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Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Confidence Intervals

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...

Improper Integrals: Infinite Intervals

Improper Integrals: Infinite Intervals

An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...

Definition and Measurement of Pressure: Atmospheric Pressure, Barometer, and Manometer

Definition and Measurement of Pressure: Atmospheric Pressure, Barometer, and Manometer

Gas pressure is caused by force exerted by gas molecules colliding with the surfaces of objects. Although the force of each collision is very small, any surface of an appreciable area experiences a large number of collisions in a short time, which can result in high pressure.

Absolute and Local Extreme Values

Absolute and Local Extreme Values

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...

Variation of Atmospheric Pressure

Variation of Atmospheric Pressure

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at...

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Related Experiment Video

Updated: Feb 3, 2026

Behavioral Assessment of Hearing in 2 to 4 Year-old Children: A Two-interval, Observer-based Procedure Using Conditioned Play-based Responses

Behavioral Assessment of Hearing in 2 to 4 Year-old Children: A Two-interval, Observer-based Procedure Using Conditioned Play-based Responses

Published on: January 23, 2017

Forecasting extreme atmospheric events with a recurrence-interval-analysis-based autoregressive conditional duration

Yue-Hua Dai¹, Zhi-Qiang Jiang^1,2, Wei-Xing Zhou^3,4,5

¹School of Business, East China University of Science and Technology, Shanghai, 200237, China.

Scientific Reports

|November 4, 2018

Summary

Forecasting extreme air pollution is crucial for public health. New models integrating recurrence interval analysis with autoregressive conditional duration (ACD) and spatial factors accurately predict pollution event recurrence.

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Exploring the Effects of Atmospheric Forcings on Evaporation: Experimental Integration of the Atmospheric Boundary Layer and Shallow Subsurface

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Published on: June 8, 2015

Area of Science:

Environmental Science
Atmospheric Science
Data Science

Background:

Air pollution poses significant risks to urban populations, necessitating accurate forecasting of extreme events.
Effective prediction aids in scheduling outdoor activities and implementing pollution mitigation strategies.

Purpose of the Study:

To develop and validate advanced models for predicting extreme air pollution recurrence intervals.
To integrate Recurrence Interval Analysis (RIA) with Autoregressive Conditional Duration (ACD) models.
To extend the ACD model to a Spatially Autoregressive Conditional Duration (SACD) model for enhanced spatial analysis.

Main Methods:

Integration of Recurrence Interval Analysis (RIA) with the Autoregressive Conditional Duration (ACD) model.
Development of a Spatially Autoregressive Conditional Duration (SACD) model incorporating spatial dependency.
Utilizing hourly air quality data (six pollutants, AQI) from 12 Beijing monitoring stations (2013-2016).

Main Results:

The SACD model demonstrated that spatial factors significantly explain recurrence intervals in neighboring stations.
One-step forecasts using RIA-ACD(1,1) and RIA-SACD(1,1,1) models predicted 90% of recurrence intervals under 72 hours.
Model consistency with real-world data across various time lags and stations confirmed predictive feasibility.

Conclusions:

The proposed RIA-ACD and RIA-SACD models offer a feasible approach for predicting extreme air pollution events.
The inclusion of a spatial term effectively enhances the predictive accuracy of the models.
These findings support the development of better air quality management strategies through advanced forecasting.