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Propagation of Uncertainty from Systematic Error01:10

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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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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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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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Foraging animals use dynamic Bayesian updating to model meta-uncertainty in environment representations.

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Mice foraging behavior adapts to changing environments. They use a hierarchical Bayesian strategy to handle uncertainty, optimizing decisions in volatile conditions by tracking both local and global environmental statistics.

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Area of Science:

  • Behavioral Ecology
  • Computational Neuroscience
  • Decision Science

Background:

  • Foraging theory, including the marginal value theorem (MVT), models optimal patch-leaving strategies in predictable environments.
  • Natural environments present uncertainty due to variable parameters and unpredicted statistical changes, creating meta-uncertainty.
  • Understanding animal strategies for foraging under meta-uncertainty and their neural basis is largely unknown.

Purpose of the Study:

  • To investigate patch-leaving decisions in mice under conditions of meta-uncertainty.
  • To develop a novel behavioral task and computational framework for studying foraging under changing environmental statistics.
  • To elucidate the cognitive and neural mechanisms underlying adaptive foraging in volatile environments.

Main Methods:

  • Developed a novel behavioral task for head-fixed and freely moving mice involving stochastic variation of between-patch travel time and within-patch reward depletion rate.
  • Applied a computational framework to model foraging behavior under varying levels of first-order (local variability) and second-order (global statistics) uncertainty.
  • Analyzed patch residence times and compared them to predictions from the marginal value theorem and heuristic strategies.

Main Results:

  • Mice behavior aligned with the MVT in low-uncertainty conditions, outperforming simple heuristic strategies.
  • In highly variable environments, mouse behavior was best explained by a hierarchical Bayesian model incorporating both local variability and dynamic global statistics.
  • This suggests mice employ sophisticated Bayesian inference to manage meta-uncertainty during foraging.

Conclusions:

  • Mice utilize a hierarchical Bayesian strategy to forage efficiently in volatile environments with meta-uncertainty.
  • This adaptive strategy allows animals to distinguish between environmental fluctuations and genuine changes in statistical properties.
  • The findings provide a foundation for exploring the neural basis of decision-making under naturalistic uncertainty.