An official website of the United States government
Abstract Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.
more »
« less
Hybrid elicitation and quantile-parametrized likelihood
Abstract This paper extends the application of quantile-based Bayesian inference to probability distributions defined in terms of quantiles of observable quantities. Quantile-parameterized distributions are characterized by high shape flexibility and parameter interpretability, making them useful for eliciting information about observables. To encode uncertainty in the quantiles elicited from experts, we propose a Bayesian model based on the metalog distribution and a variant of the Dirichlet prior. We discuss the resulting hybrid expert elicitation protocol, which aims to characterize uncertainty in parameters by asking questions about observable quantities. We also compare and contrast this approach with parametric and predictive elicitation methods.
more »
« less
- Award ID(s):
- 2153019
- PAR ID:
- 10522245
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Statistics and Computing
- Volume:
- 34
- Issue:
- 1
- ISSN:
- 0960-3174
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar property if and only if is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable , we give simple canonical algorithms for the batch and the online adversarial setting, that learn a -multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property is not elicitable by itself, but is elicitable conditionally on another elicitable property , then there is a canonical algorithm that jointly multicalibrates and ; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.more » « less
-
We make a connection between multicalibration and property elicitation and show that (under mild technical conditions) it is possible to produce a multicalibrated predictor for a continuous scalar distributional property G if and only if G is elicitable. On the negative side, we show that for non-elicitable continuous properties there exist simple data distributions on which even the true distributional predictor is not calibrated. On the positive side, for elicitable G, we give simple canonical algorithms for the batch and the online adversarial setting, that learn a G-multicalibrated predictor. This generalizes past work on multicalibrated means and quantiles, and in fact strengthens existing online quantile multicalibration results. To further counter-weigh our negative result, we show that if a property G1 is not elicitable by itself, but is elicitable conditionally on another elicitable property G0, then there is a canonical algorithm that jointly multicalibrates G1 and G0; this generalizes past work on mean-moment multicalibration. Finally, as applications of our theory, we provide novel algorithmic and impossibility results for fair (multicalibrated) risk assessment.more » « less
-
Abstract The concentration of chlorophyll‐a (CHL) is an important proxy for autotrophic biomass and primary production in the ocean. Quantifying trends and variability in CHL are essential to understanding how marine ecosystems are affected by climate change. Previous analyses have focused on assessing trends in CHL mean, but little is known about observed changes in CHL extremes and variance. Here we apply a quantile regression model to detect trends in CHL distribution over the period of 1997–2022 for several quantiles. We find that the magnitude of trends in upper quantiles of global CHL (>90th) are larger than those in lower quantiles (≤50th) and in the mean, suggesting a growing asymmetry in CHL distribution. On a regional scale, trends in different quantiles are statistically significant at high latitude, equatorial, and oligotrophic regions. Assessing changes in CHL distribution has potential to yield a more comprehensive understanding of climate change impacts on CHL.more » « less
-
Abstract Accurate classification of high‐dimensional data is important in many scientific applications. We propose a family of high‐dimensional classification methods based upon a comparison of the component‐wise distances of the feature vector of a sample to the within‐class population quantiles. These methods are motivated by the fact that quantile classifiers based on these component‐wise distances are the most powerful univariate classifiers for an optimal choice of the quantile level. A simple aggregation approach for constructing a multivariate classifier based upon these component‐wise distances to the within‐class quantiles is proposed. It is shown that this classifier is consistent with the asymptotically optimal classifier as the sample size increases. Our proposed classifiers result in simple piecewise‐linear decision rule boundaries that can be efficiently trained. Numerical results are shown to demonstrate competitive performance for the proposed classifiers on both simulated data and a benchmark email spam application.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11222-023-10325-0
