Likelihood Principle

A Likelihood Principle is a mathematical principle that asserts that all of the information in a sample is contained in the likelihood function.

• See: Bayesian Statistics, Statistical Inference, Information, Sampling (Statistics), Likelihood Function, Conditional Probability Distribution, Probability Density Function, Random Variable, Stopping Rule.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Likelihood_principle Retrieved:2014-5-30.
  • In statistics, the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a sample 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.

2017

• http://www2.isye.gatech.edu/~brani/isyebayes/bank/handout2.pdf Retrieved:2017-12-3.
  • In the inference about θ, after x is observed, all relevant experimental information is contained in the likelihood function for the observed x. Furthermore, two likelihood functions contain the same information about θ if they are proportional to each other.

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