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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: 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...

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...

Problem-Solving: Tuning of a Guitar String

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In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or the mass per unit length. This is simply called the linear density. If the string's linear density is constant along the string, then the linear density is simply the total mass divided by the total length.
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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.

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...

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Related Experiment Video

Updated: Dec 8, 2025

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

Tuning movement for sensing in an uncertain world.

Chen Chen^1,2, Todd D Murphey^1,3, Malcolm A MacIver^1,2,3,4

¹Center for Robotics and Biosystems, Northwestern University, Evanston, United States.

|September 22, 2020

Summary

Animals

Keywords:

computational biology decision making exploration-exploitation infotaxis neuroscience optimal foraging optimal search search algorithm systems biology

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Last Updated: Dec 8, 2025

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

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Published on: April 13, 2016

Frame-by-Frame Video Analysis of Idiosyncratic Reach-to-Grasp Movements in Humans

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Published on: January 15, 2018

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Area of Science:

Behavioral Ecology
Neuroscience
Robotics

Background:

Animals exhibit unexplained sensory organ movements during target tracking.
Existing theories (infotaxis, gain adaptation, etc.) inadequately explain these movements.
Previous models show poor agreement between predicted and measured animal trajectories.

Purpose of the Study:

To propose and validate a new theory for sensory organ movements during animal navigation.
To unify metabolic costs with information theory for predicting sensor motion.
To provide a framework for designing robotic sensor movement strategies.

Main Methods:

Developed the energy-constrained proportional betting (ECPB) theory.
Modeled sensory organ movement probability based on information gain and energy cost.
Validated ECPB predictions against empirical data from multiple species and sensory modalities.

Main Results:

ECPB theory demonstrated strong agreement with measured trajectories of fish, mammals, insects, and moths.
The model successfully predicts sensory organ movements across diverse animal tracking behaviors.
The theory integrates energetic constraints with information-theoretic principles.

Conclusions:

Energy-constrained proportional betting offers a unified explanation for animal sensory organ movements.
This theory bridges the gap between metabolic costs and information processing in biological systems.
ECPB provides a foundation for optimizing robotic sensor movement for enhanced performance.