmarked by low‐level acoustic cues, or even when cued by a pitch change, only the first of the two structures was learned. However, both structures were learned when there was an explicit (...) cue to the midstream change or when exposure to the second structure was tripled in duration. These results demonstrate that successful extraction of the structure in an auditory statistical learning task reduces the ability to learn subsequent structures, unless the presence of two structures is marked explicitly or the exposure to the second is quite lengthy. The mechanisms by which learners detect and use changes in distributional information to maintain sensitivity to multiple structures are discussed from both behavioral and computational perspectives. (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)

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)

This thesis describes a method to control rare events in non-equilibrium systems by applying physical forces to those systems but without relying on numerical simulation techniques, such as copying rare events. In order to study this method, the book draws on the mathematical structure of equilibrium statistical mechanics, which connects large deviation functions with experimentally measureable thermodynamic functions. Referring to this specific structure as the "phenomenological structure for the large deviation principle", the author subsequently extends it (...) to time-series statistics that can be used to describe non-equilibrium physics. The book features pedagogical explanations and also shows many open problems to which the proposed method can be applied only to a limited extent. Beyond highlighting these challenging problems as a point of departure, it especially offers an effective means of description for rare events, which could become the next paradigm of non-equilibrium statistical mechanics. (shrink)

Clark Glymour, Richard Scheines, Peter Spirtes and Kevin Kelly. Discovering Causal Structure: Artifical Intelligence, Philosophy of Science and Statistical Modeling.

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many (...) connections. These regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many (...) connections. These regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

Researchers rely on psychometric principles when trying to gain understanding of unobservable psychological phenomena disconfounded from the methods used. Psychometric models provide us with tools to support this endeavour, but they are agnostic to the meaning researchers intend to attribute to the data. We define method effects as resulting from actions which weaken the psychometric structure of measurement, and argue that solution to this confounding will ultimately rest on testing whether data collected fit a psychometric model based on a (...) substantive theory, rather than a search for a model that best fits the data. We highlight the importance of taking the notions of fundamental measurement seriously by reviewing distinctions between the Rasch measurement model and more generalised 2PL and 3PL IRT models. We then present two lines of research that highlight considerations of making method effects explicit in experimental designs. First, we contrast the use of experimental manipulations to study measurement reactivity during the assessment of metacognitive processes with factor-analytic research of the same. The former suggests differential performance-facilitating and -inhibiting reactivity as a function of other individual differences, whereas factor-analytic research suggests a ubiquitous monotonically predictive confidence factor. Second, we evaluate differential effects of context and source on within-individual variability indices of personality derived from multiple observations, highlighting again the importance of a structured and theoretically grounded observational framework. We conclude by arguing that substantive variables can act as method effects and should be considered at the time of design rather than after the fact, and without compromising measurement ideals. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many (...) connections. These regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

In the Bayesian framework, a language learner should seek a grammar that explains observed data well and is also a priori probable. This paper proposes such a measure of prior probability. Indeed it develops a full statistical framework for lexicalized syntax. The learner's job is to discover the system of probabilistic transformations (often called lexical redundancy rules) that underlies the patterns of regular and irregular syntactic constructions listed in the lexicon. Specifically, the learner discovers what transformations apply in the (...) language, how often they apply, and in what contexts. It considers simpler systems of transformations to be more probable a priori. Experiments show that the learned transformations are more effective than previous statistical models at predicting the probabilities of lexical entries, especially those for which the learner had no direct evidence. (shrink)

This volume presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic (...) symmetry, as well as their applications in the real world. (shrink)

The commentaries indicate a general agreement that one source of reduction of base-rate neglect involves making structural relations among relevant sets transparent. There is much less agreement, however, that this entails dual systems of reasoning. In this response, we make the case for our perspective on dual systems. We compare and contrast our view to the natural frequency hypothesis as formulated in the commentaries.

The poverty of stimulus argument is one of the most controversial arguments in the study of language acquisition. Here we follow previous approaches challenging the assumption of impoverished primary linguistic data, focusing on the specific problem of auxiliary (AUX) fronting in complex polar interrogatives. We develop a series of corpus analyses of child-directed speech showing that there is indirect statistical information useful for correct auxiliary fronting in polar interrogatives and that such information is sufficient for distinguishing between grammatical and (...) ungrammatical generalizations, even in the absence of direct evidence. We further show that there are simple learning devices, such as neural networks, capable of exploiting such statistical cues, producing a bias toward correct AUX questions when compared to their ungrammatical counterparts. The results suggest that the basic assumptions of the poverty of stimulus argument may need to be reappraised. (shrink)

The computations involved in statistical learning have long been debated. Here, we build on work suggesting that a basic memory process, chunking, may account for the processing of statistical regularities into larger units. Drawing on methods from the memory literature, we developed a novel paradigm to test statistical learning by leveraging a robust phenomenon observed in serial recall tasks: that short‐term memory is fundamentally shaped by long‐term distributional learning. In the statistically induced chunking recall (SICR) task, participants (...) are exposed to an artificial language, using a standard statistical learning exposure phase. Afterward, they recall strings of syllables that either follow the statistics of the artificial language or comprise the same syllables presented in a random order. We hypothesized that if individuals had chunked the artificial language into word‐like units, then the statistically structured items would be more accurately recalled relative to the random controls. Our results demonstrate that SICR effectively captures learning in both the auditory and visual modalities, with participants displaying significantly improved recall of the statistically structured items, and even recall specific trigram chunks from the input. SICR also exhibits greater test–retest reliability in the auditory modality and sensitivity to individual differences in both modalities than the standard two‐alternative forced‐choice task. These results thereby provide key empirical support to the chunking account of statistical learning and contribute a valuable new tool to the literature. (shrink)

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

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)

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

In the last years, the surprising bosonic behavior that a many-fermion system may acquire has raised interest because of theoretical and practical reasons. This trans-statistical behavior is usually considered to be the result of approximation modeling methods generally employed by physicists when faced with complexity. In this paper, we take a tensor product structure and an ontology of properties approach and provide two versions of a toy model in order to argue that trans-statistical behavior allows for a (...) realistic interpretation. (shrink)

It is argued that the symmetry and anti-symmetry of the wave functions of systems consisting of identical particles have nothing to do with the observational indistinguishability of these particles. Rather, a much stronger conceptual indistinguishability is at the bottom of the symmetry requirements. This can be used to argue further, in analogy to old arguments of De Broglie and Schrödinger, that the reality described by quantum mechanics has a wave-like rather than particle-like structure. The question of whether quantum statistics (...) alone can give rise to empirically observable correlations between results of distant measurements is also discussed. (shrink)

Recent advances in the field of statistical learning have established that learners are able to track regularities of multimodal stimuli, yet it is unknown whether the statistical computations are performed on integrated representations or on separate, unimodal representations. In the present study, we investigated the ability of adults to integrate audio and visual input during statistical learning. We presented learners with a speech stream synchronized with a video of a speaker’s face. In the critical condition, the visual (...) (e.g. /gi/) and auditory (e.g. /mi/) signals were occasionally incongruent, which we predicted would produce the McGurk illusion, resulting in the perception of an audiovisual syllable (e.g. /ni/). In this way, we used the McGurk illusion to manipulate the underlying statistical structure of the speech streams, such that perception of these illusory syllables facilitated participants’ ability to segment the speech stream. Our results therefore demonstrate that participants can integrate audio and visual input to perceive the McGurk illusion during statistical learning. We interpret our findings as support for modality-interactive accounts of statistical learning. (shrink)

The approaching ways in religious phenomenon quantitative studies are, most of the times, based only on the evolution of adherent flows and population structure from a religious point of view. In this pape, an integrated statistical indicators system will be designed. The main purpose of the system is to enhance the quality and coherence of the religious phenomenon. The most important indicators from the integrated system are: context indicators (political, economical, socio-cultural, demographical), basic indicators, level and structure (...) indicators, participation indicators, resource indicators (spiritual, human and pecuniary), quality, efficiency and outcomes (religious freedom, social connections, international relationships). Designing a complete, coherent system of indicators is necessary for a correct approach in studying the religious phenomenon. Statistical indicators can supply quantitative data for the operational description of the religious phenomenon. The indicators’ system makes possible not only a descriptive analysis but also some advanced statistical techniques (e.g. regression and correlation method). (shrink)

This paper shows how to define probability distributions over linguistically realistic syntactic structures in a way that permits us to define language learning and language comprehension as statistical problems. We demonstrate our approach using lexical‐functional grammar (LFG), but our approach generalizes to virtually any linguistic theory. Our probabilistic models are maximum entropy models. In this paper we concentrate on statistical inference procedures for learning the parameters that define these probability distributions. We point out some of the practical problems (...) that make straightforward ways of estimating these distributions infeasible, and develop a “pseudo‐likelihood” estimation procedure that overcomes some of these problems. This method raises interesting questions concerning the nature of the data available to a language learner and the modularity of language learning and processing. (shrink)

We present a new approach to the old problem of how to incorporate the role of the observer in statistics. We show classical probability theory to be inadequate for this task and take refuge in the epsilon-model, which is the only model known to us caapble of handling situations between quantum and classical statistics. An example is worked out and some problems are discussed as to the new viewpoint that emanates from our approach.

A key motivation for Universal Grammar (UG) is developmental: UG can help children acquire the linguistic knowledge that they do as quickly as they do from the data that's available to them. Some of the most fruitful recent work in language acquisition has combined ideas about different hypothesis space building blocks with domain‐general statistical learning. Statistical learning can then provide a way to help navigate the hypothesis space in order to converge on the correct hypothesis. Reinforcement learning is (...) a principled way to update the probability of a categorical option that's in competition with other categorical options. There are two prominent options for linking theory theoretical representations: the Uniformity of Theta Assignment Hypothesis (UTAH) and the relativized form of that theory, relativized UTAH. The learning strategy of Pearl and Sprouse shares the intuition with subjacency that there's a local structural anomaly when syntactic islands occur. (shrink)

The application of statistical methods and models both in the natural and social sciences is nowadays a trivial fact which nobody would deny. Bold analogies even suggest the application of the same statistical models to fields as different as statistical mechanics and economics, among them the case of the young and controversial discipline of Econophysics . Less trivial, however, is the answer to the philosophical question, which has been raised ever since the possibility of “commuting” statistical (...) thinking and models between natural and social sciences emerged: whether such a methodological kinship would imply some kind of more profound unity of the natural and the social domain. Starting with Adolphe Quetelet (1796-1874) and ending with the Vienna Circle (from the late 1920s until the 1940s), this paper offers a brief historical and philosophical reconstruction of some important stages in the development of statistics as “commuting” between the natural and the social sciences. This reconstruction is meant to highlight (with respect to the authors under consideration): (1) the existence of a significant correlation between the readiness to “transfer” statistical thinking from natural to social sciences and vice versa, on the one hand, and the standpoints on the issue of the unity/disunity of science, on the other; (2) the historical roots and the fortunes of the analogy between statistical models of society and statistical models of gases. (shrink)

This paper’s main contention is that some basically methodological developments in science which are apparently distant and unrelated can be seen as part of a sequential story. Focusing on general inferential and epistemological matters, the paper links occurrences separated by both in time and space, by formal and representational issues rather than social or disciplinary links. It focuses on a few limited aspects of several cognitive practices in medical and biological contexts separated by geography, disciplines and decades, but connected by (...) long term transdisciplinary representational and inferential structures and constraints. The paper intends to show a given set of knowledge claims based on organizing statistically empirical data can be seen to have been underpinned by a previous, more familiar, and probably more natural, narrative handling of similar evidence. To achieve that this paper moves from medicine in France in the late eighteenth and early nineteenth century to the second half of the nineteenth century in England among gentleman naturalists, following its subject: the shift from narrative depiction of hereditary transmission of physical peculiarities to posterior statistical articulations of the same phenomena. Some early defenders of heredity as an important causal presence in the understanding of life adopted singular narratives, in the form of case stories from medical and natural history traditions, to flesh out a special kind of causality peculiar to heredity. This work tries to reconstruct historically the rationale that drove the use of such narratives. It then shows that when this rationale was methodologically challenged, its basic narrative and probabilistic underpinings were transferred to the statistical quantificational tools that took their place. (shrink)

Statistical tests of the primality of some numbers look similar to statistical tests of many nonmathematical, clearly empirical propositions. Yet interpretations of probability prima facie appear to preclude the possibility of statistical tests of mathematical propositions. For example, it is hard to understand how the statement that n is prime could have a frequentist probability other than 0 or 1. On the other hand, subjectivist approaches appear to be saddled with ‘coherence’ constraints on rational probabilities that require (...) rational agents to assign extremal probabilities to logical and mathematical propositions. In the light of these problems, many philosophers have come to think that there must be some way to generalize a Bayesian statistical account. In this article I propose that a classical frequentist approach should be reconsidered. I conclude that we can give a conditional justification of statistical testing of at least some mathematical hypotheses: if statistical tests provide us with reasons to believe or bet on empirical hypotheses in the standard situations, then they also provide us with reasons to believe or bet on mathematical hypotheses in the structurally similar mathematical cases. (shrink)

Determining optimal units of representing morphologically complex words in the mental lexicon is a central question in psycholinguistics. Here, we utilize advances in computational sciences to study human morphological processing using statistical models of morphology, particularly the unsupervised Morfessor model that works on the principle of optimization. The aim was to see what kind of model structure corresponds best to human word recognition costs for multimorphemic Finnish nouns: a model incorporating units resembling linguistically defined morphemes, a whole-word model, (...) or a model that seeks for an optimal balance between these two extremes. Our results showed that human word recognition was predicted best by a combination of two models: a model that decomposes words at some morpheme boundaries while keeping others unsegmented and a whole-word model. The results support dual-route models that assume that both decomposed and full-form representations are utilized to optimally process complex words within the mental lexicon. (shrink)

Statistical significance is almost universally equated with the attribution to some population of nonchance influences as the source of structure in the data. But statistical significance can be divorced from both parameter estimation and probability as, instead, a statement about the atypicality or lack of exchangeability over some distinction of the data relative to some set. From this perspective, the criticisms of significance tests evaporate.

Classical statistical mechanics has commanded a modest but steady amount of attention from philosophers of science. By contrast, there has been an almost total neglect of relativistic statistical mechanics, or more precisely, a neglect of the prospects and problems of producing a relativistic version of classical statistical mechanics. The neglect is undeserved, for this area offers a fascinating array of case studies for those concerned with the history and sociology of science, with the structure and dynamics (...) of scientific theories, or with foundations problems in physics. This paper is dedicated to the goal of ending the neglect. Towards this end, I will survey some of the issues which arise in attempting to marry statistical-thermodynamics with relativity theory. The choice of the issues to be discussed and their treatment naturally reflect my own preferences and prejudices, and I cannot hope for the reader’s agreement on all points. (shrink)

Unsupervised statistical learning is the standard setting for the development of the only advanced visual system that is both highly sophisticated and versatile, and extensively studied: that of monkeys and humans. In this extended abstract, we invoke philosophical observations, computational arguments, behavioral data and neurobiological findings to explain why computer vision researchers should care about (1) unsupervised learning, (2) statistical inference, and (3) the visual brain. We then outline a neuromorphic approach to structural primitive learning motivated by these (...) considerations, survey a range of neurobiological findings and behavioral data consistent with it, and conclude by mentioning some of the more challenging directions for future research. (shrink)

Statistical methods used by healthcare entities enable the collection of various information about the structure and characteristics of treated patients. They are an important source of knowledge, and form a database that plays an important role in entity management theory. In the presented study, we analysed the hospital stays of patients treated in all hospital wards of the 3rd City Hospital in Łodź during 2012. The following, in particular, were taken into account: admittance procedure, discharge procedure, age and (...) sex of hospitalised persons. Patients in over 55% of cases were admitted using the sud- den admittance procedure. At the same time, over 3/4 of the stays ended with a referral for further treatment in ambulatory conditions, and death occurred in approx. 5% of hospitalisations. By comparing the discharge procedures, the percentage of deaths in the Anaesthesiology and Intensive Care Wards can be seen clearly. Internal wards are next in turn. The biggest differences in the length of hospitalisation between the studied institution and the NFZ data concern the E77, A49, A48, A87, A33, D18, E16, E61 and G37 groups. (shrink)