Bayesian learning of models for estimating uncertainty in alert systems: application to air traffic conflict avoidance

Alert systems detect critical events which can happen in the short term. Uncertainties in data and in the models used for detection cause alert errors. In the case of air traffic control systems such as Short-Term Conflict Alert (STCA), uncertainty increases errors in alerts of separation loss. Statistical methods that are based on analytical assumptions can provide biased estimates of uncertainties. More accurate analysis can be achieved by using Bayesian Model Averaging, which provides estimates of the posterior probability distribution of a prediction. We propose a new approach to estimate the prediction uncertainty, which is based on observations that the uncertainty can be quantified by variance of predicted outcomes. In our approach, predictions for which variances of posterior probabilities are above a given threshold are assigned to be uncertain. To verify our approach we calculate a probability of alert based on the extrapolation of closest point of approach. Using Heathrow airport flight data we found that alerts are often generated under different conditions, variations in which lead to alert detection errors. Achieving 82.1% accuracy of modelling the STCA system, which is a necessary condition for evaluating the uncertainty in prediction, we found that the proposed method is capable of reducing the uncertain component. Comparison with a bootstrap aggregation method has demonstrated a significant reduction of uncertainty in predictions. Realistic estimates of uncertainties will open up new approaches to improving the performance of alert systems

Representing Markov processes as dynamic non-parametric Bayesian networks

We prove that a k-th order Markov process has a dynamic NPBN representation. Guidance is given on how to obtain the various dependence metrics that are sufficient and necessary. We additionally derive the conditions required to perform conditioning which can be analytically done for the Gaussian case. One of the advantages consists in having a clear vision on the dependence dynamics expressed through the time copula and rank correlation. Compared to classic stochastic process based modelling, this may shed light on non-stationarity concerning dependence. It thus enhances the description/characterization of dependencies. More precisely, for Levy processes whose increments are independent and stationary, the associated time-copula may thus be non-stationary as is shown taking the example of the Brownian motion. The applicability of the Markov process representation may find interest in various fields ranging from finance, where Markov processes such as the geometric Brownian motion is key for stock pricing, to deterioration modelling, speech recognition, etc. Basically, these are the areas into which Markovian features have been successfully tested and validated. In this regard, we illustrate our findings through an example focused around the Brownian motion

Representing Markov processes as dynamic non-parametric Bayesian networks

We prove that a k-th order Markov process has a dynamic NPBN representation. Guidance is given on how to obtain the various dependence metrics that are sufficient and necessary. We additionally derive the conditions required to perform conditioning which can be analytically done for the Gaussian case. One of the advantages consists in having a clear vision on the dependence dynamics expressed through the time copula and rank correlation. Compared to classic stochastic process based modelling, this may shed light on non-stationarity concerning dependence. It thus enhances the description/characterization of dependencies. More precisely, for Levy processes whose increments are independent and stationary, the associated time-copula may thus be non-stationary as is shown taking the example of the Brownian motion. The applicability of the Markov process representation may find interest in various fields ranging from finance, where Markov processes such as the geometric Brownian motion is key for stock pricing, to deterioration modelling, speech recognition, etc. Basically, these are the areas into which Markovian features have been successfully tested and validated. In this regard, we illustrate our findings through an example focused around the Brownian motion

Bayesian network-based models for bridge network management

SLP_HCERES2020International audienceMaintenance for highway bridges is crucial in order to keep the network in a satisfactory condi-tion for users but is also a costly affair. This paper proposes a dynamic, Bayesian network-based model to provide cost-efficient strategies in the context of bridge network management. Characteristics related to un-certainties in both the degradation phase and subsequent maintenance strategies are handled through the de-sirable probabilistic dependencies properties BNs possess. The extension to a specific version of Influence di-agrams allows formulating the optimization part of the problem in order to eventually provide long-term strategies as well as minimize expected costs. To that end, a case study that tackles both conditional and un-conditional cases is presented