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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

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PREDICTION INTERVALS FOR INTEGRALS OF GAUSSIAN RANDOM FIELDS.

Victor De Oliveira¹, Bazoumana Kone¹

¹Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA.

Computational Statistics & Data Analysis

|November 29, 2014

Summary

This study introduces bootstrap methods for more accurate prediction intervals of Gaussian random fields block averages. These novel algorithms improve coverage probability for spatial data analysis.

Keywords:

Block average Bootstrap calibration Change of support problem Geostatistics Kriging Spatial average

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Area of Science:

Geostatistics
Spatial Statistics
Environmental Science

Background:

Gaussian random fields are widely used to model spatial phenomena.
Accurate prediction intervals are crucial for reliable spatial data analysis.
Existing methods for block averages may lack sufficient coverage probability.

Purpose of the Study:

To develop and evaluate new bootstrap calibration algorithms for prediction intervals of Gaussian random fields block averages.
To improve the coverage probability of prediction intervals compared to standard plug-in methods.
To apply these methods for estimating block averages of environmental contaminants.

Main Methods:

Proposed two bootstrap calibration algorithms: indirect and direct.
Utilized simulation studies to assess algorithm performance.
Applied the methods to estimate chromium traces in a contaminated region.

Main Results:

Both indirect and direct bootstrap algorithms demonstrated improved coverage probability.
The simulation study confirmed the effectiveness of the proposed procedures.
Successful application to real-world environmental data for chromium estimation.

Conclusions:

Bootstrap calibration offers a robust approach for constructing reliable prediction intervals for block averages.
The proposed methods enhance the accuracy of spatial predictions in geostatistical applications.
These techniques are valuable for environmental monitoring and risk assessment.