Probabilistic Contexts Research Articles

Law-invariant return and star-shaped risk measures

This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts.

Expected distractor context biases the attentional template for target shapes.

Visual search is supported by an internal representation of the target, the attentional template. However, which features are diagnostic of target presence critically depends on the distractors. Accordingly, previous research showed that consistent distractor context shapes the attentional template for simple targets, with the template emphasizing diagnostic dimensions (e.g., color or orientation) in blocks of trials. Here, we investigated how distractor expectations bias attentional templates for complex shapes, and tested whether such biases reflect intertrial priming or can be instantiated flexibly. Participants searched for novel shapes (cued by name) in two probabilistic distractor contexts: Either the target's orientation or rectilinearity was unique (80% validity). Across four experiments, performance was better when the distractor context was expected, indicating that target features in the expected diagnostic dimension were emphasized. Attentional templates were biased by distractor expectations when distractor context was blocked, also for participants reporting no awareness of the manipulation. Interestingly, attentional templates were also biased when distractor context was cued on a trial-by-trial basis, but only when the two contexts were consistently presented at distinct spatial locations. These results show that attentional templates can flexibly and adaptively incorporate expectations about target-distractor relations when looking for the same object in different contexts. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Deep Time Series Forecasting With Shape and Temporal Criteria.

This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the ability to provide sharp predictions in deterministic and probabilistic contexts. To handle these challenges, we propose to incorporate shape and temporal criteria in the training objective of deep models. We define shape and temporal similarities and dissimilarities, based on a smooth relaxation of Dynamic Time Warping (DTW) and Temporal Distortion Index (TDI), that enable to build differentiable loss functions and positive semi-definite (PSD) kernels. With these tools, we introduce DILATE (DIstortion Loss including shApe and TimE), a new objective for deterministic forecasting, that explicitly incorporates two terms supporting precise shape and temporal change detection. For probabilistic forecasting, we introduce STRIPE++ (Shape and Time diverRsIty in Probabilistic for Ecasting), a framework for providing a set of sharp and diverse forecasts, where the structured shape and time diversity is enforced with a determinantal point process (DPP) diversity loss. Extensive experiments and ablations studies on synthetic and real-world datasets confirm the benefits of leveraging shape and time features in time series forecasting.

Ensemble-Based Forecast of Volcanic Clouds Using FALL3D-8.1

Operational forecasting of volcanic ash and SO2 clouds is challenging due to the large uncertainties that typically exist on the eruption source term and the mass removal mechanisms occurring downwind. Current operational forecast systems build on single-run deterministic scenarios that do not account for model input uncertainties and their propagation in time during transport. An ensemble-based forecast strategy has been implemented in the FALL3D-8.1 atmospheric dispersal model to configure, execute, and post-process an arbitrary number of ensemble members in a parallel workflow. In addition to intra-member model domain decomposition, a set of inter-member communicators defines a higher level of code parallelism to enable future incorporation of model data assimilation cycles. Two types of standard products are automatically generated by the ensemble post-process task. On one hand, deterministic forecast products result from some combination of the ensemble members (e.g., ensemble mean, ensemble median, etc.) with an associated quantification of forecast uncertainty given by the ensemble spread. On the other hand, probabilistic products can also be built based on the percentage of members that verify a certain threshold condition. The novel aspect of FALL3D-8.1 is the automatisation of the ensemble-based workflow, including an eventual model validation. To this purpose, novel categorical forecast diagnostic metrics, originally defined in deterministic forecast contexts, are generalised here to probabilistic forecasts in order to have a unique set of skill scores valid to both deterministic and probabilistic forecast contexts. Ensemble-based deterministic and probabilistic approaches are compared using different types of observation datasets (satellite cloud detection and retrieval and deposit thickness observations) for the July 2018 Ambae eruption in the Vanuatu archipelago and the April 2015 Calbuco eruption in Chile. Both ensemble-based approaches outperform single-run simulations in all categorical metrics but no clear conclusion can be extracted on which is the best option between these two.

Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers

Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics teachers (PSMTs) reason under uncertainty? A multiple case study design was operated in which a purposive sample of PSMTs was selected to justify their reasoning in two probabilistic contexts while their responses were coded by NVivo, and corresponding categories were developed. As a result, PSMTs’ probabilistic reasoning was classified into mathematical (M), subjective (S), and outcome-oriented (O). Besides, several biases emerged along with these modes of reasoning. While M thinkers shared equiprobability and insensitivity to prior probability, the prediction bias and the belief of Allah’s willingness were yielded among S thinkers. Also, the causal conception spread among O thinkers.

Analysing Probability Teaching Practices in Primary Education: What Tasks Do Teachers Implement?

This study analyses probability tasks proposed by primary education teachers to promote probabilistic literacy. To this end, eight class sessions at various levels of the Chilean educational system were recorded on video and analysed through the ”probability tasks” dimension from the “Observation Instrument for Probability Classes” (IOC-PROB), which includes five components: use of resources, probabilistic contexts, cognitive challenge, procedures and strategies, and probability meanings. The results show that probability tasks focus mainly on technical knowledge, causing the probability class to become an arithmetic class in which only formulas are applied, mechanically and with no meaning. As a result, we see no use of technological resources, a low use of physical materials, and an absolute predominance of solving decontextualised exercises. We conclude that it is necessary to enhance the probability teaching practices based on lesson plans that consider a wide variety of resources and contexts to gradually advance towards a representation of probabilistic knowledge that relies on conventional procedures and notations.

The Yun transform in probabilistic and statistical contexts: Weibull baseline case and its applications in reliability theory

In this paper, we present a new family of distributions based on a particular case of a transform introduced by Yun (2014). Among others, this transform demonstrates great flexibility and nice mathematical properties which can be useful in a statistical context (continuous derivatives of all order, simplicity of the inverse transform, etc.). We propose a new three-parameter distribution from this family, namely the Yun–Weibull (YW) distribution. Some statistical properties of this distribution are studied, involving flexible hazard rate shapes. Subsequently, the statistical inference of the YW distribution is investigated. The parameters are estimated by employing the maximum likelihood estimation method. We establish the existence and uniqueness of the obtained estimators. The YW distribution is applied to fit two practical data sets. As a main result of our analysis, the new distribution is found to be more appropriate to these data sets than other competitive distributions. Moreover, the uniqueness of the parameter estimates of the YW distribution is studied using the profile log-likelihood function visually under the two practical data sets.

Strategies for selecting and evaluating information

Within the domain of psychology, Optimal Experimental Design (OED) principles have been used to model how people seek and evaluate information. Despite proving valuable as computational-level methods to account for people’s behaviour, their descriptive and explanatory powers remain largely unexplored. In a series of experiments, we used a naturalistic crime investigation scenario to examine how people evaluate queries, as well as outcomes, in probabilistic contexts. We aimed to uncover the psychological strategies that people use, not just to assess whether they deviated from OED principles. In addition, we explored the adaptiveness of the identified strategies across both one-shot and stepwise information search tasks. We found that people do not always evaluate queries strictly in OED terms and use distinct strategies, such as by identifying a leading contender at the outset. Moreover, we identified aspects of zero-sum thinking and risk aversion that interact with people’s information search strategies. Our findings have implications for building a descriptive account of information seeking and evaluation, accounting for factors that currently lie outside the realm of information-theoretic OED measures, such as context and the learner’s own preferences.

Glutamatergic Contribution to Probabilistic Reasoning and Jumping to Conclusions in Schizophrenia: A Double-Blind, Randomized Experimental Trial

BackgroundImpaired probabilistic reasoning and the jumping-to-conclusions reasoning bias are hallmark features of schizophrenia (SCZ), yet the neuropharmacological basis of these deficits remains unclear. Here we tested the hypothesis that glutamatergic neurotransmission specifically contributes to jumping to conclusions and impaired probabilistic reasoning in SCZ. MethodsA total of 192 healthy participants received either NMDA receptor agonists/antagonists (D-cycloserine/dextromethorphan), dopamine type 2 receptor agonists/antagonists (bromocriptine/haloperidol), or placebo in a randomized, double-blind, between-subjects design. In addition, we tested 32 healthy control participants matched to 32 psychotic inpatients with SCZ—a state associated with compromised probabilistic reasoning due to reduced glutamatergic neurotransmission. All experiments employed two versions of a probabilistic reasoning (beads) task, which required participants to either sample individual amounts of sensory information to infer correct decisions or provide explicit probability estimates for presented sensory information. Our task instantiations assessed both information sampling and explicit probability estimates in different probabilistic contexts (easy vs. difficult conditions) and changing sensory information through random transitions among easy, difficult, and ambiguous trial types. ResultsFollowing administration of D-cycloserine, haloperidol, and bromocriptine, healthy participants displayed data-gathering behavior that was normal compared with placebo and was adequate in the context of all employed task conditions and trial level difficulties. However, healthy participants receiving dextromethorphan displayed a jumping-to-conclusions bias, abnormally increased probability estimates, and overweighting of sensory information. These effects were mirrored in patients with SCZ performing the same versions of the beads task. ConclusionsOur findings provide novel neuropharmacological evidence linking reduced glutamatergic neurotransmission to impaired information sampling and to disrupted probabilistic reasoning, namely to overweighting of sensory evidence, in patients with SCZ.

Study of Uncertainties and Objective Function Modeling Effects on Probabilistic Optimization Results

Abstract In this work, we study the effect of uncertainties modeling and the choice of objective function on the results of optimization design problems in deterministic and probabilistic contexts. Uncertainties modeling are studied in two cases identified in the literature. The results show how the choice of two different objective functions, which lead to the same results in deterministic case, may lead to opposite results in probabilistic case. Also, the results show how the uncertainties modeling type can affect the antagonism between mean and standard deviation in the reliability-based robust design optimization (RBRDO) problems. Three mechanical applications chosen from the literature are used to illustrate these cases.

Cheating: One common morality for gains and losses but two components of morality itself

AbstractPrevious studies show that decision makers (DMs) lie more to avoid a loss than achieve a gain. Two compelling mechanisms might explain this observation. One assumes that lying is a risky activity and relates to the shape of the monetary value function described by prospect theory, which assumes (a) increased risk taking for loss frames and (b) an asymmetry between the perceived values of losses and gains. The other relates to the importance of self‐esteem functions as expressed in self‐concept maintenance models, self‐esteem issues being weighed against monetary issues. This alternative explanation assumes that a loss frame serves as a factor lowering moral considerations. We report an experimental study presenting sets of lotteries to DMs, once in a moral context and once in a traditional probabilistic context. The results show that DMs take less risk when lotteries are presented in a moral context. It is also shown that DMs take more risk for losses than gains, this holding for both the moral and probabilistic contexts. This latter result suggests that loss/gain asymmetry can be completely explained by prospect theory factors, and framing makes no difference to the valuing of moral considerations.

Cheating: One Common Morality for Gain and Losses, but Two Components of Morality Itself

Previous studies show that decision makers lie more to avoid a loss than achieve a gain. Two compelling mechanisms might explain this observation. One assumes that lying is a risky activity, and relates to the shape of the monetary value function described by prospect theory, which assumes: (1) increased risk-taking for loss frames, and; (2) an asymmetry between the perceived values of losses and gains. The other relates to the importance of self-esteem functions as expressed in self-concept maintenance models, self-esteem issues being weighed against monetary issues. This alternative explanation assumes that a loss frame serves as a factor lowering moral considerations. We report an experimental study presenting sets of lotteries to decision makers (DMs), once in a moral context and once in a traditional probabilistic context. The results show that DMs take less risk when lotteries are presented in a moral context. It is also shown that DMs take more risk for losses than gains, this holding for both the moral and probabilistic contexts. This latter result suggests that loss/gain asymmetry can be completely explained by prospect theory factors, while framing makes no difference to the valuing of moral considerations.

Integrating modality-specific expectancies for the deployment of spatial attention

The deployment of spatial attention is highly sensitive to stimulus predictability. Despite evidence for strong crossmodal links in spatial attentional systems, it remains to be elucidated how concurrent but divergent predictions for targets in different sensory modalities are integrated. In a series of behavioral studies, we investigated the processing of modality-specific expectancies using a multimodal cueing paradigm in which auditory cues predicted the location of visual or tactile targets with modality-specific cue predictability. The cue predictability for visual and tactile targets was manipulated independently. A Bayesian ideal observer model with a weighting factor was applied to trial-wise individual response speed to investigate how the two probabilistic contexts are integrated. Results showed that the degree of integration depended on the level of predictability and on the divergence of the modality-specific probabilistic contexts (Experiments 1–2). However, when the two probabilistic contexts were matched in their level of predictability and were highly divergent (Experiment 3), higher separate processing was favored, especially when visual targets were processed. These findings suggest that modality-specific predictions are flexibly integrated according to their reliability, supporting the hypothesis of separate modality-specific attentional systems that are however linked to guarantee an efficient deployment of spatial attention across the senses.

Probabilistic implication bases in FCA and probabilistic bases of GCIs in

A probabilistic formal context is a triadic context the third dimension of which is a set of worlds equipped with a probability measure. After a formal definition of this notion, this document introduces probability of implications with respect to probabilistic formal contexts, and provides a construction for a base of implications the probabilities of which exceed a given lower threshold. A comparison between confidence and probability of implications is drawn, which yields the fact that both measures do not coincide. Furthermore, the results are extended towards the lightweight description logic with probabilistic interpretations, and a method for computing a base of general concept inclusions the probabilities of which are greater than a pre-defined lower bound is proposed. Additionally, we consider so-called probabilistic attributes over probabilistic formal contexts, and provide a method for the axiomatization of implications over probabilistic attributes.

Some epistemological ramifications of the Borel–Kolmogorov paradox

This paper discusses conditional probability $$P(A{\vert }B)$$ , or the probability of A given B. When $$P(B)>0$$ , the ratio formula determines $$P(A {\vert } B)$$ . When $$P(B)=0$$ , the ratio formula breaks down. The Borel–Kolmogorov paradox suggests that conditional probabilities in such cases are indeterminate or ill-posed. To analyze the paradox, I explore the relation between probability and intensionality. I argue that the paradox is a Frege case, similar to those that arise in many probabilistic and non-probabilistic contexts. The paradox vividly illustrates how an agent’s way of representing an entity can rationally influence her credal assignments. I deploy my analysis to defend Kolmogorov’s relativistic treatment of conditional probability.

An alternative comprehensive framework using belief functions for parameter and model uncertainty analysis in nuclear probabilistic risk assessment applications

In nuclear power plants, probabilistic risk assessment insights contribute to achieve a safe design and operation. In this context, the decision-making process must be robust and uncertainties must be taken into account and controlled. In general, the uncertainties in a nuclear probabilistic risk assessment context can be categorized as either aleatory or epistemic. The epistemic uncertainty, which can be subdivided into parameter and model uncertainties, is recognized to have an important impact on actual results of probabilistic risk assessment. Traditionally, the approach of an epistemic uncertainty analysis in nuclear probabilistic risk assessment often relies on the probabilistic approach in which parameter uncertainty is treated by using an assigned probability distribution, e.g. the log-normal one, and model uncertainty can be taken into account through sensitivity studies. Such an approach has been recognized in several recent researchs to present limitations regarding the impacts of assigning probability distribution in case of rare operating feedback data. In order to overcome such a limitation, in this article we propose a comprehensive approach for uncertainty analysis from the parameter and model uncertainties modeling to the final step of the decision-making process using the Dempster-Shafer theory, which is recognized to be more general than the probabilistic approach. We also show that the traditional probabilistic approach, currently used in probabilistic risk assessment practice, can be totally integrated in this framework. Finally, the proposed framework is illustrated and compared with the traditional approach through a practical example from EDF Nuclear Power Plants probabilistic risk assessment application. Some discussions and conclusions for industrial probabilistic risk assessment contexts will be given.

Observing Branching Structure through Probabilistic Contexts

Probabilistic automata (PAs) constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior, such as distributed algorithms and network protocols. The behavior of PAs is commonly defined using schedulers (also called adversaries or strategies), which resolve all nondeterministic choices based on past history. From the resulting purely probabilistic structures, trace distributions can be extracted, whose intent is to capture the observable behavior of a PA. However, when PAs are composed via an (asynchronous) parallel composition operator, a global scheduler may establish strong correlations between the behavior of system components and, for example, resolve nondeterministic choices in one PA based on the outcome of probabilistic choices in the other. It is well known that, as a result of this, the (linear-time) trace distribution precongruence is not compositional for PAs. In his 1995 Ph.D. thesis, Segala has shown that the (branching-time) probabilistic simulation preorder is compositional for PAs. In this paper, we establish that the simulation preorder is, in fact, the coarsest refinement of the trace distribution preorder that is compositional. We prove our characterization result by providing (1) a context of a given PA ${\cal A}$, called the tester, which may announce the state of ${\cal A}$ to the outside world, and (2) a specific global scheduler, called the observer, which ensures that the state information that is announced is actually correct. Now when another PA ${\cal B}$ is composed with the tester, it may generate the same external behavior as the observer only when it is able to simulate ${\cal A}$ in the sense that whenever ${\cal A}$ goes to some state $s$, ${\cal B}$ can go to a corresponding state $u$, from which it may generate the same external behavior. Our result shows that probabilistic contexts together with global schedulers are able to exhibit the branching structure of PAs.

VIII?Epistemic Deference: The Case of Chance

Epistemic deference is the phenomenon in which one person uses the deliverances of some information source, perhaps the opinions of another person, as a model for what to believe. The paper aims to clarify the nature of epistemic deference in probabilistic contexts, to explain the conditions under which deference is appropriate, and to examine deference to objective chances, as epitomized in David Lewis's Principal Principle. This latter analysis will show, in contrast with views that portray chance as an ideal inductive logician with total recall, that our deference to chance is grounded in contingent limitations on our ability to access information and our recognition that the physical probabilities that instantiate the actual chances codify all the types of information that humans are able to possess.

Observing Branching Structure through Probabilistic Contexts

Probabilistic automata (PAs) constitute a general framework for modeling and analyzing discrete event systems that exhibit both nondeterministic and probabilistic behavior, such as distributed algorithms and network protocols. The behavior of PAs is commonly defined using schedulers (also called adversaries or strategies), which resolve all nondeterministic choices based on past history. From the resulting purely probabilistic structures, trace distributions can be extracted, whose intent is to capture the observable behavior of a PA. However, when PAs are composed via an (asynchronous) parallel composition operator, a global scheduler may establish strong correlations between the behavior of system components and, for example, resolve nondeterministic choices in one PA based on the outcome of probabilistic choices in the other. It is well known that, as a result of this, the (linear-time) trace distribution precongruence is not compositional for PAs. In his 1995 Ph.D. thesis, Segala has shown that the (branching-time) probabilistic simulation preorder is compositional for PAs. In this paper, we establish that the simulation preorder is, in fact, the coarsest refinement of the trace distribution preorder that is compositional. We prove our characterization result by providing (1) a context of a given PA ${\cal A}$, called the tester, which may announce the state of ${\cal A}$ to the outside world, and (2) a specific global scheduler, called the observer, which ensures that the state information that is announced is actually correct. Now when another PA ${\cal B}$ is composed with the tester, it may generate the same external behavior as the observer only when it is able to simulate ${\cal A}$ in the sense that whenever ${\cal A}$ goes to some state s, ${\cal B}$ can go to a corresponding state u, from which it may generate the same external behavior. Our result shows that probabilistic contexts together with global schedulers are able to exhibit the branching structure of PAs.

GUARANTEED NONLINEAR PARAMETER ESTIMATION FOR CONTINUOUS-TIME DYNAMICAL MODELS

This paper is about parameter estimation for models described by a continuous-time state equation from discrete-time measurements. Guaranteed solutions to this problem are proposed in probabilistic and bounded-error contexts, based on Müller's theorems and interval analysis. In a probabilistic context where parameter estimation boils down to parameter optimization, this makes it possible to characterize the set of all globally optimal parameter vectors. In a bounded-error context, this allows the characterization of the set of all parameter vectors that are consistent with the error bounds, measurements and model structure. The resulting methodology is illustrated on a simulated example of anaerobic fermentation process.