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Related Concept Videos

Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5%...
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Accuracy, limits, and approximation01:28

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Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
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Uncertainty in Measurement: Accuracy and Precision03:37

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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. 
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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.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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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.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Statistical Analysis: Overview01:11

Statistical Analysis: Overview

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When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
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A Tactile Automated Passive-Finger Stimulator TAPS
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Frequentist accuracy of Bayesian estimates.

Bradley Efron1

  • 1Stanford University.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|June 20, 2015
PubMed
Summary

Bayesian estimation with uninformative priors can yield estimates lacking logical force. This study presents a frequentist method to assess Bayesian estimates, providing a standard deviation formula and connecting it to the parametric bootstrap.

Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Bayesian estimation commonly uses uninformative priors when prior experience is absent.
  • These priors aim for minimal influence but can result in estimates needing further justification.

Purpose of the Study:

  • To develop a frequentist assessment method for Bayesian point estimates.
  • To provide a formula for calculating the frequentist standard deviation of Bayesian estimates.

Main Methods:

  • Derivation of a simple formula for the frequentist standard deviation of a Bayesian point estimate.
  • Utilizing simulation data already generated for the point estimate to compute the standard deviation.
  • Exploring connections within exponential family models and the parametric bootstrap.

Main Results:

Keywords:
MCMCabc intervalsgeneral accuracy formulahierarchical and empirical Bayesparametric bootstrap

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  • A straightforward formula quantifies the frequentist standard deviation of Bayesian point estimates.
  • The standard deviation can be obtained from the same simulations used for the point estimate.
  • Exponential family models simplify calculations and link to the parametric bootstrap.

Conclusions:

  • The proposed frequentist assessment offers a way to evaluate Bayesian estimates derived from uninformative priors.
  • The method integrates seamlessly with existing simulation procedures.
  • This approach enhances the rigor and interpretability of Bayesian estimates in data analysis.