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In statistics, the likelihood principle is a controversial principle of statistical inference that asserts that, given a statistical model, all of the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a conditional probability distribution considered as a function of its distributional parameterization argument, conditioned on the data argument. For example, consider a model which gives the probability density function of observable random variable ''X'' as a function of a parameter θ. Then for a specific value ''x'' of ''X'', the function ''L''(θ | ''x'') = P(''X''=''x'' | θ) is a likelihood function of θ: it gives a measure of how "likely" any particular value of θ is, if we know that ''X'' has the value ''x''. Two likelihood functions are equivalent if one is a scalar multiple of the other. The likelihood principle states that all information from the data relevant to inferences about the value of θ is found in the equivalence class. The strong likelihood principle applies this same criterion to cases such as sequential experiments where the sample of data that is available results from applying a stopping rule to the observations earlier in the experiment.〔Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms. OUP. ISBN 0-19-920613-9〕 ==Example== Suppose *''X'' is the number of successes in twelve independent Bernoulli trials with probability θ of success on each trial, and *''Y'' is the number of independent Bernoulli trials needed to get three successes, again with probability θ (= 1/2 for a coin-toss) of success on each trial. Then the observation that ''X'' = 3 induces the likelihood function :, while the observation that ''Y'' = 12 induces the likelihood function : The likelihood principle says that as the data is the same in both cases the inferences drawn about the value of θ should also be the same. In addition, all the inferential content in the data about the value of θ is contained in the two likelihoods, and is the same if they are proportional to one another. This is the case in the above example, reflecting the fact that the difference between observing ''X'' = 3 and observing ''Y'' = 12 lies not in the actual data, but merely in the design of the experiment. Specifically, in one case, one has decided in advance to try twelve times; in the other, to keep trying until three successes are observed. The inference about θ should be the same, and this is reflected in the fact that the two likelihoods are proportional to each other. This is not always the case, howevever. The use of frequentist methods involving p-values leads to different inferences for the two cases above (), showing that the outcome of frequentist methods depends on the experimental procedure, and thus violates the likelihood principle. 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「Likelihood principle」の詳細全文を読む スポンサード リンク
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