Belief Distribution Research Articles

The implications of pricing on social learning

Two firms produce substitute goods of unknown quality. At each stage the firms set prices and a consumer with private information and unit demand buys from one of the firms. Both firms and consumers see the entire history of prices and purchases. Will such markets aggregate information? Will the firm with the superior product necessarily prevail? We adapt the classic social‐learning model by introducing strategic dynamic pricing. We provide necessary and sufficient conditions for asymptotic learning. In contrast to previous results, we show that asymptotic learning can occur when signals are bounded, namely, happens when the density of the consumers at the boundaries of the posterior belief distribution goes to zero. We refer to this property of the signal structure as the “vanishing margins” property.

Towards achieving consistent opinion fusion in group decision making with complete distributed preference relations

Belief distribution (BD) is a scheme of representing qualitative information with subjective uncertainty and imprecision. Distributed preference relation (DPR) extends BDs to the form of pairwise comparison by expressing the preferred, non-preferred, indifferent, and uncertain degrees of one decision alternative over another. However, previous studies on DPR only require comparison of adjacent alternatives, and consensus reaching is not considered fully in the decision making process. To solve this problem, a complete DPR model is presented in this paper to support group decision making (GDM). First, a consistency index is defined to measure the consistency level of the complete DPR representing experts’ judgments. Second, an automatic adjustment algorithm is proposed to improve the consistency of DPRs with unacceptable consistency to an acceptable level. Third, the evidential reasoning (ER) algorithm is utilized to aggregate all the DPRs together, and an optimization model is further constructed to generate experts’ weights, which maximizes the degree of consensus among experts. A GDM example is provided to illustrate the applicability and validity of the proposed DPR model, and comparative analysis demonstrates the potential of the proposed method in supporting real-world GDM problems.

Sullying Sights

ABSTRACT In this article, an account of the architecture of the cognitive contamination system is offered, according to which the contamination system can generate contamination representations in circumstances that do not satisfy the norms of contamination, including in cases of mere visual contact with disgusting objects. It is argued that this architecture is important for explaining the content, logic, distribution, and persistence of maternal impression beliefs – according to which fetal defects are caused by the pregnant mother’s experiences and actions – which in turn provide important evidence of the architecture of the cognitive contamination system.

CRMI: Confidence-Rich Mutual Information for Information-Theoretic Mapping

This letter focuses on information-theoretic active mapping and exploration with beam-based range sensing robots. Traditional works based on hand-engineered inverse sensor model (ISM) mapping or kernel inference methods lead to imbalanced accuracy and efficiency. This motivates us to propose a new approach to compute mutual information more accurately, based on the continuous belief distribution over the occupancy map and called confidence-rich mutual information (CRMI). Specifically, we explicitly model the measurement dependencies between grid cells within the same measurement cone at each time step and derive the CRMI for each cell on all beams by introducing a more general beam-based sensor cause model (SCM), rather than the customized ISM. The time efficiency for CRMI mapping allows for online implementation as well. Extensive simulations and experiments show the desired exploratory behavior to unexplored and obscured regions for CRMI-based robot controllers in the unstructured and cluttered scene, even in large scale environment.

A rational inattention unemployment trap

We show that introducing rational inattention into a model with uninsurable unemployment risk can generate multiple steady states, when the model with full information has a unique steady state. The model features persistent, heterogeneous labour market expectations, consistent with survey evidence. In a heterogeneous agent New Keynesian model, rational inattention to the future hiring rate generates three steady states: an unemployment trap with mild deflation and a low (but positive) job hiring rate, a middle steady state with moderate employment and inflation, and an ‘employment trap’ with high employment and inflation. Large mutations in the distribution of household beliefs can shift the economy between steady states.

Distributional Metareasoning for Heuristic Search

Heuristic search methods are widely used in many real-world autonomous systems. Yet, people always want to solve search problems that are larger than time allows. To address these challenging problems, even suboptimally, a planning agent should be smart enough to intelligently allocate its computational resources, to think carefully about where in the state space it should spend time searching. For finding optimal solutions, we must examine every node that is not provably too expensive. In contrast, to find suboptimal solutions when under time pressure, we need to be very selective about which nodes to examine. In this work, we will demonstrate that estimates of uncertainty, represented as belief distributions, can be used to drive search effectively. This type of algorithmic approach is known as metareasoning, which refers to reasoning about which reasoning to do. We will provide examples of improved algorithms for real-time search, bounded-cost search, and situated planning.

A generalized soft likelihood function in combining multi-source belief distribution functions

A generalized soft likelihood function in combining multi-source belief distribution functions

Feasible Joint Posterior Beliefs

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. For two agents, ...

A Unified Bi-Directional Model for Natural and Artificial Trust in Human–Robot Collaboration

We introduce a novel capabilities-based bi-directional multi-task trust model that can be used for trust prediction from either a human or a robotic trustor agent. Tasks are represented in terms of their capability requirements, while trustee agents are characterized by their individual capabilities. Trustee agents' capabilities are not deterministic; they are represented by belief distributions. For each task to be executed, a higher level of trust is assigned to trustee agents who have demonstrated that their capabilities exceed the task's requirements. We report results of an online experiment with 284 participants, revealing that our model outperforms existing models for multi-task trust prediction from a human trustor. We also present simulations of the model for determining trust from a robotic trustor. Our model is useful for control authority allocation applications that involve human-robot teams.

Explainable data-driven optimization for complex systems with non-preferential multiple outputs using belief rule base

To better handle problems with non-preferential multi-outputs (NPMO), a new approach is proposed in this study by employing the belief rule base (BRB) to provide a superior nonlinearity modeling ability as well as good explainability. The new approach is thus called NPMO–BRB. First, a new optimization model is constructed where the optimization objective is the integration of multi-outputs and respective constraints are designed. Then, a new optimization algorithm with a new customized gene makeup is designed where the NPMO–BRB inferencing process is embedded in the fitness calculation procedure. A practical case study on Changsha Metro Line 4 is studied to use multiple geological parameters to infer multiple operational parameters. Case study results show that NPMO–BRB has shown superior performance in comparison with the random forest (RF), the backpropagation neural network (BPNN), the Gradient Gaussian Process (GPR), as well as multiple separate BRBs. Owing to the explainability provided by the NPMO–BRB approach, further investigations into the belief distribution comparison reveal more information that can be used as practical work guidelines.

CMS-BN: A cognitive modeling and simulation environment for human performance assessment, part 1 — methodology

Cognitive modeling and simulation studies how a human dynamically interacts with the external world. Human performance assessment based on this concept has long been researched in both cognitive sciences and engineering disciplines. However, existing methods have difficulties in describing the uncertain relationships in a human’s knowledge and in considering the uncertainties in the cognitive process. To tackle these issues, we propose a novel cognitive modeling and simulation environment (CMS-BN) by introducing Bayesian networks to represent a human’s knowledge and Monte Carlo simulation to account for the uncertainties in the cognitive process. The proposed environment explicitly models information perception, reasoning and response in a human’s cognitive process. Information perception works as a filtering mechanism to downselect signals from the external world. Reasoning and response are modeled as traversing the human knowledge base represented as a Bayesian network to retrieve knowledge and updating human belief and attention distribution accordingly. Uncertainties in the cognitive process are characterized through Monte Carlo simulation. The proposed environment also models the interplay between the cognitive process and two performance shaping factors, stress and fatigue, though additional factors can be further considered. We expect the proposed environment to be useful in human reliability analysis and human performance improvement.

Gender Inequalities in Markets

Various forms of inequality, such as the gender, race, and class systems of inequality, operate and intersect in societies and markets. In this review, I discuss specifically the gender system of inequality. I focus on market interactions, conceptualizing them as the building blocks for gender inequalities in markets. My objective is to give an account of the complex interplay between the unequal distributions of resources, stereotypes and cultural beliefs about gender, and the law. I start by describing the persistence of gender inequality in markets. Building on studies in social psychology, I then identify the ways in which stereotypes and cultural beliefs about gender constantly, and unconsciously, frame our market interactions. Lastly, I discuss the limits of the law in altering the ways in which we interact in markets and the potential of the law to bring about lasting change.

Estimating force of infection from serologic surveys with imperfect tests.

BackgroundThe force of infection, or the rate at which susceptible individuals become infected, is an important public health measure for assessing the extent of outbreaks and the impact of control programs.Methods and findingsWe present Bayesian methods for estimating force of infection using serological surveys of infections which produce a lasting immune response, accounting for imperfections of the test, and uncertainty in such imperfections. In this estimation, the sensitivity and specificity can either be fixed, or belief distributions of their values can be elicited to allow for uncertainty. We analyse data from two published serological studies of dengue, one in Colombo, Sri Lanka, with a single survey and one in Medellin, Colombia, with repeated surveys in the same individuals. For the Colombo study, we illustrate how the inferred force of infection increases as the sensitivity decreases, and the reverse for specificity. When 100% sensitivity and specificity are assumed, the results are very similar to those from a standard analysis with binomial regression. For the Medellin study, the elicited distribution for sensitivity had a lower mean and higher variance than the one for specificity. Consequently, taking uncertainty in sensitivity into account resulted in a wide credible interval for the force of infection.ConclusionsThese methods can make more realistic estimates of force of infection, and help inform the choice of serological tests for future serosurveys.

Knowledge structure-based consensus-reaching method for large-scale multiattribute group decision-making

Large-scale multiattribute group decision-making (LMGDM) requires a large number of participants with different knowledge structures. This study proposed an LMGDM consensus-reaching method in which the experts’ knowledge structures are fully considered. An information extraction mechanism is constructed to extract incomplete inference information with the form of belief distribution (BD), and the Dempster–Shafer theory of evidence is adopted to make discounting and combinations for the BDs. To reduce their number, the experts are classified into different clusters by using the extended K-means approach, and two levels of consensus measures are both calculated to determine whether the experts involved in each cluster have reached a satisfactory level of consensus. If that consensus level is not reached, a feedback mechanism is activated to advise the identified experts to adjust their assessments, which allows them to change clusters during the consensus-reaching process. Through repeating the feedback mechanism, the assessments are improved until the satisfactory consensus levels are reached. A multi-objective linear programming method is established to obtain the optimal solution that satisfies all clusters as much as possible. Finally, a numerical comparison and discussion are undertaken to demonstrate the superiority of the proposed method.

The Importance of Price Beliefs in Consumer Search

A consumer’s decision to engage in search depends on the beliefs the consumer has about an unknown product characteristic (e.g., price). Because beliefs are rarely observed, researchers typically assume that consumers have rational expectations or update beliefs consistent with Bayesian updating. These assumptions are restrictive and do not enable the researcher or the retailer to price discriminate among consumers on the basis of heterogeneity in beliefs. The authors use Monte Carlo experiments to show how these assumptions affect estimates of search cost. Next, they design an incentive-aligned online study in which participants search over the price of a homogeneous good, and the authors elicit distributions of price beliefs before and after each search. Drawing on data collected from a nationally representative panel, they find substantial heterogeneity in prior price beliefs, such that participants update their beliefs in response to search outcomes but deviate from Bayesian updating in that they underreact to new information. Importantly, the authors show that (1) assuming Bayesian updating does not significantly bias search cost estimates at the aggregate level if the researcher accounts for heterogeneous prior beliefs, (2) eliciting heterogeneity in prior expected prices is much more important than eliciting heterogeneity in prior price uncertainty, and (3) a retailer can increase profits through third-degree price discrimination by recognizing the heterogeneity in prior beliefs.

Bayesian persuasion with costly messages

We study a model of Bayesian persuasion in which the Sender commits to a signal structure, privately observes the signal realization, and then sends a message to the Receiver at a cost that depends on both the signal realized and the message sent. Our setup weakens the Sender's commitment to truthfully reveal information in Bayesian persuasion. We provide sufficient conditions for full communication by the Sender in the Sender-preferred equilibrium, and these conditions are satisfied under many commonly studied communication games. Under these conditions, the Sender's (lack of) commitment in the persuasion problem is quantified as a communication cost to induce a belief distribution for the Receiver. We apply this approach to study test design and information provision by lobbyists.

Eliciting Beliefs as Distributions in Online Surveys

AbstractCitizens’ beliefs about uncertain events are fundamental variables in many areas of political science. While beliefs are often conceptualized in the form of distributions, obtaining reliable measures in terms of full probability densities is a difficult task. In this letter, we ask if there is an effective way of eliciting beliefs as distributions in the context of online surveys. Relying on experimental evidence, we evaluate the performance of five different elicitation methods designed to capture citizens’ uncertain expectations. Our results suggest that an elicitation method originally proposed by Manski (2009) performs well. It measures average citizens’ subjective belief distributions reliably and is easily implemented in the context of regular (online) surveys. We expect that a wider use of this method will lead to considerable improvements in the study of citizens’ expectations and beliefs.

You Know What I Know: Interviewer Knowledge Effects in Subjective Expectation Elicitation.

Directly eliciting individuals' subjective beliefs via surveys is increasingly popular in social science research, but doing so via face-to-face surveys has an important downside: the interviewer's knowledge of the topic may spill over onto the respondent's recorded beliefs. Using a randomized experiment that used interviewers to implement an information treatment, we show that reported beliefs are significantly shifted by interviewer knowledge. Trained interviewers primed respondents to use the exact numbers used in the training, nudging them away from higher answers; recorded responses decreased by about 0.3 standard deviations of the initial belief distribution. Furthermore, respondents with stronger prior beliefs were less affected by interviewer knowledge. We suggest corrections for this issue from the perspectives of interviewer recruitment, survey design, and experiment setup.

Rationalizing rational expectations: Characterizations and tests

In this paper, we build a new test of rational expectations based on the marginal distributions of realizations and subjective beliefs. This test is widely applicable, including in the common situation where realizations and beliefs are observed in two different data sets that cannot be matched. We show that whether one can rationalize rational expectations is equivalent to the distribution of realizations being a mean‐preserving spread of the distribution of beliefs. The null hypothesis can then be rewritten as a system of many moment inequality and equality constraints, for which tests have been recently developed in the literature. The test is robust to measurement errors under some restrictions and can be extended to account for aggregate shocks. Finally, we apply our methodology to test for rational expectations about future earnings. While individuals tend to be right on average about their future earnings, our test strongly rejects rational expectations.

A Unified Bi-directional Model for Natural and Artificial Trust in Human–Robot Collaboration

We introduce a novel capabilities-based bidirectional multi-task trust model that can be used for trust prediction from either a human or a robotic trustor agent. Tasks are represented in terms of their capability requirements, while trustee agents are characterized by their individual capabilities. Trustee agents’ capabilities are not deterministic; they are represented by belief distributions. For each task to be executed, a higher level of trust is assigned to trustee agents who have demonstrated that their capabilities exceed the task’s requirements. We report results of an online experiment with 284 participants, revealing that our model outperforms existing models for multi-task trust prediction from a human trustor. We also present simulations of the model for determining trust from a robotic trustor. Our model is useful for control authority allocation applications that involve human–robot teams.