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CLs (from Confidence Levels) is a statistical method for setting upper limits (also called ''exclusion limits'') on model parameters, a particular form of interval estimation used for parameters that can take only non-negative values. "The method's name is ... misleading, as the CLs exclusion region is not a confidence interval." It was first introduced by physicists working at the LEP experiment at CERN and has since been used by many high energy physics experiments. It is a frequentist method in the sense that the properties of the limit are defined by means of error probabilities, however it differs from standard confidence intervals in that the stated confidence level of the interval is not equal to its coverage probability. The reason for this deviation is that standard upper limits based on a most powerful test necessarily produce empty intervals with some fixed probability when the parameter value is zero, and this property is considered undesirable by most physicists and statisticians.〔 〕 Upper limits derived with the CLs method always contain the zero value of the parameter and hence the coverage probability at this point is always 100%. The definition of CLs does not follow from any precise theoretical framework of statistical inference and is therefore described sometimes as ''ad hoc''. It has however close resemblance to concepts of ''statistical evidence'' proposed by the statistician Allan Birnbaum. == Definition == Let ''X'' be a random sample from a probability distribution with a real non-negative parameter . A ''CLs'' upper limit for the parameter ''θ'', with confidence level , is a statistic (i.e., observable random variable) which has the property: The inequality is used in the definition to account for cases where the distribution of ''X'' is discrete and an equality can not be achieved precisely. If the distribution of ''X'' is continuous then this should be replaced by an equality. Note that the definition implies that the coverage probability is always larger than . An equivalent definition can be made by considering a hypothesis test of the null hypothesis against the alternative . Then the numerator in (), when evaluated at , correspond to the type-I error probability () of the test (i.e., is rejected when ) and the denominator to the power (). The criterion for rejecting thus requires that the ratio will be smaller than . This can be interpreted intuitively as saying that is excluded because it is less likely to observe such an extreme outcome as ''X'' when is true than it is when the alternative is true. The calculation of the upper limit is usually done by constructing a test statistic and finding the value of for which : where is the observed outcome of the experiment. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「CLs upper limits (particle physics)」の詳細全文を読む スポンサード リンク
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