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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.
Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict in Bayesi
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the
In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients do not exi
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate Bayesian Com
In (exploratory) factor analysis, the loading matrix is identified only up to orthogonal rotation. For identifiability, one thus often takes the loading matrix to be lower triangular with positive diagonal entries. In Bayesian inference, a standard p