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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

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Quantifying the uncertainty of human activity recognition using a Bayesian machine learning method: a prediction

Hiroshi Mamiya¹, Daniel Fuller²

¹Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Canada.

Physical Activity and Nutrition

|October 15, 2025

Summary

Bayesian Additive Regression Trees (BART), a novel machine learning method, accurately predicts physical activity status from wearable device data. This advancement allows for better integration of physical activity predictions into built environment research.

Keywords:

Bayesian additive regression tree machine learning population physical activity wearable device

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Last Updated: Jan 15, 2026

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Evaluation of a Smartphone-based Human Activity Recognition System in a Daily Living Environment

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Published on: December 11, 2015

Combining Eye-tracking Data with an Analysis of Video Content from Free-viewing a Video of a Walk in an Urban Park Environment

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Published on: May 7, 2019

Area of Science:

Machine learning applications in public health
Wearable sensor data analysis
Environmental health research

Background:

Machine learning accurately predicts physical activity using accelerometer data from wearable devices.
Investigating the built environment's impact on population physical activity is crucial.
Traditional methods lack prediction uncertainty quantification, unlike Bayesian Additive Regression Trees (BART).

Purpose of the Study:

To evaluate the performance of Bayesian Additive Regression Trees (BART) for predicting physical activity status.
To assess BART's capability in quantifying prediction uncertainty.
To explore BART's potential in built environment research.

Main Methods:

Applied multinomial BART and random forest to accelerometer data from 37 participants (25,424 time points).
Utilized leave-one-person-out cross-validation for performance evaluation.
Assessed prediction accuracy, F1 scores, and confusion matrices.

Main Results:

Both BART and random forest demonstrated comparable prediction performances.
BART successfully quantified prediction uncertainty through posterior predictive distribution.
The methods showed high accuracy in predicting physical activity status.

Conclusions:

BART is a promising machine learning method for predicting physical activity status.
BART can enhance the integration of predicted physical activity into built environment research.
Future studies should explore the association between the environment and BART-predicted physical activity.