Likelihood

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Likelihood is a statistical term referring to the probability of obtaining a particular set of observations given some model of the system. It is a term in Bayes' theorem.

[edit] Bayes theorem

Bayes theorem is used to assess the effectiveness of some model or hypothesis in explaining the observations from some experiment. It is represented by the following equation:

P( model | data ) = P( data | model ) P ( model ) / P(data)

In this equation, P() is read as "the probability of", and | is read as "given", i.e. in words

The probability of the model given the data is equal to the probability of the data given the model multiplied by probability of the model and divided by the probability of the data

The terms in this equation all have names:

  • P ( model ) is called the prior probability.
  • P( data | model ) is called the likelihood.
  • P( model | data ) is called the posterior probability.
  • P(data) is distribution of data only.

[edit] Examples of Bayes theorem

Bayes theorem gives a rigorous method for using observations (data) to update your understanding of a system (model). In crystallography, diffraction data is used to update generic information about protein structures (standard residue geometries, amino acid sequence) into an understanding of the full tertiary structure. However, Bayes theorem is more famously used (or abused) in legal and medical areas, and can produce seemingly counter-intuitive results. Here are some examples:

--Kevin Cowtan 02:59, 25 April 2008 (CDT)

--Updated by Martyn Winn 27 April 2010

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