Sets of Priors Reflecting Prior-Data Conflict and Agreement

Walter, Gero; Coolen, Frank P. A.

doi:10.1007/978-3-319-40596-4_14

Cited by 6 publications

(6 citation statements)

References 9 publications

(24 reference statements)

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“…These opportunities have not yet been explored and provide a wide field for further research. An example is our currently ongoing investigation into extending the present model to allow also for an appropriate reflection of very strong agreement between prior and data (Walter and Coolen 2016).…”

Section: Discussionmentioning

confidence: 87%

Robust Bayesian Reliability for Complex Systems under Prior-Data Conflict

Walter

Coolen

2018

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is straightforward in the Bayesian approach by using an informative prior distribution. A problem called prior-data conflict then can arise: observed data seem very surprising from the viewpoint of the prior, i.e., information from data is in conflict with prior assumptions. Models based on conjugate priors can be insensitive to prior-data conflict, in the sense that the spread of the posterior distribution does not increase in case of such a conflict, thus conveying a false sense of certainty. An approach to mitigate this issue is presented, by considering sets of prior distributions to model limited knowledge on Weibull distributed component lifetimes, treating systems with arbitrary layout using the survival signature. This approach can be seen as a robust Bayesian procedure or imprecise probability method that reflects surprisingly early or late component failures by wider system reliability bounds.

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Section: Discussionmentioning

confidence: 87%

Robust Bayesian Reliability for Complex Systems under Prior-Data Conflict

Walter

Coolen

2018

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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“…It has the potential to reveal data‐prior conflict (i.e., mismatch between an informative prior distribution and the observed data). If so, the difference between the bounds is an emerging property from conflicting information between priors and data, which would not be seen in a standard Bayesian analysis (Walter & Coolen, 2016).…”

Section: Discussionmentioning

confidence: 99%

“…Robust Bayesian analysis has been used to evaluate the sensitivity to the choice of priors (e.g., the choice of family or hyperparameters of the prior distribution) (Berger, 1990; Roos et al., 2015). An alternative use of “robust” Bayesian analysis is to apply Bayesian inference over a set of priors for quantifying uncertainty about parameters, resulting in uncertainty quantified by bounded (imprecise) probability (Walley, 1991; Walter & Coolen, 2016). Used in this way, robust Bayesian analysis is based on statistical principles for inference within the theory of imprecise probability (Walley, 1991).…”

Section: Introductionmentioning

confidence: 99%

“…However, in some situations scientific experts might struggle to agree on a precise subjective probability (O'Hagan et al., 2006). This difficulty could raise a concern when experts are directly quantifying uncertainty in a quantity of interest, or for Bayesian updating based on information in data that is sparse, weak or conflicting (Walley, 1991; Walter & Coolen, 2016). To account for the issue of specifying a precise probability and because approximate quantitative expressions of uncertainty may be enough to inform decision making, EFSA et al.…”

Section: Introductionmentioning

confidence: 99%

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A suggestion for the quantification of precise and bounded probability to quantify epistemic uncertainty in scientific assessments

2022

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An honest communication of uncertainty about quantities of interest enhances transparency in scientific assessments. To support this communication, risk assessors should choose appropriate ways to evaluate and characterize epistemic uncertainty. A full treatment of uncertainty requires methods that distinguish aleatory from epistemic uncertainty. Quantitative expressions for epistemic uncertainty are advantageous in scientific assessments because they are nonambiguous and enable individual uncertainties to be characterized and combined in a systematic way. Since 2019, the European Food Safety Authority (EFSA) recommends assessors to express epistemic uncertainty in conclusions of scientific assessments quantitatively by subjective probability. A subjective probability can be used to represent an expert judgment, which may or may not be updated using Bayes's rule to integrate evidence available for the assessment and could be either precise or approximate. Approximate (or bounded) probabilities may be enough for decision making and allow experts to reach agreement on certainty when they struggle to specify precise subjective probabilities. The difference between the lower and upper bound on a subjective probability can also be used to reflect someone's strength of knowledge. In this article, we demonstrate how to quantify uncertainty by bounded probability, and explicitly distinguish between epistemic and aleatory uncertainty, by means of robust Bayesian analysis, including standard Bayesian analysis through precise probability as a special case. For illustration, the two analyses are applied to an intake assessment.

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“…We plan to exploit more use of prior-data conflict and also strong prior-data agreement (Walter and Coolen 2016) to reflect the robot's epistemic limitations. Requirements to be verified for a robot should come from a higher level, e.g.…”

mentioning

confidence: 99%

Probabilistic Model Checking of Robots Deployed in Extreme Environments

Zhao¹,

Robu²,

Flynn³

et al. 2019

AAAI

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Robots are increasingly used to carry out critical missions in extreme environments that are hazardous for humans. This requires a high degree of operational autonomy under uncertain conditions, and poses new challenges for assuring the robot's safety and reliability. In this paper, we develop a framework for probabilistic model checking on a layered Markov model to verify the safety and reliability requirements of such robots, both at pre-mission stage and during runtime. Two novel estimators based on conservative Bayesian inference and imprecise probability model with sets of priors are introduced to learn the unknown transition parameters from operational data. We demonstrate our approach using data from a real-world deployment of unmanned underwater vehicles in extreme environments.

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Sets of Priors Reflecting Prior-Data Conflict and Agreement

Cited by 6 publications

References 9 publications

Robust Bayesian Reliability for Complex Systems under Prior-Data Conflict

Robust Bayesian Reliability for Complex Systems under Prior-Data Conflict

A suggestion for the quantification of precise and bounded probability to quantify epistemic uncertainty in scientific assessments

Probabilistic Model Checking of Robots Deployed in Extreme Environments

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