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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

10.7K
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.
A...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

10.0K
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...
10.0K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

11.7K
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...
11.7K
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

8.9K
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...
8.9K
Confidence Coefficient01:24

Confidence Coefficient

10.6K
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...
10.6K
Prediction Intervals01:03

Prediction Intervals

3.4K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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Confidence Interval Constraint-Based Regularization Framework for PET Quantization.

F Kucharczak, F Ben Bouallegue, O Strauss

    IEEE Transactions on Medical Imaging
    |December 19, 2018
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel tomographic reconstruction framework using confidence interval constraints. This method improves image quality by preventing over-smoothing and optimizing bias-variance trade-offs.

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    Area of Science:

    • Medical Imaging
    • Computational Science

    Background:

    • Traditional regularization methods in tomographic reconstruction often minimize a combined cost function.
    • These methods can lead to over-smoothing and suboptimal bias-variance trade-offs.

    Purpose of the Study:

    • To present a new generic regularized reconstruction framework for tomographic reconstruction.
    • To introduce confidence interval constraints as an alternative to scalar-weighted regularization.

    Main Methods:

    • A two-step reconstruction process is proposed.
    • Step 1: Direct estimation of confidence intervals for reconstructed values.
    • Step 2: Utilization of confidence intervals as constraints for regularization.

    Main Results:

    • The framework prevents over-smoothing by strictly enforcing interval-valued data-fitting constraints.
    • Offers improved spatial and statistical bias/variance trade-offs.
    • Demonstrated competitiveness against existing regularization schemes.

    Conclusions:

    • The proposed framework offers a robust alternative for tomographic reconstruction.
    • Confidence interval constraints provide enhanced control over solution properties.
    • Validated through simulations and real PET data.