November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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9.17 LIKELIHOOD RATIO TEST
Next, we describe a decision problem that is related to estimation and is based on the likelihood function. In many applications, we are interested in deciding which of two models is most likely to be correct given one or more samples of a random variable. For example, let X be a measurable random variable from which we are to decide if the underlying model has parameter 
or 
. Such a scenario can be represented by the following two hypotheses:
(9.269) 
where an additive noise random variable V has been included. H0 is called the null hypothesis, meaning that it is the default model, and the goal is to determine from X if 
is true instead of 
. When 
, the null hypothesis means that the sample contains only noise in this example.
Definition: Likelihood Ratio ...
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