This Element has two main aims. The first one is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study (...) of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'. (shrink)

Bioscientists generate far more data than their minds can handle, and this trend is likely to continue. With the aid of a small set of versatile tools for mathematical modeling and statistical assessment, bioscientists can explore their real-world systems without experiencing data overflow. This article outlines an approach for combining modern high-throughput, low-cost, but non-selective biospectroscopy measurements with soft, multivariate biochemometrics data modeling to overview complex systems, test hypotheses, and making new discoveries. From preliminary, broad hypotheses (...) and goals, many relevant samples are selected and measured with respect to many informative variables. The resulting tables represent a “cacophony” of data. From these, the most relevant and reliable “underlying harmonies and rhythms” are extracted and tested statistically, displayed for interpretation, and used for prediction. Outliers are detected automatically. Interesting subsets of samples can then be chosen for in-depth analyses in subsequent research cycles. This pragmatic, top-down approach takes advantage of developments in both “soft,” data-driven modeling and “hard,” knowledge-driven cultures. Data analytical examples show how information-rich biospectroscopy can be used for characterizing and quantifying known and unknown chemical constituents and physical phenomena in intact biosamples. This is based on a combination of deductive “hard” and inductive “soft” modeling. The examples represent NIR spectra of biochemical mixtures, FTIR spectra of a microbiological fermentation process, and FTIR analysis of fatty acids in milk for functional genomics. (shrink)

Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe (...) a general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

As a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it (...) allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice. (shrink)

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium in terms of (...) Bose‐Einstein statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London's model. (shrink)

Understanding modeling in biology requires understanding how biology is organized as a discipline and how this organization influences the research practices of biologists. Biology includes a wide range of sub-disciplines, such as cell biology, population biology, evolutionary biology, molecular biology, and systems biology among others. Biologists in sub-disciplines such as cell, molecular, and systems biology believe that the use of a few experimental models allows them to discover biological universals, whereas biologists in sub-disciplines such as ecology and evolutionary biology (...) believe that the use of many different experimental and mathematical models is necessary in order to do this. Many practitioners of both approaches misunderstand best practices of modeling, especially those related to model testing. We stress the need for biologists to better engage with best practices and for philosophers of biology providing normative guidance for biologists to better engage with current developments in biology. This is especially important as biology transitions from a “data-poor” to a “data-rich” discipline. If 21st century biology is going to capitalize on the unprecedented availability of ecological, evolutionary, and molecular data, of computational resources, and of mathematical and statistical tools, biologists will need a better understanding of what modeling is and can be. (shrink)

In this essay, I consider the use of mathematical statistics in the study of biological systems in the field, using as case studies the work of Ruth Geyer Shaw and her colleagues at the University of Minnesota. To address practical issues, like how to enhance prairie restoration, and how to prepare for (and perhaps prevent) the effect of rapid climate change, she and her colleagues combine mathematical modeling and intensive data collection in the field. Using ANOVA and (...) the more versatile approach of Aster Models, they show the effects of inbreeding (which follows from the fragmentation of prairie) to lower the fitness of plant populations. They study the genetic variance of plants in stable populations, which is important when that population must deal with changing conditions. And they study the consequences of rapid climate change: even good genetic variance and initial fitness may not save a given population from extinction. This leads to a new alliance of science with local, state, federal and global politics. (shrink)

The folding of RNA sequences into secondary structures is a simple yet biophysically grounded model of a genotype–phenotype map. Its computational and mathematical analysis has uncovered a surprisingly rich statistical structure characterized by shape space covering, neutral networks and plastogenetic congruence. I review these concepts and discuss their evolutionary implications. BioEssays 24:1164–1177, 2002. © 2002 Wiley‐Periodicals, Inc.

Statistical learning refers to the ability to identify structure in the input based on its statistical properties. For many linguistic structures, the relevant statistical features are distributional: They are related to the frequency and variability of exemplars in the input. These distributional regularities have been suggested to play a role in many different aspects of language learning, including phonetic categories, using phonemic distinctions in word learning, and discovering non-adjacent relations. On the surface, these different aspects share few (...) commonalities. Despite this, we demonstrate that the same computational framework can account for learning in all of these tasks. These results support two conclusions. The first is that much, and perhaps all, of distributional statistical learning can be explained by the same underlying set of processes. The second is that some aspects of language can be learned due to domain-general characteristics of memory. (shrink)

Over the past century, private tutoring in many countries has increased dramatically. Moreover, the main disadvantage of PT is that has a byproduct and a characteristic on the educational system in developing countries in terms of contributing to conditions such as large class sizes, low public expenditures, and an inadequate number of universities. In Saudi Arabia, the spread of PT at school and university levels has yet to be addressed by researchers. One goal of this examination was to research the (...) spread of PT in relation to mathematics being taught at school and university levels. This investigation used quantitative data of the questionnaire to determine the reasons for the spread. A total of 1000 students responded from University of Ha’il. The edge plans given results that are associated and like the assessment that is performed with the whole data. The current study found that a good family financial situation and lack of parental supervision of the children were significant factors underlying the spread of private tutoring at school and university levels. (shrink)

“Hard obscurantism” is a species of the genus scholarly obscurantism. A rough intensional definition of hard obscurantism is that models and procedures become ends in themselves, dissociated from their explanatory functions. In the present article, I exemplify and criticize hard obscurantism by examining the writings of eminent economists and political scientists.

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)

In this article, we review approaches to modeling a connection between spatial and mathematical thinking across development. We critically evaluate the strengths and weaknesses of factor analyses, meta-analyses, and experimental literatures. We examine those studies that set out to describe the nature and number of spatial and mathematical skills and specific connections between these abilities, especially those that included children as participants. We also find evidence of strong spatial-mathematical connections and transfer from spatial interventions to (...) class='Hi'>mathematical understanding. Finally, we map out the kinds of studies that could enhance our understanding of the mechanisms by which spatial and mathematical processing are connected and the principles by which mathematical outcomes could be enhanced through spatial training in educational settings. (shrink)

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

This study examines the associations of constructivist beliefs and classroom climate on teachers' self-efficacy in instruction, classroom management, and student engagement among Australian secondary mathematics teachers. To do this, it uses the integrated model of teachers' self-efficacy with the concept of analysis of teaching tasks. The study uses structural equation modeling to analyze data from 495 mathematics teachers in the Teaching and Learning International Survey 2013. The results reveal the integrated model is a valid theoretical framework to explain Australian (...) secondary mathematics teachers' self-efficacy. Teachers' constructivist beliefs and classroom climate are positively and statistically significantly related to teachers' self-efficacy in instruction, classroom management and student engagement. In contrast, constructivist beliefs have no significant correlation with classroom climate. (shrink)

Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit also (...) concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth. (shrink)

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural (...) analysis of the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

RESUMEN Introducción: La dimensión ambiental constituye un proceso esencial en la formación de profesionales, de modo que en el desempeño de su profesión puedan educar hacia el desarrollo sostenible a las futuras generaciones. Objetivo: Representar en un modelo pedagógico la lógica de la dimensión ambiental en la formación laboral investigativa de los profesionales en la universidad. Materiales y métodos: Se utilizaron métodos teóricos, empíricos y matemáticos-estadísticos. Resultados: Elaboración del modelo pedagógico de dimensión ambiental en la formación laboral investigativa de los (...) profesionales en formación. El modelo está estructurado en tres subsistemas: uno teórico, se centra en la integración de saberes pedagógico ambientales a partir de las relaciones que se establecen entre sus componentes, otro metodológico, el cual resume la proyección ambiental de la formación laboral investigativa y un subsistema procedimental, que manifiesta la instrumentación transformadora ambiental que debe ocurrir en los estudiantes. El modelo aporta una cualidad sinérgica que le imprime identidad, totalidad y contribuye a su autodesarrollo. Conclusiones: Con la elaboración del modelo se revelan nuevas interpretaciones que se manifiestan como relaciones teóricas funcionales surgidas entre los componentes de los subsistemas que lo integran y a la vez, entre los subsistemas como macro componentes. La validación del modelo resultó estadísticamente significativa, mediante la instrumentación de una estrategia pedagógica para la dimensión ambiental en la formación laboral investigativa. ABSTRACT Introduction: The environmental component is an essential process in the training of professionals, that enables them to educate future generations towards sustainable development. Objective: To represent in a pedagogical model the logic of the environmental dimension in the research training of professionals. Materials and methods: Theoretical, empirical and mathematical-statistical methods were used. Findings: The development of the pedagogical model of environmental dimension in research and labor training of professionals. The model is structured in three subsystems: the first focuses on the integration of environmental pedagogical knowledge from the relationships established between its components; the second is of a methodological character and summarizes the environmental projection of research training; whereas the third one is procedural, expressing the environmental transformative instrumentation that must occur in students. The model provides a synergistic quality that consolidates identity, totality and contributes to its self-development. Conclusions: With the elaboration of the model new interpretations are revealed that are manifested as functional theoretical relations arising between the components of the subsystems that integrate it and at the same time, between the subsystems as macro components. The evaluation of the model was statistically significant, through the instrumentation of a pedagogical strategy for the environmental dimension in the research and labor training. (shrink)

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features (...) of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs. -/- . (shrink)

In this expository article, a presentation is given of A.C. Crombie's life work in the history of science, Styles of Scientific Thinking in the European Tradition. The History of Argument and Explanation in the Mathematical and Biomedical Sciences and Arts (1994). The importance of this work for the philosophy of science and epistemology is comparable to the more renowned work of the 1960's and '70s, but threatens to be paradoxically overlooked because of its gigantic proportions. (No thorough study of (...) the book appeared up to now.) Crombie's earlier work started from a provocative version of continuism in the debate about the rise of modern science, ascribing the origin of the experimental tradition to methodological forebears in the thirteenth century (Grosseteste). Rather than revivifying this quarrel now, Crombie has offered us an emergentist picture of the rise of six subsequent major styles of science (using grand units of analysis) from the Greeks up to Darwin. These styles of thinking are superimposed upon another in that the definite breakthrough of each next style is consequent upon the recognition of the proper limits of the full grown previous style. In a first group, Crombie assembles three major styles for revealing regularities in individual phenomena, i.e. where the consideration of the collective to which the phenomenon belongs is not required for recognizing the regularity. Here we have (S1) the ancient style of postulating principles and entities according to a more or less apriorical evidence type or in axiomatic fashion; (S2) the experimental tradition from Alhazen up to Newton, and (S3) the style of hypothetical modelling, combining the former two in the vein of the rational artist as an (ultimately, also cognitive) engineer. In a second group the styles dealing with regularities discoverable only in a collectivity of phenomena are dealt with. Here we have the (S4) probabilistic style superimposed on the classical picture of rationality made up by the achieved styles in the first group. Then (S5) the taxonomic style is ready to be combined, finally, with S4, in order to discover the statistical economy of living nature in (S6), the 'genetic' style, culminating in Darwin's history of nature (which was to be expected). On the other hand, the latter style is traced back to the 16th and 17th century project of a history of languages and culture, of knowledge, and of mankind (which is a more surprising connection made by Crombie). In a final section some philosophical remarks are made regarding Crombie's project; mainly with respect to the larger perspective, in Crombie's terms, of an 'intellectual anthropology', or alternatively, in terms of a 'comparative epistemology'. Also the absence of a real analysis of the very concept of style is noted. (shrink)

This study presents a wastewater-based mathematical model for assessing the transmission dynamics of the SARS-CoV-2 pandemic in Miami-Dade County, Florida. The model, which takes the form of a deterministic system of nonlinear differential equations, monitors the temporal dynamics of the disease, as well as changes in viral RNA concentration in the county’s wastewater system (which consists of three sewage treatment plants). The model was calibrated using the wastewater data during the third wave of the SARS-CoV-2 pandemic in Miami-Dade (specifically, (...) the time period from July 3, 2021 to October 9, 2021). The calibrated model was used to predict SARS-CoV-2 case and hospitalization trends in the county during the aforementioned time period, showing a strong correlation between the observed (detected) weekly case data and the corresponding weekly data predicted by the calibrated model. The model’s prediction of the week when maximum number of SARS-CoV-2 cases will be recorded in the county during the simulation period precisely matches the time when the maximum observed/reported cases were recorded (which was August 14, 2021). Furthermore, the model’s projection of the maximum number of cases for the week of August 14, 2021 is about 15 times higher than the maximum observed weekly case count for the county on that day (i.e., the maximum case count estimated by the model was 15 times higher than the actual/observed count for confirmed cases). This result is consistent with the result of numerous SARS-CoV-2 modeling studies (including other wastewater-based modeling, as well as statistical models) in the literature. Furthermore, the model accurately predicts a one-week lag between the peak in weekly COVID-19 case and hospitalization data during the time period of the study in Miami-Dade, with the model-predicted hospitalizations peaking on August 21, 2021. Detailed time-varying global sensitivity analysis was carried out to determine the parameters (wastewater-based, epidemiological and biological) that have the most influence on the chosen response function—the cumulative viral load in the wastewater. This analysis revealed that the transmission rate of infectious individuals, shedding rate of infectious individuals, recovery rate of infectious individuals, average fecal load per person per unit time and the proportion of shed viral RNA that is not lost in sewage before measurement at the wastewater treatment plant were most influential to the response function during the entire time period of the study. This study shows, conclusively, that wastewater surveillance data can be a very powerful indicator for measuring (i.e., providing early-warning signal and current burden) and predicting the future trajectory and burden (e.g., number of cases and hospitalizations) of emerging and re-emerging infectious diseases, such as SARS-CoV-2, in a community. (shrink)

In empirical modeling, an important desiderata for deeming theoretical entities and processes as real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwines with the question of how statistical methods link data to statistical and substantive theories and models. Different answers to this question have important methodological consequences for inference, which are intertwined with a contrast between the ontological commitments of the two types of models. The key (...) to untangling them is the realization that behind every substantive model there is a statistical model that pertains exclusively to the probabilistic assumptions imposed on the data. It is not that the methodology determines whether to be a realist about entities and processes in a substantive field. It is rather that the substantive and statistical models refer to different entities and processes, and therefore call for different criteria of adequacy. (shrink)

This volume, the third in this Springer series, contains selected papers from the four workshops organized by the ESF Research Networking Programme "The Philosophy of Science in a European Perspective" in 2010: Pluralism in the Foundations of Statistics Points of Contact between the Philosophy of Physics and the Philosophy of Biology The Debate on Mathematical Modeling in the Social Sciences Historical Debates about Logic, Probability and Statistics The volume is accordingly divided in four sections, each of them containing (...) papers coming from the workshop focussing on one of these themes. While the programme's core topic for the year 2010 was probability and statistics, the organizers of the workshops embraced the opportunity of building bridges to more or less closely connected issues in general philosophy of science, philosophy of physics and philosophy of the special sciences. However, papers that analyze the concept of probability for various philosophical purposes are clearly a major theme in this volume, as it was in the previous volumes of the same series. This reflects the impressive productivity of probabilistic approaches in the philosophy of science, which form an important part of what has become known as formal epistemology - although, of course, there are non-probabilistic approaches in formal epistemology as well. It is probably fair to say that Europe has been particularly strong in this area of philosophy in recent years.​. (shrink)

Mathematical modeling is a convenient way for characterization of complex ecosystems. This approach was applied to study the dynamics of zooplankton in Lake Sevan (Armenia) at different stages of anthropogenic eutrophication with the use of a novel method called discrete modeling of dynamical systems with feedback (DMDS). Simulation demonstrated that the application of this method helps in characterization of inter- and intra-component relationships in a natural ecosystem. This method describes all possible pairwise inter-component relationships like “plus–plus,” “minus–minus,” (...) “plus–minus,” “plus–zero,” “minus–zero,” and “zero–zero” that occur in most ecosystems. Based on the results, a working hypothesis was formulated. It was found that the sensitivity to weak external influence in zooplanktons was the greatest during the mid period of eutrophication in Lake Sevan, whereas in the final stages of eutrophication, an outbreak in the biomass production of cyanobacteria was evident. To support this approach, a weak external disturbance in the form of magnetic storm was used to see its effect on species Daphnia longispina sevanica. A statistically significant correlation between the frequency of magnetic storms and the number of this species was revealed and an increase in the number of toxic cyanobacteria species as a consequence of eutrophication. This paper, for the first time, suggests a DMDS method, to diagnose impact of anthropogenic eutrophication on environment. (shrink)

Although every emerging infectious disease occurs in a unique context, the behaviour of previous pandemics offers an insight into the medium- and long-term outcomes of the current threat. Where an informative historical analogue exists, epidemiologists and policymakers should consider how the insights of the past can inform current forecasts and responses.

Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief—the first of its kind to represent rational requirements on agents who undergo certainty loss.

The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system (...) or some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to the form typically discussed, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally. (shrink)

A long history of research has revealed many neurophysiological changes and concomitant behavioral impacts of sleep deprivation, sleep restriction, and circadian rhythms. Little research, however, has been conducted in the area of computational cognitive modeling to understand the information processing mechanisms through which neurobehavioral factors operate to produce degradations in human performance. Our approach to understanding this relationship is to link predictions of overall cognitive functioning, or alertness, from existing biomathematical models to information processing parameters in a cognitive architecture, (...) leveraging the strengths from each to develop a more comprehensive explanation. The integration of these methodologies is used to account for changes in human performance on a sustained attention task across 88 h of total sleep deprivation. The integrated model captures changes due to time awake and circadian rhythms, and it also provides an account for underlying changes in the cognitive processes that give rise to those effects. The results show the potential for developing mechanistic accounts of how fatigue impacts cognition, and they illustrate the increased explanatory power that is possible by combining theoretical insights from multiple methodologies. (shrink)

The underrepresentation of females in mathematics-related fields may be explained by gender differences in mathematics self-concept (rather than ability) favoring males. Mathematics self-concept typically declines with student age, differs with student ethnicity, and is sensitive to teacher influence in early schooling. We investigated whether change in mathematics self-concept occurred within the context of a longitudinal intervention to raise and sustain teacher expectations of student achievement. This experimental study was conducted with a large sample of New Zealand primary school students and (...) their teachers. Data were analyzed using longitudinal multilevel modeling with mathematics self-concept as the dependent variable and time (which represents students’ increasing age each year), gender, and ethnicity entered as predictors and achievement in mathematics included as a control variable. Interaction terms were also explored to investigate changes over time for different groups. All students demonstrated a small increase in mathematics self-concept over the 3-year period of the current study but mathematics self-concept was consistently greater for boys than girls. Māori, Asian, and Other students’ initial mathematics self-concept was higher than that of New Zealand European and Pacific Islanders’ (after controlling for achievement differences). However, a statistically significant decline in mathematics self-concept occurred for Māori students alone by the end of the study. The expected age-related reduction over time in student mathematics self-concept appeared to be mitigated in association with the longitudinal study. Nevertheless, the demonstration of a comparatively lower mathematics self-concept remained for girls overall and declined for Māori. Our results reinforce implications for future research into mathematics self-concept as a possible determinant of female student career choices. (shrink)

In both theoretical and applied modeling in behavioral sciences, it is common to choose a mathematical specification of functional form and distribution of unobservables on grounds of analytic convenience without support from explicit theoretical postulates. This article discusses the issue of deriving particular qualitative hypotheses about functional form restrictions in structural models from intuitive theoretical axioms. In particular, we focus on a family of postulates known as dimensional invariance. Subsequently, we discuss how specific qualitative postulates can be reformulated (...) so as to allow for conventional statistical hypothesis testing, and we also derive details of a particular likelihood ratio test procedure. An empirical application of the testing procedure is carried out, based on data from a Stated Preference survey. (shrink)

Sortition, i.e. random appointment for public duty, has been employed by societies throughout the years as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case. Therefore, these random procedures play an important role in the course of a case, and should comply with (...) some principles, such as transparency and complete auditability. Nevertheless, these principles are neglected by random procedures in some judicial systems, which are performed in secrecy and are not auditable by the involved parties. The assignment of cases in the Brazilian Supreme Court is an example of such a procedure, for it is performed using procedures unknown to the parties involved in the judicial cases. This article presents a review of how sortition has been historically employed by societies and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. A statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court. As final remarks, guidelines for the development of good randomization procedures are outlined. (shrink)

Mathematical models provide explanations of limited power of specific aspects of phenomena. One way of articulating their limits here, without denying their essential powers, is in terms of contrastive explanation.

Much has been written about the free energy principle (FEP), and much misunderstood. The principle has traditionally been put forth as a theory of brain function or biological self-organisation. Critiques of the framework have focused on its lack of empirical support and a failure to generate concrete, falsifiable predictions. I take both positive and negative evaluations of the FEP thus far to have been largely in error, and appeal to a robust literature on scientific modelling to rectify the situation. A (...) prominent account of scientific modelling distinguishes between model structure and model construal. I propose that the FEP be reserved to designate a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error. To this end, I deliver first an account of the phenomenon of model transfer and the breakdown between model structure and model construal. In the second section, I offer an overview of the formal elements of the framework, tracing their history of model transfer and illustrating how the formalism comes apart from any interpretation thereof. Next, I evaluate existing comprehensive critical assessments of the FEP, and hypothesise as to potential sources of existing confusions in the literature. In the final section, I distinguish between what I hold to be the FEP—taken to be a modelling language or modelling framework—and what I term “FEP models.”. (shrink)

Modelling with Words is an emerging modelling methodology closely related to the paradigm of Computing with Words introduced by Lotfi Zadeh. This book is an authoritative collection of key contributions to the new concept of Modelling with Words. A wide range of issues in systems modelling and analysis is presented, extending from conceptual graphs and fuzzy quantifiers to humanist computing and self-organizing maps. Among the core issues investigated are - balancing predictive accuracy and high level transparency in learning - scaling (...) linguistic algorithms to high-dimensional data problems - integrating linguistic expert knowledge with knowledge derived from data - identifying sound and useful inference rules - integrating fuzzy and probabilistic uncertainty in data modelling. (shrink)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by (...) explaining in simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

In this paper, we argue that rather than exclusively focusing on trying to determine if an idealized model fits a particular account of scientific explanation, philosophers of science should also work on directly analyzing various explanatory schemas that reveal the steps and justification involved in scientists’ use of highly idealized models to formulate explanations. We develop our alternative methodology by analyzing historically important cases of idealized statistical modeling that use a three-step explanatory schema involving idealization, mathematical operation, (...) and explanatory interpretation. (shrink)

We analyze the effects of the introduction of new mathematical tools on an old branch of physics by focusing on lattice fluids, which are cellular automata -based hydrodynamical models. We examine the nature of these discrete models, the type of novelty they bring about within scientific practice and the role they play in the field of fluid dynamics. We critically analyze Rohrlich's, Fox Keller's and Hughes' claims about CA-based models. We distinguish between different senses of the predicates “phenomenological” and (...) “theoretical” for scientific models and argue that it is erroneous to conclude, as they do, that CA-based models are necessarily phenomenological in any sense of the term. We conversely claim that CA-based models of fluids, though at first sight blatantly misrepresenting fluids, are in fact conservative as far as the basic laws of statistical physics are concerned and not less theoretical than more traditional models in the field. Based on our case-study, we propose a general discussion of the prospect of CA for modeling in physics. We finally emphasize that lattice fluids are not just exotic oddities but do bring about new advantages in the investigation of fluids' behavior. (shrink)

The Handbook of Computational Social Science is a comprehensive reference source for scholars across multiple disciplines. It outlines key debates in the field, showcasing novel statistical modeling and machine learning methods, and draws from specific case studies to demonstrate the opportunities and challenges in CSS approaches. The Handbook is divided into two volumes written by outstanding, internationally renowned scholars in the field. This first volume focuses on the scope of computational social science, ethics, and case studies. It covers (...) a range of key issues, including open science, formal modeling, and the social and behavioral sciences. This volume explores major debates, introduces digital trace data, reviews the changing survey landscape, and presents novel examples of computational social science research on sensing social interaction, social robots, bots, sentiment, manipulation, and extremism in social media. The volume not only makes major contributions to the consolidation of this growing research field, but also encourages growth into new directions. With its broad coverage of perspectives (theoretical, methodological, computational), international scope, and interdisciplinary approach, this important resource is integral reading for advanced undergraduates, postgraduates and researchers engaging with computational methods across the social sciences, as well as those within the scientific and engineering sectors. (shrink)

This paper reports an experimental comparison of attitudes toward time and toward money in experience-based decisions. Preferences were elicited under rank-dependent utility for prospects with two or three consequences expressed either in time or in monetary units. Probabilities were unknown but learned through sampling. More specifically, time and money were compared under two conditions. In a first experiment, both consequences and probabilities of prospects were unknown and learned through sequential sampling. In a second experiment, the possible consequences were revealed after (...) the sampling. A real incentive system was implemented for both time and money. The heterogeneity of preferences was assessed for time and for money through individual and mixed modeling estimations. We observe that the nature of consequences (time or money) modifies probability weighting in terms of elevation and sensitivity. Subjects exhibit more optimism and less sensitivity to probability changes when deciding about time than about money. Revealing the consequences impacts the shape of the utility function and leaves probability weighting unchanged. We also observe that the real incentives have no effect except for the reduction in decision errors. This effect is stronger for money than for time. (shrink)

Statistical model specification and validation raise crucial foundational problems whose pertinent resolution holds the key to learning from data by securing the reliability of frequentist inference. The paper questions the judiciousness of several current practices, including the theory-driven approach, and the Akaike-type model selection procedures, arguing that they often lead to unreliable inferences. This is primarily due to the fact that goodness-of-fit/prediction measures and other substantive and pragmatic criteria are of questionable value when the estimated model is statistically misspecified. (...) Foisting one's favorite model on the data often yields estimated models which are both statistically and substantively misspecified, but one has no way to delineate between the two sources of error and apportion blame. The paper argues that the error statistical approach can address this Duhemian ambiguity by distinguishing between statistical and substantive premises and viewing empirical modeling in a piecemeal way with a view to delineate the various issues more effectively. It is also argued that Hendry's general to specific procedures does a much better job in model selection than the theory-driven and the Akaike-type procedures primary because of its error statistical underpinnings. (shrink)

Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten sub-models (...) that could be modelled and tested independently: the sub-models of tissue reactions, ionic movements, oedema development, glutamate excitotoxicity, spreading depression, NO synthesis, inflammation, necrosis, apoptosis, and reperfusion. Then, we figured out markers, identified mediators and chose the level of complexity to model these sub-models. We first applied this integrative approach to build a model based on cytotoxic oedema development following a stroke. Although this model includes only three sub-models and would need to integrate more mechanisms in each of these sub-models, the characteristics and the time and spatial evolution of penumbra obtained by simulation are qualitatively and, to some extent, quantitatively consistent with those observed using medical imaging after a permanent occlusion or after an occlusion followed by a reperfusion. (shrink)

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Endothelial cells which form the lining of neighbouring blood vessels respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. Capillary sprouts are formed which migrate towards the tumour eventually penetrating it and permitting vascular growth to take place. It (...) is during this stage of growth that the insidious process of invasion of surrounding tissues can and does take place. A model mechanism for angiogenesis is presented which includes the diffusion of the TAF into the surrounding host tissue and the response of the endothelial cells to the chemotactic stimulus. Numerical simulations of the model are shown to compare very well with experimental observations. The subsequent vascular growth of the tumour is discussed with regard to a classical reaction-diffusion pre-pattern model. (shrink)

Utilities of health states are often estimated to support public decisions in health care. People’s preferences may be imprecise, for lack of actual trade-off experience. We show how to elicit the utilities accounting for imprecision, discover the main drivers of imprecision, and compare several approaches to modelling health state utility data in the fuzzy setting. We extended the time trade-off questionnaire, to elicit utilities of states defined in the EQ-5D-3L descriptive system in184 respondents. Our study demonstrates that respondents are capable (...) of assessing their own imprecision and rigorous mathematical modelling is possible. The imprecision is larger than as inferred from the standard TTO method and is larger than estimation error, even in our smallish sample. Non-trading in TTO often results from imprecision, rather than lexicographic preferences for longevity over quality. People are especially imprecise in assessing the impact of usual activities on utility; also, the internal inconsistency of a health state increases the imprecision. Fuzzy least squares method seems best suited to assign disutilities to individual dimensions, while separately modelling the location of utility and amount of imprecision seems best to produce value sets. If crisp parameters are estimated, accounting for imprecision changes the results little. (shrink)

The author finds no support for the claim that J. M. Keynes had severe reservations, in general, as opposed to particular, concerning the application of mathematical, logical and statistical methods in economics. These misinterpretations rest on the omission of important source material as well as a severe misconstrual ofThe Treatise on Probability (1921).