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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Related Experiment Video

Updated: Nov 3, 2025

Establishing a Competing Risk Regression Nomogram Model for Survival Data
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Comparing quantile regression methods for probabilistic forecasting of NO2 pollution levels.

Sebastien Pérez Vasseur1, José L Aznarte2

  • 1Artificial Intelligence Department, Universidad Nacional de Educación a Distancia - UNED, c/Juan del Rosal, 16, Madrid, Spain.

Scientific Reports
|June 3, 2021
PubMed
Summary

Forecasting air quality is crucial for managing traffic restrictions. This study compared probabilistic models for nitrogen dioxide (NO2) prediction, finding quantile gradient boosted trees performed best, though simpler models offered comparable results with less complexity.

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Area of Science:

  • Environmental Science
  • Atmospheric Chemistry
  • Data Science

Background:

  • Authorities use traffic restrictions to manage high nitrogen dioxide (NO2) concentrations.
  • Accurate forecasting of NO2 levels is essential for timely intervention.
  • Probabilistic forecasting offers advantages over point-forecasting for predicting pollutant distributions.

Purpose of the Study:

  • To compare the performance of 10 state-of-the-art quantile regression models for NO2 concentration forecasting.
  • To evaluate these models for predicting the full distribution of NO2 concentrations.
  • To identify optimal probabilistic models for urban air quality management.

Main Methods:

  • Utilized 10 quantile regression models to predict NO2 concentration distributions.
  • Applied a semi-parametric approach by deriving distribution parameters from predicted quantiles.
  • Evaluated models for forecasting horizons up to 60 hours in an urban setting.

Main Results:

  • Quantile gradient boosted trees demonstrated superior performance in predicting both point values and full NO2 distributions.
  • Quantile k-nearest neighbors with linear regression achieved comparable results with significantly reduced training time and complexity.
  • The study provides a comprehensive comparison of probabilistic models for NO2 forecasting.

Conclusions:

  • Probabilistic forecasting models are effective for predicting NO2 concentration exceedances and pollution peaks.
  • Quantile gradient boosted trees are highly effective, but simpler models like quantile k-nearest neighbors offer a practical alternative.
  • The findings support the use of advanced statistical methods for proactive air quality management.