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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 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.

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

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: 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...

Hindsight Biases

Hindsight Biases

Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Can you relate this to the phrase "Hindsight is 20/20" now?

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Related Experiment Video

Updated: Sep 14, 2025

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

Published on: September 16, 2015

Estimation-uncertainty affects decisions with and without learning opportunities.

Kristoffer C Aberg^1,2, Levi Antle^3,4, Rony Paz^5,6

¹Department of Brain Sciences, Weizmann Institute of Science, Rehovot, Israel. kc.aberg@gmail.com.

Nature Communications

|July 21, 2025

Summary

This summary is machine-generated.

Estimation-uncertainty, how often an option is sampled, influences long-term decisions even without new learning opportunities. This sampling bias persists, impacting choices independently of expected outcomes in reinforcement learning.

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Area of Science:

Cognitive Neuroscience
Behavioral Economics
Computational Neuroscience

Background:

Reinforcement learning (RL) involves outcome expectations and estimation-uncertainty, which influences exploration.
The long-term impact of estimation-uncertainty on decisions without further learning or exploration remains unclear.

Purpose of the Study:

To investigate if estimation-uncertainty from a reinforcement learning phase affects subsequent decisions without feedback.
To determine if this effect is independent of outcome expectations.

Main Methods:

A reinforcement learning phase with feedback was conducted.
A subsequent test phase without feedback assessed decision biases.
Computational modeling was used to fit behavioral data.

Main Results:

Sampling rates acquired during learning correlated with decision biases in the test phase.
Estimation-uncertainty improved computational model fits, especially for less-sampled options.
Findings were replicated across two independent datasets.

Conclusions:

Estimation-uncertainty acquired during reinforcement learning can create lasting decision biases.
This bias operates independently of outcome expectations.
Estimation-uncertainty is a crucial factor in understanding human decision-making.