Objective Probability Research Articles

Framing From Experience: Cognitive Processes and Predictions of Risky Choice.

A framing bias shows risk aversion in problems framed as "gains" and risk seeking in problems framed as "losses," even when these are objectively equivalent and probabilities and outcomes values are explicitly provided. We test this framing bias insituations where decision makers rely on their own experience, sampling the problem's options (safe and risky) and seeing the outcomes before making a choice. In Experiment 1, we replicate the framing bias in description-based decisions and find risk indifference in gains and losses in experience-based decisions. Predictions of an Instance-Based Learning model suggest that objective probabilities as well as the number of samples taken are factors that contribute to the lack of framing effect. We test these two factors in Experiment 2 and find no framing effect when a few samples are taken but when large samples are taken, the framing effect appears regardless of the objective probability values. Implications of behavioral results and cognitive modeling are discussed.

Differences in probability weighting for individual travelers: a managed lane choice application

Using a 2012 stated preference survey based on a traveler’s most recent actual trip, this study predicts traveler choices between general purpose lanes and managed lanes for a freeway in Houston, Texas. The choice model incorporates probability weighting for risky travel times. The results indicate significant improvement in predicative power over a model that excludes weighting, confirming non-linearity in the probability weighting function. The maximum value of time (VOT) measures calculated in this study are lower than estimated in many previous route choice studies. This highlights the importance of incorporating individual weights for travel risks. Travelers’ underweighting of travel time risks would help explain the lower VOTs found in our study because respondents consider route choice decision-making as a gamble, but assign their own probabilities of occurrence to arriving at their destination on time, late, or early. We find that traveler groups are heterogeneous and the different weights developed for different groups of travelers can be used to better understand their probabilities. Segmentation analysis indicates that Age may serve to proxy the effects of more experience over time, or changing driving abilities, or changes in one’s sense of optimism or pessimism at different ages. Gender and Income also play a role in how the objective probabilities presented to respondents were translated into subjective probabilities.

The framing effect and skin conductance responses.

Individuals often rely on simple heuristics when they face complex choice situations under uncertainty. Traditionally, it has been proposed that cognitive processes are the main driver to evaluate different choice options and to finally reach a decision. Growing evidence, however, highlights a strong interrelation between judgment and decision-making (JDM) on the one hand, and emotional processes on the other hand. This also seems to apply to judgmental heuristics, i.e., decision processes that are typically considered to be fast and intuitive. In this study, participants are exposed to different probabilities of receiving an unpleasant electric shock. Information about electric shock probabilities is either positively or negatively framed. Integrated skin conductance responses (ISCRs) while waiting for electric shock realization are used as an indicator for participants' emotional arousal. This measure is compared to objective probabilities. I find evidence for a relation between emotional body reactions measured by ISCRs and the framing effect. Under negative frames, participants show significantly higher ISCRs while waiting for an electric shock to be delivered than under positive frames. This result might contribute to a better understanding of the psychological processes underlying JDM. Further studies are necessary to reveal the causality underlying this finding, i.e., whether emotional processes influence JDM or vice versa.

Reduction of compound lotteries with objective probabilities: Theory and evidence

The reduction of compound lotteries axiom (ROCL) has assumed a central role in the evaluation of behavior toward risk and uncertainty. We present experimental evidence on its validity in the domain of objective probabilities. Our battery of lottery pairs includes simple one-stage lotteries, two-stages compound lotteries, and their actuarially equivalent one-stage lotteries. We find violations of ROCL and that behavior is better characterized by a source-dependent version of the Rank-Dependent Utility model rather than Expected Utility Theory. Since we use the popular “1-in-K” random lottery incentive mechanism payment procedure in our main test, our experiment explicitly recognizes the impact that this payment procedure may have on preferences. Thus we also collect data using the “1-in-1” payment procedure. We do not infer any violations of ROCL when subjects are only given one decision to make. These results are supported by both structural estimation of latent preferences as well as non-parametric analysis of choice patterns. The random lottery incentive mechanism, used as payment protocol, itself induces an additional layer of “compounding” by design that might create confounds in tests of ROCL. Therefore, we provide a word of caution for experimenters interested in studying ROCL for other purposes, such as the relationship between ambiguity attitudes and attitudes toward compound lotteries, to carefully think about the design to study ROCL, payment protocols and their interaction with the preferences being elicited.

ERP effects and perceived exclusion in the Cyberball paradigm: Correlates of expectancy violation?

A virtual ball-tossing game called Cyberball has allowed the identification of neural structures involved in the processing of social exclusion by using neurocognitive methods. However, there is still an ongoing debate if structures involved are either pain- or exclusion-specific or part of a broader network. In electrophysiological Cyberball studies we have shown that the P3b component is sensitive to exclusion manipulations, possibly modulated by the probability of ball possession of the participant (event “self”) or the presumed co-players (event “other”). Since it is known from oddball studies that the P3b is not only modulated by the objective probability of an event, but also by subjective expectancy, we independently manipulated the probability of the events “self” and “other” and the expectancy for these events. Questionnaire data indicate that social need threat is only induced when the expectancy for involvement in the ball-tossing game is violated. Similarly, the P3b amplitude of both “self” and “other” events was a correlate of expectancy violation. We conclude that both the subjective report of exclusion and the P3b effect induced in the Cyberball paradigm are primarily based on a cognitive process sensitive to expectancy violations, and that the P3b is not related to the activation of an exclusion-specific neural alarm system.

Subjective Probability in Behavioral Economics and Finance: A Radical Reformulation

Behavioral finance depends intimately on the notion of subjective probability, which has been universally treated as one of the two forms of probability. A substantial body of work and recent experimental results show conclusively that this approach is invalid: subjective and objective probabilities cannot be treated as two sides of the same coin. This raises serious questions about calculations based on that assumption, decisions based on those calculations, and what to do if assigning numerical values and calculating expected values based on subjective probabilities is invalid. This paper presents a radical re-formulation of subjective probability, showing that what have been called “subjective probabilities” are properly formulated as uncertainty appraisals, re-descriptions of states of affairs carrying tautological implications for action. A novel formulation of the decision maker's field-of-view, based on the concept of Actor, Observer, and Critic roles, combined with the uncertainty appraisal formulation, is used to develop new methods for evaluating data, finding patterns in data, and integrating probabilities and uncertainty appraisals, that is, those aspects that have, until now, been called “subjective probabilities.”

An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

We present a novel approach to constructing objective prior distributions for discrete parameter spaces. These types of parameter spaces are particularly problematic, as it appears that common objective procedures to design prior distributions are problem specific. We propose an objective criterion, based on loss functions, instead of trying to define objective probabilities directly. We systematically apply this criterion to a series of discrete scenarios, previously considered in the literature, and compare the priors. The proposed approach applies to any discrete parameter space, making it appealing as it does not involve different concepts according to the model. Supplementary materials for this article are available online.

A Quantum Finance Model

Both academic research and practical application of mathematical finance have been extremely fruitful since the seminal work of Black-Scholes-Merton in the early 1970s. In this framework, the prices of financial assets are modeled as stochastic processes in probability spaces inside which the machinery of stochastic calculus is a powerful tool. The fundamental asset pricing theorem states that the absence of arbitrage opportunities in a market is equivalent to the existence of a probability measure, equivalent to the objective probability, under which the discounted prices of the assets become local martingales. This linkage between finance on the one hand and the probability theory on the other is the key to the success of mathematical finance. In this note, we show that it is possible to extend the classical probability model to a quantum probability model. The classical stochastic calculus is replaced by its quantum counterpart on the Boson Fock space. In particular, we show that the fundamental asset pricing theorem remains valid in this non-commutative setting. As an application, prices of quantum European options are obtained.

Probabilistic combination of classification rules and its application to medical diagnosis

Application of machine learning to medical diagnosis entails facing two major issues, namely, a necessity of learning comprehensible models and a need of coping with imbalanced data phenomenon. The first one corresponds to a problem of implementing interpretable models, e.g., classification rules or decision trees. The second issue represents a situation in which the number of examples from one class (e.g., healthy patients) is significantly higher than the number of examples from the other class (e.g., ill patients). Learning algorithms which are prone to the imbalance data return biased models towards the majority class. In this paper, we propose a probabilistic combination of soft rules, which can be seen as a probabilistic version of the classification rules, by introducing new latent random variable called conjunctive feature. The conjunctive features represent conjunctions of values of attribute variables (features) and we assume that for given conjunctive feature the object and its label (class) become independent random variables. In order to deal with the between class imbalance problem, we present a new estimator which incorporates the knowledge about data imbalanceness into hyperparameters of initial probability of objects with fixed class labels. Additionally, we propose a method for aggregating sufficient statistics needed to estimate probabilities in a graph-based structure to speed up computations. At the end, we carry out two experiments: (1) using benchmark datasets, (2) using medical datasets. The results are discussed and the conclusions are drawn.

REMOVED: The valuation of social impact bonds: An introductory perspective with the Peterborough SIB

Social impact bonds (SIBs) are financial assets whose objective is to attract investors to fund social programs by providing them an incentive if the project meets its predefined targets. This article aimed at proposing a reflection about the development of a pricing method for this kind of financial assets in an uncertain environment. After having defined SIBs and presenting their intrinsic uncertainty in the first section, I will present, in the second one, an existing SIB (called Peterborough SIB) in financial terms. Afterwards, the last section offered an introductory perspective on the potential development of a Wang transformation based pricing method applied to this Peterborough SIB. By using this statistical operator as a statistical technique for converting objective probabilities (past observations) into subjective estimates of these probabilities, this paper investigates a specific way of integrating the uncertainty in related the valuation of SIBs.

Natural probabilistic information

Natural information refers to the information carried by natural signs such as that smoke is thought to carry natural information about fire. A number of influential philosophers have argued that natural information can also be utilized in a theory of mental content. The most widely discussed account of natural information (due to Dretske, in Knowledge and the flow of information, 1981/1999) holds that it results from an extremely strong relation between sign and signified (i.e. a conditional probability of 1). Critics have responded that it is doubtful that there are many strong relations of this sort in the natural world due to variability between signs and signified. In light of this observation, a promising suggestion is that much of the interesting natural information carried by natural signs is really information with a probabilistic content. However, Dretske’s theory cannot account for this information because it would require implausible second order objective probabilities. Given the most plausible understanding of the probabilities involved here, I argue that it is only sequences of traditional natural signs (not individual signs) that carry this probabilistic information. Several implications of this idea will be explored.

Counting steps: a finitist approach to objective probability in physics

We propose a new interpretation of objective probability in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set-up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the ‘distance’ (in terms of physical resources) between a physical state and another, and (3) the size of the set of time-complexity functions that are compatible with the physical resources required to reach a physical state from another. This view (a) exorcises ‘ignorance’ from statistical physics, and (b) underlies a new interpretation to non-relativistic quantum mechanics.

Cheating or Coincidence? Statistical Method Employing the Principle of Maximum Entropy for Judging Whether a Student Has Committed Plagiarism

Elements of correspondence (“coincidences”) between a student’s solutions to an assigned set of quantitative problems and the solutions manual for the course textbook may suggest that the stu-dent copied the work from an illicit source. Plagiarism of this kind, which occurs primarily in fields such as the natural sciences, engineering, and mathematics, is often difficult to establish. This paper derives an expression for the probability that alleged coincidences in a student’s paper could be attributable to pure chance. The analysis employs the Principle of Maximum Entropy (PME), which, mathematically, is a variational procedure requiring maximization of the Shannon-Jaynes entropy function augmented by the completeness relation for probabilities and known information in the form of expectation values. The virtue of the PME as a general method of inferential reasoning is that it generates the most objective (i.e. least biased) probability distribution consistent with the given information. Numerical examination of test cases for a range of plausible conditions can yield outcomes that tend to exonerate a student who otherwise might be wrongfully judged guilty of cheating by adjudicators unfamiliar with the surprising properties of random processes.

THE DENOMINATOR NEGLECT IN DECISION-MAKING

IntroductionIf you want to buy a lottery ticket, would you choose from a pile in which one out of ten is a winner, or would you choose from a pile in which nine out of a hundred are winners? If you prefer to choose from the second pile, you probably pay more attention to the numerator than to the denominator. This phenomenon is not rare; it is called denominator neglect, or ratio-bias phenomenon (in the present study I use the term denominator neglect). Denominator neglect is focusing on relative frequencies of numerators (Reyna & Brainerd, 2008), paying attention to numerators (number of times an event has happened) and inadequate attention to denominators (overall number of opportunities for an event to happen) (e.g., Garcia-Retamero, Galesic, & Gigerenzer, 2010; Okan, Garcia-Retamero, Cokely, & Maldonado, 2011; Passerini, Macchi, & Bagassi, 2012), for instance, whether nine winning lottery tickets is few or many depends on the overall number of lottery tickets.According to Alonso and Fernandez-Berrocal (2003) one reason of denominator neglect is that people better understand whole numbers than ratios (people automatically code frequencies) and second reason is that people better understand low numbers than large numbers. Low numbers are more concrete than large numbers and, furthermore, people have a social circle of around 100-200 people, so understanding probabilities with larger denominator may be difficult (Garcia-Retamero & Galesic, 2011). For example, in terms of the occurrence of side effects, people have problems imagining the incidence of 1-in-1000, 1-in-10000, etc. Understanding numerical information seems to be important because it can lead to accurate judgement and decision making, especially in medical treatment when people focus more on treated and non-treated people who die and they do not consider the overall number of patients. In another study, Alonso and Fernandez-Berrocal (2003) found that people made irrational decisions; they chose options with less objective probability due to higher numerator than in the alternative option.Pacini and Epstein (1999) examined some determinants of denominator neglect and they found that participants scoring low in rational thinking made more suboptimal responses in Jellybean tasks. In another study, Alonso and Fernandez-Berrocal (2003) found that people who chose the suboptimal options had lower score in rationality measured by Need for Cognition Scale, and Toplak, West, and Stanovich (2013) found that cognitive reflection predicted resistance to denominator neglect.In previous studies (Alonso & Fernandez-Berrocal, 2003; Garcia-Retamero & Galesic, 2011; Pacini & Epstein, 1999; Toplak, West, & Stanovich, 2013) denominator neglect was described in terms of its frequencies and its predictors. In the present study, the main aim was to replicate the above-mentioned findings: a) to examine the degree of denominator neglect and b) to verify possible relations of denominator neglect with cognitive ability, motive for rational thinking integration, preference of cognitive style, and cognitive reflection. The present study enriched denominator neglect research by using the Jellybean task with equal versus unequal and small versus large probabilities, next, by using self-reported scales as well as performance task to measure cognitive abilities, and by motivation of participants for optimal (maximal) performance.In Study 1 simple Jellybean task was used - 3 tasks with unequal low probabilities and relationship between denominator neglect and cognitive ability and motive for rational integration was verified. In Study 2 more complex Jellybean task was used (14 items) and the effect of equality of probability (equal vs. unequal) and degree of probability (low vs. high) were examined, as well as relationships between denominator neglect and motive for rational integration and thinking dispositions. In contrast to Study 1, participants were incentivized by extra credits dependent on the accuracy of their choices in the Jellybean task. …

Support relation analysis and decision making for safe robotic manipulation tasks

In this article, we describe an approach to address the issue of automatically building and using high-level symbolic representations that capture physical interactions between objects in static configurations. Our work targets robotic manipulation systems where objects need to be safely removed from piles that come in random configurations. We assume that a 3D visual perception module exists so that objects in the piles can be completely or partially detected. Depending on the outcome of the perception, we divide the issue into two sub-issues: (1) all objects in the configuration are detected; (2) only a subset of objects are correctly detected. For the first case, we use notions from geometry and static equilibrium in classical mechanics to automatically analyze and extract act and support relations between pairs of objects. For the second case, we use machine learning techniques to estimate the probability of objects supporting each other. Having the support relations extracted, a decision making process is used to identify which object to remove from the configuration so that an expected minimum cost is optimized. The proposed methods have been extensively tested and validated on data sets generated in simulation and from real world configurations for the scenario of unloading goods from shipping containers.

An Automated High-Level Saliency Predictor for Smart Game Balancing

Successfully predicting visual attention can significantly improve many aspects of computer graphics: scene design, interactivity and rendering. Most previous attention models are mainly based on low-level image features, and fail to take into account high-level factors such as scene context, topology, or task. Low-level saliency has previously been combined with task maps, but only for predetermined tasks. Thus, the application of these methods to graphics (e.g., for selective rendering) has not achieved its full potential. In this article, we present the first automated high-level saliency predictor incorporating two hypotheses from perception and cognitive science that can be adapted to different tasks. The first states that a scene is comprised of objects expected to be found in a specific context as well objects out of context which are salient (scene schemata) while the other claims that viewer’s attention is captured by isolated objects (singletons). We propose a new model of attention by extending Eckstein’s Differential Weighting Model. We conducted a formal eye-tracking experiment which confirmed that object saliency guides attention to specific objects in a game scene and determined appropriate parameters for a model. We present a GPU-based system architecture that estimates the probabilities of objects to be attended in real- time. We embedded this tool in a game level editor to automatically adjust game level difficulty based on object saliency, offering a novel way to facilitate game design. We perform a study confirming that game level completion time depends on object topology as predicted by our system.

A fast method for estimation of the impact probability of near-Earth objects

A fast method for estimation of the impact probability of near-Earth objects

Good-Turing frequency estimation in a finite population.

Good-Turing frequency estimation (Good, ) is a simple, effective method for predicting detection probabilities of objects of both observed and unobserved classes based on observed frequencies of classes in a sample. The method has been used widely in several disciplines, such as information retrieval, computational linguistics, text recognition, and ecological diversity estimation. Nevertheless, existing studies assume sampling with replacement or sampling from an infinite population, which might be inappropriate for many practical applications. In light of this limitation, this article presents a modification of the Good-Turing estimation method to account for finite population sampling. We provide three practical extensions of the modified method, and we examine performance of the modified method and its extensions in simulation experiments.

Detecting a dynamic object on a complex background from a low-contrast point image on an optoelectronic device

This paper proposes a method of detecting dynamic objects on an image from an optoelectronic device when there is a complex background formed by dense cumulus and altocumulus clouds. The image of the object is a small (point), low-contrast image. The fractal-correlation method is based on the use of a sample in the form of the ratio of the likelihood functions of close-by alternative situations of the type “only a complex background is observed in the viewing zone of the optoelectronic device” or “a dynamic object on a complex background is observed in the viewing zone of the optoelectronic device.” An algorithm is constructed for detecting a dynamic object as a binary accumulator, using the local, most powerful criterion. The critical limit for making a decision is determined according to the Neyman–Pearson lemma for the allowable false-detection probability of a dynamic object. Modelling is used to establish the high effectiveness of the method.

Change or stick? Anticipation processes associated with subjective and objective probability of winning in a Monty Hall Dilemma task

The pandemic outbreak at the beginning of 2020 had changed the ways and perception of consumers using products abruptly. The study examined consumer traits (i.e., impulse buying tendency, shopping enjoyment tendency, consumer mood) and situational factors (i.e., individual situation, website quality, motivational activities by retailers, and product attributes) to their online impulse buying. The sample was 290 criteria-met respondents and collected using the survey method, distributing the questionnaire, and applying the Structural Equation Model (SEM) to analyze the findings. The research founds that firstly, there were three accepted hypotheses in which the influencing factors of online impulse buying, such as impulse buying tendency, consumer mood, and motivational activities by retailers. Secondly, other factors such as shopping enjoyment tendency, individual situation, website quality, and product attributes were not the determinants. It implied that the on-going phenomena of changing consumers' online impulse buying driven by their traits should be the critical factors for any sellers to reap and optimize the available opportunities during the pandemic's sudden change.