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4.1 notation For this chapter, we’ll need to introduce additional notation to handle the concepts from probability. See table 4.1 for a summary. Random variables are denoted by capital, non-subscribed, roman letters. Only A, the random α, is used frequently. Another small change from the standard notation is that lower case roman letters a, b, l , r denote scalar parameters or bounded intervals.1 These will be clear from context. For instance, they are used in the example below. There are two other novelties: the expectation operator E [⋅] and the stan- dard deviation operator Std [⋅]. Given a continuous random variable2 A with a density function ρ(x) on the interval [l , r], then we define (4.1) 1 In the notation defined in section 2.1, scalars were Greek symbols. Switching to roman for a few scalars helps inter- pretability for this chapter. 2 Such random variables are quite special, but they suffice for this chapter. E[A] = Evaluating the expectation of a function corresponds to r l √ tor r l E[f(A)] = The standard deviation operator is defined in terms of the expectation opera- ρ(x)dx. f(x)ρ(x)dx. (4.2) (4.3) 4.1 ⋅ notation 57 Std [A] = A good background on probability is Grinstead and Snell [1997]. E [(A − E [A])2]. Symbol A Beta(a,b,[l,r]) Beta(⋅, ⋅) δij E [⋅] Std [⋅] Meaning a random variable for α the Beta distribution, see section 4.4.1 the Beta function the Kronecker delta the expectation operator the standard deviation operator Table 4.1 – Additional notation for the random alpha PageRank model. Capital roman letters, such as A, denote random variables in this chapter.PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
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