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Poisson Probability Distribution

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...

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Related Experiment Video

Updated: Jun 9, 2025

Methodology for Establishing a Community-Wide Life Laboratory for Capturing Unobtrusive and Continuous Remote Activity and Health Data

Methodology for Establishing a Community-Wide Life Laboratory for Capturing Unobtrusive and Continuous Remote Activity and Health Data

Published on: July 27, 2018

Changepoint detection on daily home activity pattern: a sliced Poisson process method.

Israel Martínez-Hernández¹, Rebecca Killick¹

¹School of Mathematical Sciences, Lancaster University, Lancaster, LA1 4YW, United Kingdom.

|October 21, 2024

Summary

This summary is machine-generated.

Detecting changes in daily behavior patterns can signal health decline. This study models daily activities as Poisson processes to identify significant day-to-day behavioral shifts for early health monitoring.

Keywords:

B-spline basis PELT changepoints detection segmentation sequence of inhomogeneous Poisson processes

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Area of Science:

Health monitoring
Behavioral science
Statistical modeling

Background:

Home-based disease prevention and health improvement are revolutionizing healthcare.
Monitoring changes in daily activities can indicate potential health problems.
Distinguishing day-to-day pattern changes from within-day variations is crucial for accurate health assessment.

Purpose of the Study:

To develop a method for detecting changes in daily behavior patterns, differentiating them from normal daily fluctuations.
To model daily activity data to identify significant shifts indicative of potential health decline.
To provide a visualized and interpretable approach for tracking health trends over time.

Main Methods:

Modeling daily event times as realizations of an inhomogeneous Poisson process with time-varying rates.
Developing a change detection methodology for sequences of these inhomogeneous Poisson processes.
Evaluating the approach using simulated home activity data.

Main Results:

The proposed methodology effectively detects changes in daily behavior patterns across consecutive days.
The approach allows for visualization and interpretation of detected changes and trends over time.
Simulated data evaluation demonstrated the utility of local change information for identifying shifts in daily activity.

Conclusions:

This method offers a novel approach to monitoring health by detecting subtle changes in daily behavior patterns.
The inhomogeneous Poisson process model provides a robust framework for analyzing temporal activity data.
The ability to visualize trends aids in the early detection of potential health decline from home-based activity.