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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

2.5K
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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Bootstrapping01:24

Bootstrapping

782
The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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Survival Tree01:19

Survival Tree

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Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
Constructing a...
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Confidence Intervals01:21

Confidence Intervals

9.1K
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 confidence...
9.1K
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

8.7K
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...
8.7K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

9.9K
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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Related Experiment Videos

Constructing Optimal Prediction Intervals by Using Neural Networks and Bootstrap Method.

Abbas Khosravi, Saeid Nahavandi, Dipti Srinivasan

    IEEE Transactions on Neural Networks and Learning Systems
    |September 13, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces an optimized bootstrap method using neural networks for better prediction intervals (PIs). The technique significantly enhances PI quality, providing narrower intervals with improved coverage probability.

    Related Experiment Videos

    Area of Science:

    • Statistics
    • Machine Learning
    • Data Science

    Background:

    • Accurate prediction intervals (PIs) are crucial for uncertainty quantification in statistical modeling.
    • Existing bootstrap techniques for PI construction can be suboptimal, leading to wider intervals and less reliable coverage.
    • Neural networks (NNs) offer powerful tools for complex function approximation, potentially improving variance estimation.

    Purpose of the Study:

    • To develop an efficient and optimized technique for constructing prediction intervals (PIs).
    • To leverage neural networks (NNs) and a novel PI-based cost function for improved variance estimation within the bootstrap method.
    • To enhance the quality and reliability of PIs compared to existing methods.

    Main Methods:

    • An innovative PI-based cost function was designed for training neural networks (NNs).
    • NNs were employed to estimate the target variance crucial for the bootstrap method.
    • An optimization algorithm was developed to minimize the cost function and tune NN parameters.
    • The proposed method was evaluated across seven synthetic and real-world datasets.

    Main Results:

    • The optimized bootstrap method demonstrated a significant improvement in PI quality, exceeding 28% over existing techniques.
    • The developed method resulted in narrower prediction intervals.
    • The constructed PIs exhibited coverage probabilities exceeding the nominal confidence level.
    • The optimization algorithm effectively minimized the cost function and adjusted NN parameters.

    Conclusions:

    • The proposed optimized bootstrap technique offers a superior approach for constructing prediction intervals.
    • The integration of neural networks and a PI-based cost function enhances variance estimation accuracy.
    • This method leads to more reliable and informative prediction intervals, crucial for decision-making under uncertainty.