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Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

681
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...
681
Uncertainty: Overview00:59

Uncertainty: Overview

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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.
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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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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...
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Decision Making: P-value Method01:09

Decision Making: P-value Method

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The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim  is also stated. These statements can act as null and alternative hypotheses:  a null hypothesis would be a neutral statement while the alternative hypothesis can...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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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...
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Expected Value01:15

Expected Value

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The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:
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Related Experiment Video

Updated: Jun 29, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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Foraging Under Uncertainty Follows the Marginal Value Theorem with Bayesian Updating of Environment Representations.

James Webb1,2, Paul Steffan1, Benjamin Y Hayden3

  • 1Department of Neuroscience, Baylor College of Medicine, Houston, TX, USA.

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Summary

Mice foraging behavior aligns with a modified marginal value theorem (MVT) in uncertain environments. They learn and adapt to changing reward rates, demonstrating sophisticated decision-making under volatility.

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Area of Science:

  • Behavioral Ecology
  • Neuroscience
  • Computational Biology

Background:

  • Foraging theory, particularly the marginal value theorem (MVT), explains optimal patch-leaving strategies in predictable environments.
  • Natural environments are often stochastic, requiring foragers to adapt to uncertainty, a limitation of the standard MVT.
  • Understanding animal decision-making in volatile conditions is crucial for behavioral ecology and neuroscience.

Conclusions:

  • Mice can efficiently forage in volatile environments by dynamically updating their internal models of reward availability.
  • The findings support a modified MVT that accounts for learning and adaptation in uncertain conditions.
  • This study provides a foundation for investigating the neural basis of foraging under uncertainty using systems neuroscience approaches.