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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.

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Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State.

Xuze Zhang¹, Saumyadipta Pyne^2,3, Benjamin Kedem¹

¹Department of Mathematics and Institute for Systems Research, University of Maryland, College Park, MD 20742, USA.

Entropy (Basel, Switzerland)

|June 2, 2021

Summary

This study introduces a computational framework to fuse data from multiple sources, enabling accurate estimation of rare health event probabilities. This method overcomes limitations of small datasets for improved disease modeling and risk assessment.

Keywords:

data fusion density ratio model disease outbreak goodness-of-fit model selection variable tilt

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Area of Science:

Statistics
Epidemiology
Computational Biology

Background:

Estimating tail probabilities of health events is challenging with small, limited datasets.
Existing methods struggle with missing lower or upper tail data.

Purpose of the Study:

To develop a computational framework for fusing multi-source observations to estimate tail probabilities.
To address the estimation of multivariate tail probabilities using limited reference data.

Main Methods:

Utilized a density ratio model with variable tilts for univariate and multivariate analysis.
Employed the Akaike Information Criterion (AIC) for model selection.
Fused data from multiple small samples for regional prediction.

Main Results:

Successfully computed tail probabilities unobtainable from empirical distributions alone.
Developed a validated model for regional pertussis case prediction in Washington state.
Demonstrated improved probability estimates through data fusion.

Conclusions:

The proposed framework effectively fuses data to enhance tail probability estimation in disease modeling.
This approach provides a robust method for predicting health events with limited data.
The density ratio model offers a powerful tool for analyzing complex health event data.