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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 't,' or...

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...

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 particular...

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.

Random Error

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...

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Updated: Jun 4, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Risk, unexpected uncertainty, and estimation uncertainty: Bayesian learning in unstable settings.

Elise Payzan-LeNestour¹, Peter Bossaerts

¹University of New South Wales, Sydney, Australia. elise@unsw.edu.au

Plos Computational Biology

|February 2, 2011

Summary

Humans learn using Bayesian updating, distinguishing risk, ambiguity, and unexpected uncertainty. However, aversion to ambiguity and unawareness of unexpected uncertainty limit Bayesian learning capacity.

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Last Updated: Jun 4, 2026

An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

Cognitive Science
Neuroscience
Decision Science

Background:

Recent evidence suggests human learning aligns with Bayesian updating, not reinforcement algorithms, in complex tasks.
Understanding human perception and handling of uncertainty is crucial for cognitive and decision science.

Purpose of the Study:

To investigate the implications of Bayesian updating for human appreciation of different uncertainty types.
To examine how risk, estimation uncertainty (ambiguity), and unexpected uncertainty influence learning rates.
To explore the boundaries of human Bayesian learning capacity under varying structural uncertainty.

Main Methods:

A six-arm restless bandit task was employed to model human learning.
Three distinct levels of uncertainty (risk, ambiguity, unexpected uncertainty) were analyzed.
Learning rates were tracked, and Bayesian updating models were compared against reinforcement learning models.

Main Results:

Bayesian learners differentiate between risk, ambiguity, and unexpected uncertainty.
Human participants demonstrated an aversion to ambiguity, contrary to exploration theories.
Performance degraded, and Bayesian updating was no better than reinforcement learning when structural uncertainty was high.

Conclusions:

Humans can distinguish multiple uncertainty types, but ambiguity aversion and unawareness of unexpected uncertainty pose limitations.
The capacity for sophisticated Bayesian learning is constrained by task complexity and instructional framing.
Further research is needed to understand the neural underpinnings and adaptive strategies for managing uncertainty in learning.