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A quantitative approach to conduct a specific type of stress test on road networks is presented in this article. The objective is to help network managers determine whether their networks would perform adequately during and after the occurrence of hazard events. Conducting a stress test requires (i) modifying an existing risk model (i.e., a model to estimate the probable consequences of hazard events) by representing at least one uncertainty in the model with values that are considerably worse than median or mean values, and (ii) developing criteria to conclude if the network has an adequate post-hazard performance. Specifically, the stress test conducted in this work is focused on the uncertain behavior of individual objects that are part of a network when these are subjected to hazard loads. Here, the relationships between object behavior and hazard load are modeled using fragility functions and functional capacity loss functions. To illustrate the quantitative approach, a stress test is conducted for an example road network in Switzerland, which is affected by floods and rainfall-triggered mudflows. Beyond the focus of the stress test, this work highlights the importance of using a probabilistic approach when conducting stress tests for temporal and spatially distributed networks.

Abstract. The Bayesian decision theory is neo-Bernoullian in that it proves, by way of a consistency derivation, that Bernoulli's utility function is the only appropriate function by which to translate, for a given initial wealth, gains and losses to their corresponding utilities. But the Bayesian decision theory deviates from Bernoulli's original expected utility theory in that it offers up an alternative for the traditional criterion of choice of expectation value maximization, as it proposes to choose that decision which has associated with it the utility probability distribution which maximizes the mean of the expectation value and the lower and upper confidence bounds.

Abstract. In this paper we present a Bayesian logistic regression analysis. It is found that if one wishes to derive the posterior distribution of the probability of some event, then, together with the traditional Bayes Theorem and the integrating out of nuissance parameters, the Jacobian transformation is an essential added ingredient. The application of the product rule gives the posterior of the unknown logistic regression coef¿cients. The Jacobian transformation then maps the posterior of these regression coef¿cients to the posterior of the corresponding probability of some event and some nuisance parameters. Finally, by way of the sumrule the nuissance parameters are integrated out.

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