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Statistical Inference I
Published in Michael Baron, Probability and Statistics for Computer Scientists, 2019
The population parameter θ is not random. It is a population feature, independent of any random sampling procedure, and therefore, it remains constant. On the other hand, the interval is computed from random data, and therefore, it is random. The coverage probabilitycoverage probability refers to the chance that our interval covers a constant parameter θ.
A new method in introducing the uniformly most accurate confidence set
Published in International Journal of Mathematical Education in Science and Technology, 2022
Lin-An Chen, Chu-Lan Michael Kao
The coverage probability measures the probability that confidence set covers parameter when the true parameter is . When we consider the event that a confidence set covers a parameter value , this may be a false coverage or an accurate coverage since the true value of the parameter is unknown. Therefore, we must consider an optimal approach that minimizes the probability of false coverage, known as the least false approach, and an optimal approach that maximizes the probability of accurate coverage, known as the most accurate approach.
Prediction of Future Failures for Heterogeneous Reliability Field Data
Published in Technometrics, 2022
Colin Lewis-Beck, Qinglong Tian, William Q. Meeker
We again use Bayesian estimation for our simulation study. Performance of our prediction intervals is evaluated in terms of coverage probability. Here coverage probability is interpreted as the proportion of times that prediction intervals (for single and multiple groups) cover the true number of future within-sample failures. We do not want our prior distributions to bias the results: diffuse prior distributions (e.g., a flat prior) put probability mass on extreme values not consistent with the range of practical situations we are trying to mimic; priors that are too informative can also affect the posterior by overly constraining the likelihood. Therefore, for all factor level combinations, we specify the following weakly informative prior distributions,
On Fixed-Width Confidence Limits for the Risk Ratio with Sequential Sampling
Published in American Journal of Mathematical and Management Sciences, 2020
For practical purposes, the coverage probability was computed as the proportion of samples for which the true population parameter ρ is contained in the confidence interval J. That proportion is an estimate for the empirical coverage probability for the CI.