STAT 391 Handout 2 Smoothing the ML parameters c © 2010 Marina
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چکیده
Here discuss what to do in the case when an outcome i ∈ S is not observed in the data. This can happen when the number of outcomes m = |S| is large, so that n >> m or when the probability θ i is near 0. When i is not observed, the corresponding sufficient statistic n i = 0 and θ M L i = 0. This estimate is unacceptable unless we really believe that outcome i is impossible. In the following are presented several methods for correcting this problem. These methods go by the name of smoothing, shrinkage, discounting in the literature. 1 Laplace or Dirichlet smoothing The simplest (and least useful) discounting method is the Laplace smoothing. It is equivalent to assuming we assume we have seen one more example of each value in S). The method can be summarized as: add 1 to each count and renormalize. θ Laplace i = n i + 1 n + m for i = 1 : m (1) It can be used also with another value, ǫ < 1, in place of 1.
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تاریخ انتشار 2010