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Related Concept Videos

Uncertainty: Confidence Intervals00:54

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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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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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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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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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Creating Objects and Object Categories for Studying Perception and Perceptual Learning
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Bayesian inference with incomplete knowledge explains perceptual confidence and its deviations from accuracy.

Koosha Khalvati1, Roozbeh Kiani2,3,4, Rajesh P N Rao5,6

  • 1Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, WA, USA.

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Summary

A Bayesian framework using partially observable Markov decision processes (POMDPs) explains perceptual decisions and confidence. This model accurately predicts animal behavior and resolves apparent discrepancies between choice and confidence.

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Area of Science:

  • Cognitive neuroscience
  • Computational neuroscience
  • Decision science

Background:

  • Perceptual decisions involve inferring environmental states from noisy sensory data.
  • Understanding the computational basis of choice and confidence is crucial for decision-making research.

Purpose of the Study:

  • To propose and validate a unified Bayesian framework for explaining both choice and confidence in perceptual tasks.
  • To investigate whether apparent discrepancies between choice and confidence arise from sub-optimal inference or incomplete environmental knowledge.

Main Methods:

  • Developed a Bayesian model based on partially observable Markov decision processes (POMDPs).
  • Tested the model on monkeys performing a direction-discrimination task with post-decision wagering.
  • Analyzed model predictions against objective accuracy and subjective confidence reports.

Main Results:

  • The POMDP model successfully explained objective accuracy and predicted subjective confidence in monkeys.
  • The model replicated several known discrepancies between confidence and accuracy, such as the hard-easy effect.
  • Demonstrated that these discrepancies emerge naturally from Bayesian inference with incomplete environmental knowledge.

Conclusions:

  • Choice and confidence in perceptual tasks can be unified under a single Bayesian inference framework.
  • Apparent discrepancies between choice and confidence are not necessarily indicative of sub-optimal processes.
  • Incomplete knowledge of the environment is sufficient to explain complex confidence-accuracy relationships.