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Related Concept Videos

Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Interpretation of Confidence Intervals01:19

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
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Confidence Intervals01:21

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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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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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Confidence Interval for Estimating Population Mean01:25

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
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A Mathematical Framework for Statistical Decision Confidence.

Balázs Hangya1, Joshua I Sanders2, Adam Kepecs3

  • 1Cold Spring Harbor Laboratory, Cold Spring Harbor, New York 11724, U.S.A., and Lendület Laboratory of Systems Neuroscience, Institute of Experimental Medicine, Hungarian Academy of Sciences, Budapest, H-1083, Hungary hangya.balazs@koki.hu.

Neural Computation
|July 9, 2016
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Summary
This summary is machine-generated.

This study introduces a statistical framework for decision confidence, defining it as the probability of a correct decision based on evidence. This framework offers testable predictions for understanding confidence across various scientific fields.

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Area of Science:

  • Cognitive Science
  • Neuroscience
  • Decision Theory

Background:

  • Decision confidence is crucial for evaluating decision-making processes.
  • Existing definitions lack a unified statistical foundation.
  • Understanding confidence is vital across disciplines like psychology, neuroscience, and artificial intelligence.

Purpose of the Study:

  • To develop a normative statistical framework for decision confidence.
  • To derive general predictions independent of noise structure or specific algorithms.
  • To establish a mathematically rigorous basis for decision confidence.

Main Methods:

  • Utilized a formal Bayesian definition of decision confidence.
  • Developed a normative statistical framework.
  • Analytically proved interrelations between confidence and observable decision measures.

Main Results:

  • Established analytical proofs for interrelations between statistical decision confidence and measures like evidence discriminability, choice, and accuracy.
  • Identified empirically testable signatures of decision confidence.
  • Demonstrated that these signatures are independent of specific noise structures or confidence estimation algorithms.

Conclusions:

  • The developed framework provides a mathematically rigorous treatment of decision confidence.
  • Results lay the groundwork for a unified understanding of confidence across diverse research domains.
  • The findings enable empirical testing of decision confidence through quantifiable variables.