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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.

End Point Prediction: Gran Plot

End Point Prediction: Gran Plot

A Gran plot is used to predict the equivalence volume or endpoint of a potentiometric or acid-base titration without reaching the endpoint. Typically, titration data is collected as a function of the titrant's volume up to a point less than the equivalence volume and then transformed into a linear format. The straight line is extended to the x-axis, indicating the necessary titrant volume to achieve the equivalence point.
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Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

Region of Convergence of Laplace Tarnsform

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The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...

Time-Series Graph

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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...

Residuals and Least-Squares Property

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...

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Conformal Prediction for Time Series.

Chen Xu, Yao Xie

IEEE Transactions on Pattern Analysis and Machine Intelligence

|October 11, 2023

Summary

This summary is machine-generated.

We developed a new method for creating reliable time series prediction intervals without needing data assumptions. Our EnbPI algorithm offers efficient, scalable, and accurate forecasting for sequential data.

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Area of Science:

Time Series Analysis
Statistical Forecasting
Machine Learning

Background:

Accurate prediction intervals are crucial for time series forecasting.
Existing methods often rely on strong distributional assumptions or data splitting.
Scalability and computational efficiency are key challenges in sequential prediction.

Purpose of the Study:

To introduce a general framework for distribution-free prediction intervals for time series.
To establish theoretical bounds on the coverage and size of prediction intervals.
To present an efficient and scalable algorithm for constructing these intervals.

Main Methods:

Developed a general framework for distribution-free prediction intervals.
Established explicit bounds on coverage gaps and set differences.
Introduced the Ensemble Batch Prediction Intervals (EnbPI) algorithm.
EnbPI utilizes ensemble predictors and is related to conformal prediction but does not require exchangeability.

Main Results:

The proposed framework provides explicit bounds on prediction interval accuracy.
EnbPI offers asymptotically vanishing coverage and size gaps under certain assumptions.
EnbPI is computationally efficient, avoids data splitting, and is scalable for sequential prediction.
Extensive simulations and real-data analyses confirm EnbPI's effectiveness.

Conclusions:

EnbPI provides a robust and efficient approach for constructing distribution-free prediction intervals.
The method is suitable for sequential time series forecasting where data exchangeability is not guaranteed.
EnbPI offers a scalable and computationally advantageous alternative to existing prediction interval techniques.