Recommendations for the tuning of rare event probability estimators

Abstract

a b s t r a c tBeing able to accurately estimate rare event probabilities is a challenging issue in order to improve the reliability of complex systems. Several powerful methods such as importance sampling, importance splitting or extreme value theory have been proposed in order to reduce the computational cost and to improve the accuracy of extreme probability estimation. However, the performance of these methods is highly correlated with the choice of tuning parameters, which are very difficult to determine. In order to highlight recommended tunings for such methods, an empirical campaign of automatic tuning on a set of representative test cases is conducted for splitting methods. It allows to provide a reduced set of tuning parameters that may lead to the reliable estimation of rare event probability for various problems. The relevance of the obtained result is assessed on a series of real-world aerospace problems.

Towards the significance of taxi recommender systems in smart cities

“…2. Probabilistic: Some of the methods adopted in this category are the root of the mean square error (RMSE), mean absolute error (MAE) and so forth applied to the recommender system 23,28,34,46,51,53,87,109,149,195,[235][236][237][238][239] 3. Ranking: To categorize and evaluate the items or users based on ranking, give the idea of how much the first user is nobler than the second.…”

“…We showed the evaluation techniques in the following groups: Qualitative : Major role of this evaluation technique is to lower the error. Some approaches used are accuracy, Inference Accuracy adopted by authors 14,15,23,30,57,87,114,147,148,155,171,232‐234 in taxi recommendation. Probabilistic : Some of the methods adopted in this category are the root of the mean square error (RMSE), mean absolute error (MAE) and so forth applied to the recommender system 23,28,34,46,51,53,87,109,149,195,235‐239 Ranking : To categorize and evaluate the items or users based on ranking, give the idea of how much the first user is nobler than the second. Some examples are normalized discount cumulative gain (NDCG), precision, recall, F1 and so forth 42,46,52,55,192,240‐244 …”

Equipment Operational Reliability Evaluation Method Based on RVM and PCA-Fused Features

“…According to the Bayesian formula, we can get the posterior distribution function of the weight ω with the likelihood function equation ( 3) and a priori distribution function equation (4). at is,…”

“…e latter is obtained from the performance degradation information of the equipment, and it reflects the real time reliability of the equipment [2]. In engineering field, single or small batch equipment is widely used, and failure data are very scarce in this case, so the traditional statistical method is not suitable for the reliability evaluation of this type of mechanical equipment, such as high precision NC machine tools, nuclear power facilities, aircraft [3][4][5], and so on. In contrast, the operational reliability is more of practical significance to ensure the safety of this type of equipment because it can be obtained in real time when the condition monitoring data are sampled continuously.…”

Point process-based approaches for the reliability analysis of systems modeled by costly simulators

“…Alternatively, the splitting techniques [2,8] divide the rare event into a series of less rare events, so that the variance of the aggregate estimator is much lower than that of the direct estimator. However, for these two techniques to be effective, practical problems must be solved: the choice of the random vector for importance sampling, and the conditional sampling for splitting techniques (see [3] for advice on the control of rare event probability estimators).…”