Lecture 24 : April 21 , Large Deviation & Hypothesis Testing
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چکیده
Type: The type Pxn (or empirical probability distribution) of a sequence x1, x2, ..., xn is the relative proportion of occurrences of each symbol a ∈ X (i.e. Pxn(a) = N(a,x ) n for all a ∈ X, where N(a, x ) is the number of times the symbol a occurs in the sequence x ∈ X). The type of a sequence x is denoted as Pxn and it is a probability mass function on X . Set of types: Let Pn denote the set of types with denominator n. For example, if X={0, 1}, the set of possible types with denominator n is
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Lecture 21 : Hypothesis Testing , Method of Types and Large Deviation
One of the standard problems in statistics is to decide between two alternative explanations for the data observed. For example, in medical testing, one may wish to test whether or not a new drug is effective. Similarly, a sequence of coin tosses may reveal whether or not the coin is biased. These problems are examples of the general hypothesis-testing problem. In the simplest case, we have to ...
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