[CONF] Apache Lucene Mahout > LLR - Log-likelihood Ratio

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Space: Apache Lucene Mahout (http://cwiki.apache.org/confluence/display/MAHOUT)
Page: LLR - Log-likelihood Ratio (http://cwiki.apache.org/confluence/display/MAHOUT/LLR+-+Log-likelihood+Ratio)

Added by David Stuart:
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{excerpt}Likelihood ratio test is used to compare the fit of two models one of which is nested within the other.{excerpt}

A way of using the sensitivity and specificity of a test to see if a positive or negative result usefully changes the probability of a condition (such as a disease state) existing. Thus the value of performing the test at all can be assessed.

In a binary hypothesis testing problem, four possible outcomes can result.  Model *ℳ0* did in fact represent the best model for the data and the decision rule said it was (a correct decision) or said it wasn't (an erroneous decision).  The other two outcomes arise when model *ℳ1* was in fact true with either a correct or incorrect decision made.  The decision process operates by segmenting the range of observation values into two disjoint decision regions *ℜ0* and *ℜ1*. All values of *r* fall into either *ℜ0* or *ℜ1*. If a given *r* lies in *ℜ0*, for example, we will announce our decision "model *ℳ0* was true"; if in *ℜ1*, model *ℳ1* would be proclaimed.  To derive a rational method of deciding which model best describes the observations, we need a criterion to assess the quality of the decision process.

 See Also:
 * http://cnx.org/content/m11234/latest/
 * http://en.wikipedia.org/wiki/Likelihood-ratio_test
 * http://en.wikipedia.org/wiki/Likelihood_ratio
      

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