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Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated. More specifically, given a confidence level γ {\displaystyle \gamma } (95% and 99% are typical values), a CI is a random interval which contains the parameter being estimated γ {\displaystyle ...
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.
The confidence region is calculated in such a way that if a set of measurements were repeated many times and a confidence region calculated in the same way on each set of measurements, then a certain percentage of the time (e.g. 95%) the confidence region would include the point representing the "true" values of the set of variables being estimated.
Meaning c̅ (c with an overbar) with (from Latin cum) means with C: cytosine cervical vertebrae: C1: atlas – first cervical vertebra of the spine C2: axis – second cervical vertebra of the spine CA: carcinoma cancer: Ca: calcium carcinoma cancer: CAA: coronary artery aneurysm: c/b: complicated by: CABG: coronary artery bypass graft ...
which correspond to the above definition of CLs. The first equality just uses the definition of Conditional probability , and the second equality comes from the fact that if n ≤ n ∗ ⇒ n b ≤ n ∗ {\displaystyle n\leq n^{*}\Rightarrow n_{b}\leq n^{*}} and the number of background events is by definition independent of the signal strength.
In these hypothetical repetitions, independent data sets following the same probability distribution as the actual data are considered, and a confidence interval is computed from each of these data sets; see Neyman construction. The coverage probability is the fraction of these computed confidence intervals that include the desired but ...
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