Results for 'elicitation of probabilities'

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  1.  38
    Elicitation of Personal Probabilities and Expectations.Leonard Savage - 1971 - Journal of the American Statistical Association 66 (336):783-801.
  2.  56
    Error Propagation in the Elicitation of Utility and Probability Weighting Functions.Pavlo Blavatskyy - 2006 - Theory and Decision 60 (2-3):315-334.
    Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. (...)
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  3.  55
    The impossibility of experimental elicitation of subjective probabilities.Edi Karni & Zvi Safra - 1995 - Theory and Decision 38 (3):313-320.
  4.  51
    The influence of probabilities on the response mode bias in utility elicitation.Christopher Schwand, Rudolf Vetschera & Lea M. Wakolbinger - 2010 - Theory and Decision 69 (3):395-416.
    The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the impact (...)
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  5.  31
    Eliciting Objective Probabilities via Lottery Insurance Games.Robin Hanson - unknown
    Since utilities and probabilities jointly determine choices, event-dependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is sufficient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent’s further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they (...)
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  6.  19
    Consistency of determined risk attitudes and probability weightings across different elicitation methods.Golo-Friedrich Bauermeister, Daniel Hermann & Oliver Musshoff - 2018 - Theory and Decision 84 (4):627-644.
    In comparing different risk elicitation methods under the assumptions of expected utility theory, previous studies have found significant differences in the elicited risk attitudes. This paper extends this line of research to consider cumulative prospect theory by comparing risk attitudes and probability weightings determined using two elicitation methods: the method by Tanaka et al. :557–571, 2010; TCN method) and the method by Wakker and Deneffe :1131–1150, 1996; WD method). We demonstrate that the two methods reveal significantly different mean (...)
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  7.  4
    ma: tMlW)(D.What Remains Of Probability - 2010 - In F. Stadler, D. Dieks, W. Gonzales, S. Hartmann, T. Uebel & M. Weber (eds.), The Present Situation in the Philosophy of Science. Springer. pp. 373.
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  8.  50
    In search of good probability assessors: an experimental comparison of elicitation rules for confidence judgments.Guillaume Hollard, Sébastien Massoni & Jean-Christophe Vergnaud - 2016 - Theory and Decision 80 (3):363-387.
    In this paper, we use an experimental design to compare the performance of elicitation rules for subjective beliefs. Contrary to previous works in which elicited beliefs are compared to an objective benchmark, we consider a purely subjective belief framework. The performance of different elicitation rules is assessed according to the accuracy of stated beliefs in predicting success. We measure this accuracy using two main factors: calibration and discrimination. For each of them, we propose two statistical indexes and we (...)
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  9. Isaac Levi.on Indeterminate Probabilities - 1978 - In A. Hooker, J. J. Leach & E. F. McClennen (eds.), Foundations and Applications of Decision Theory. D. Reidel. pp. 233.
     
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  10. Philippe Mongin.Nonaddittve Probability - 1994 - In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer Academic Publishers. pp. 49.
     
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  11.  19
    Jon Williamson.Probability Logic - 2002 - In Dov M. Gabbay (ed.), Handbook of the Logic of Argument and Inference: The Turn Towards the Practical. Elsevier. pp. 397.
  12.  49
    Intuitive Probabilities and the Limitation of Moral Imagination.Arseny A. Ryazanov, Jonathan Knutzen, Samuel C. Rickless, Nicholas J. S. Christenfeld & Dana Kay Nelkin - 2018 - Cognitive Science 42 (S1):38-68.
    There is a vast literature that seeks to uncover features underlying moral judgment by eliciting reactions to hypothetical scenarios such as trolley problems. These thought experiments assume that participants accept the outcomes stipulated in the scenarios. Across seven studies, we demonstrate that intuition overrides stipulated outcomes even when participants are explicitly told that an action will result in a particular outcome. Participants instead substitute their own estimates of the probability of outcomes for stipulated outcomes, and these probability estimates in turn (...)
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  13. ERP Correlates of Verbal and Numerical Probabilities in Risky Choices: A Two-Stage Probability Processing View.Shu Li, Xue-Lei Du, Qi Li, Yan-Hua Xuan, Yun Wang & Li-Lin Rao - 2015 - Frontiers in Human Neuroscience 9:141579.
    Two kinds of probability expressions, verbal and numerical, have been used to characterize the uncertainty that people face. However, the question of whether verbal and numerical probabilities are cognitively processed in a similar manner remains unresolved. From a levels-of-processing perspective, verbal and numerical probabilities may be processed differently during early sensory processing but similarly in later semantic-associated operations. This event-related potential (ERP) study investigated the neural processing of verbal and numerical probabilities in risky choices. The results showed (...)
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  14.  36
    Factors Eliciting Corporate Fraud in Emerging Markets: Case of Firms Subject to Enforcement Actions in Malaysia.Abdul Ghafoor, Rozaimah Zainudin & Nurul Shahnaz Mahdzan - 2019 - Journal of Business Ethics 160 (2):587-608.
    This study investigates the key factors that elicit financial reporting fraud among companies in Malaysia. Using enforcement action releases issued by the Security Commission of Malaysia and Bursa Malaysia, we identify a sample of 76 firms that had committed financial reporting fraud during the period of 1996–2016. We use the fraud triangle framework and the Malaysian International Standards on Auditing 240 to identify the factors. Since the simple probit model fails to address the identification problem, we estimate our results using (...)
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  15.  43
    Eliciting ambiguity aversion in unknown and in compound lotteries: a smooth ambiguity model experimental study.Giuseppe Attanasi, Christian Gollier, Aldo Montesano & Noemi Pace - 2014 - Theory and Decision 77 (4):485-530.
    Coherent-ambiguity aversion is defined within the smooth-ambiguity model as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces two-stage lotteries with binomial, uniform, or unknown second-order probabilities. Theoretical predictions are then tested through a 10-task experiment. In tasks 1–5, risk aversion is elicited through both a portfolio choice method and a BDM mechanism. In tasks 6–10, choice-ambiguity aversion is elicited through the portfolio choice method, while value-ambiguity aversion comes about through (...)
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  16.  25
    Eliciting Uncertainties: A Two Structure Approach.Timothy Childers & Ondrej Majer - 2018 - Studia Logica 106 (3):615-636.
    We recast subjective probabilities by rejecting behaviourist accounts of belief by explicitly distinguishing between judgements of uncertainty and expressions of those judgements. We argue that this entails rejecting that orderings of uncertainty be complete. This in turn leads naturally to several generalizations of the probability calculus. We define probability-like functions over incomplete algebras that reflect a subject’s incomplete judgements of uncertainty. These functions can be further generalized to inner and outer measures that reflect approximate elicitations.
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  17. Ambiguity aversion: the explanatory power of indeterminate probabilities.Horacio Arló-Costa & Jeffrey Helzner - 2010 - Synthese 172 (1):37-55.
    Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...)
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  18.  76
    Subjective Probability Weighting and the Discovered Preference Hypothesis.Gijs van de Kuilen - 2009 - Theory and Decision 67 (1):1-22.
    Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the (...)
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  19.  8
    Eliciting and Assessing our Moral Risk Preferences.Shang Long Yeo - 2024 - American Philosophical Quarterly 61 (2):109-126.
    Suppose an agent is choosing between rescuing more people with a lower probability of success, and rescuing fewer with a higher probability of success. How should they choose? Our moral judgments about such cases are not well-studied, unlike the closely analogous non-moral preferences over monetary gambles. In this paper, I present an empirical study which aims to elicit the moral analogues of our risk preferences, and to assess whether one kind of evidence—concerning how they depend on outcome probabilities—can debunk (...)
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  20.  24
    Probabilities, Methodologies and the Evidence Base in Existential Risk Assessments.Thomas Rowe & Simon Beard - manuscript
    This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their advantages and (...)
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  21.  75
    Probabilities, Methodologies and the Evidence Base in Existential Risk Assessments.Thomas Rowe & Simon Beard - 2018
    This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their advantages and (...)
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  22.  10
    Subjective Probability Weighting and the Discovered Preference Hypothesis.Gijs Kuilen - 2009 - Theory and Decision 67 (1):1-22.
    Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the (...)
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  23.  38
    Probabilities, Methodologies and the Evidence Base in Existential Risk Assessments.Thomas Rowe & Simon Beard - manuscript
    This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their advantages and (...)
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  24.  49
    Forecasting with Imprecise Probabilities.Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane - unknown
    We review de Finetti’s two coherence criteria for determinate probabilities: coherence1defined in terms of previsions for a set of events that are undominated by the status quo – previsions immune to a sure-loss – and coherence2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a (...)
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  25. Statistical Reasoning with Imprecise Probabilities.Peter Walley - 1991 - Chapman & Hall.
    An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.
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  26.  66
    Risk aversion elicitation: reconciling tractability and bias minimization. [REVIEW]Mohammed Abdellaoui, Ahmed Driouchi & Olivier L’Haridon - 2011 - Theory and Decision 71 (1):63-80.
    Risk attitude is known to be a key determinant of various economic and financial choices. Behavioral studies that aim to evaluate the role of risk attitudes in contexts of this type, therefore, require tools for measuring individual risk tolerance. Recent developments in decision theory provide such tools. However, the methods available can be time consuming. As a result, some practitioners might have an incentive to prefer “fast and frugal” methods to clean but more costly methods. In this article, we focus (...)
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  27. Motives and implementation: On the design of mechanisms to elicit opinions.Ariel Rubinstein - manuscript
    A number of experts receive noisy signals regarding a desirable public decision. The public target is to make the best possible decision on the basis of all the information held by the experts. We compare two ``cultures.'' In one, all experts are driven only by the public motive to increase the probability that the desirable action will be taken. In the second, each expert is also driven by a private motive: to have his recommendation accepted. We show that in the (...)
     
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  28. Motives and Implementation: On the Design of Mechanisms to Elicit Opinions.Jacob Glazer & Ariel Rubinstein - unknown
    A number of experts receive noisy signals regarding a desirable public decision. The public target is to make the best possible decision on the basis of all the information held by the experts. We compare two ``cultures.'' In one, all experts are driven only by the public motive to increase the probability that the desirable action will be taken. In the second, each expert is also driven by a private motive: to have his recommendation accepted. We show that in the (...)
     
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  29. The price for information about probabilities and its relation with risk and ambiguity.Giuseppe Attanasi & Aldo Montesano - 2012 - Theory and Decision 73 (1):125-160.
    In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker’s risk and (...)
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  30.  8
    The N400 is Elicited by Meaning Changes but not Synonym Substitutions: Evidence From Persian Phrasal Verbs.Kate Stone, Naghmeh Khaleghi & Milena Rabovsky - 2023 - Cognitive Science 47 (12):e13394.
    We tested two accounts of the cognitive process underlying the N400 event‐related potential component: one that it reflects meaning‐based processing and one that it reflects the processing of specific words. The experimental design utilized separable Persian phrasal verbs, which form a strongly probabilistic, long‐distance dependency, ideal for the study of probabilistic processing. In sentences strongly constraining for a particular continuation, we show evidence that between two low‐probability words, only the word that changed the expected meaning of the sentence increased N400 (...)
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  31. The Gesta Guillelmi of William of Poitiers.William of Poitiers - 1998 - Oxford University Press UK.
    William of Poitiers began his career as a knight before studying in the schools of Poitiers and entering the Church. He became a chaplain in the household of William the Conqueror, and was able to give a first-hand account of the events of 1066-7. The Gesta Guillelmi, his unfinished biography of the king, is particularly important for its detailed description of William's campaigns in Normandy, the careful preparations he made for the invasion of England, the battle of Hastings and the (...)
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  32. Inductive inference based on probability and similarity.Matthew Weber & Daniel Osherson - unknown
    We advance a theory of inductive inference designed to predict the conditional probability that certain natural categories satisfy a given predicate given that others do (or do not). A key component of the theory is the similarity of the categories to one another. We measure such similarities in terms of the overlap of metabolic activity in voxels of various posterior regions of the brain in response to viewing instances of the category. The theory and similarity measure are tested against averaged (...)
     
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  33.  8
    A simple non-parametric method for eliciting prospect theory's value function and measuring loss aversion under risk and ambiguity.Pavlo Blavatskyy - 2021 - Theory and Decision 91 (3):403-416.
    Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our (...)
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  34. Experts in uncertainty: opinion and subjective probability in science.Roger M. Cooke (ed.) - 1991 - New York: Oxford University Press.
    This book is an extensive survey and critical examination of the literature on the use of expert opinion in scientific inquiry and policy making. The elicitation, representation, and use of expert opinion is increasingly important for two reasons: advancing technology leads to more and more complex decision problems, and technologists are turning in greater numbers to "expert systems" and other similar artifacts of artificial intelligence. Cooke here considers how expert opinion is being used today, how an expert's uncertainty is (...)
  35. The Representation of Beliefs and Desires Within Decision Theory.Richard W. Bradley - 1997 - Dissertation, The University of Chicago
    This dissertation interprets the lack of uniqueness in probability representations of agents' degrees of belief in the decision theory of Richard Jeffrey as a formal statement of an important epistemological problem: the underdetermination of our attributions of belief and desire to agents by the evidence of their observed behaviour. A solution is pursued through investigation of agents' attitudes to information of a conditional nature. ;As a first step, Jeffrey's theory is extended to agents' conditional attitudes of belief and desire by (...)
     
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  36.  30
    Theory of Probability: A Critical Introductory Treatment.Bruno de Finetti - 1979 - Wiley.
    First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics. De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that (...)
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  37.  62
    Measuring the time stability of Prospect Theory preferences.Stefan Zeisberger, Dennis Vrecko & Thomas Langer - 2012 - Theory and Decision 72 (3):359-386.
    Prospect Theory (PT) is widely regarded as the most promising descriptive model for decision making under uncertainty. Various tests have corroborated the validity of the characteristic fourfold pattern of risk attitudes implied by the combination of probability weighting and value transformation. But is it also safe to assume stable PT preferences at the individual level? This is not only an empirical but also a conceptual question. Measuring the stability of preferences in a multi-parameter decision model such as PT is far (...)
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  38.  38
    Spectra of conditionalization and typicality in the multiverse.Feraz Azhar - unknown
    An approach to testing theories describing a multiverse, that has gained interest of late, involves comparing theory-generated probability distributions over observables with their experimentally measured values. It is likely that such distributions, were we indeed able to calculate them unambiguously, will assign low probabilities to any such experimental measurements. An alternative to thereby rejecting these theories, is to conditionalize the distributions involved by restricting attention to domains of the multiverse in which we might arise. In order to elicit a (...)
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  39.  21
    Theory of Probability: A Critical Introductory Treatment.Bruno de Finetti - 1970 - New York: John Wiley.
  40.  58
    The Cognitive‐Evolutionary Model of Surprise: A Review of the Evidence. [REVIEW]Rainer Reisenzein, Gernot Horstmann & Achim Schützwohl - 2019 - Topics in Cognitive Science 11 (1):50-74.
    Research on surprise relevant to the cognitive-evolutionary model of surprise proposed by Meyer, Reisenzein, and Schützwohl is reviewed. The majority of the assumptions of the model are found empirically supported. Surprise is evoked by unexpected events and its intensity is determined by the degree if schema-discrepancy, whereas the novelty and the valence of the eliciting events probably do not have an independent effect. Unexpected events cause an automatic interruption of ongoing mental processes that is followed by an attentional shift and (...)
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  41.  12
    Violations of coalescing in parametric utility measurement.Andreas Glöckner, Baiba Renerte & Ulrich Schmidt - 2020 - Theory and Decision 89 (4):471-501.
    The majority consensus in the empirical literature is that probability weighting functions are typically inverse-S shaped, that is, people tend to overweight small and underweight large probabilities. A separate stream of literature has reported event-splitting effects and shown that they can explain violations of expected utility. This leads to the questions whether the observed shape of weighting functions is a mere consequence of the coalesced presentation and, more generally, whether preference elicitation should rely on presenting lotteries in a (...)
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  42.  63
    Individual vs. couple behavior: an experimental investigation of risk preferences. [REVIEW]Mohammed Abdellaoui, Olivier L’Haridon & Corina Paraschiv - 2013 - Theory and Decision 75 (2):175-191.
    In this article, we elicit both individuals’ and couples’ preferences assuming prospect theory (PT) as a general theoretical framework for decision under risk. Our experimental method, based on certainty equivalents, allows to infer measurements of utility and probability weighting at the individual level and at the couple level. Our main results are twofold. First, risk attitude for couples is compatible with PT and incorporates deviations from expected utility similar to those found in individual decision making. Second, couples’ attitudes towards risk (...)
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  43.  93
    Living without state-independence of utilities.Brian Hill - 2009 - Theory and Decision 67 (4):405-432.
    This article is concerned with the representation of preferences which do not satisfy the ordinary axioms for state-independent utilities. After suggesting reasons for not being satisfied with solutions involving state-dependent utilities, an alternative representation shall be proposed involving state-independent utilities and a situation-dependent factor. The latter captures the interdependencies between states and consequences. Two sets of axioms are proposed, each permitting the derivation of subjective probabilities, state-independent utilities, and a situation-dependent factor, and each operating in a different framework. The (...)
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  44. Logical foundations of probability.Rudolf Carnap - 1950 - Chicago]: Chicago University of Chicago Press.
    APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...)
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  45. Foundations of Probability.Rachael Briggs - 2015 - Journal of Philosophical Logic 44 (6):625-640.
    The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.
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  46.  32
    Reconsidering the Mind-Wandering Reader: Predictive Processing, Probability Designs, and Enculturation.Regina E. Fabry & Karin Kukkonen - 2019 - Frontiers in Psychology 9.
    Studies on mind-wandering frequently use reading as an experimental task. In these studies, reading is conceived as a cognitive process that potentially offers a contrast to mind-wandering, because it seems to be task-related, goal-directed and stimulus-dependent. More recent work attempts to avoid the dichotomy of successful cognitive processes and processes of mind-wandering found in earlier studies. We approach the issue from the perspective that texts provoke modes of cognitive involvement different from information processing and recall account that underlies many early (...)
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  47. Reconsidering the mind-wandering reader: predictive processing, probability designs, and enculturation.Regina Fabry & Karin Kukkonen - 2019 - Frontiers in Psychology 9:1-14.
    Studies on mind-wandering frequently use reading as an experimental task. In these studies, reading is conceived as a cognitive process that potentially offers a contrast to mind-wandering, because it seems to be task-related, goal-directed and stimulus-dependent. More recent work attempts to avoid the dichotomy of successful cognitive processes and processes of mind-wandering found in earlier studies. We approach the issue from the perspective that texts provoke modes of cognitive involvement different from the information processing and recall account that underlies many (...)
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  48.  21
    Two Sides of the Coin: Lack of Academic Integrity in Exams During the Corona Pandemic, Students' and Lecturers' Perceptions.Meital Amzalag, Noa Shapira & Niva Dolev - 2022 - Journal of Academic Ethics 20 (2):243-263.
    The Covid-19 pandemic that entered our lives suddenly in 2020 compelled higher education systems throughout the world to transfer to online learning, including online evaluation. A severe problem of online evaluation is that it enables various technological possibilities that facilitate students' unethical behaviors. The research aimed to investigate these behaviors, as well as the reasons for their appearance, as practiced in exams held for the first time during the Covid-19 pandemic, and to elicit students' and lecturers' perceptions of students' academic (...)
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  49. Sets of probability distributions, independence, and convexity.Fabio G. Cozman - 2012 - Synthese 186 (2):577-600.
    This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and recent developments (...)
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  50.  43
    Philosophies of Probability: Objective Bayesianism and its Challenges.Jon Williamson - 2009 - In A. Irvine (ed.), Handbook of the Philosophy of Mathematics. Elsevier.
    This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.
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