## ABSTRACT

Consider again the observed earthquake series displayed in Figure 1.1 on p. 4. The observations are unbounded counts, making the Poisson distribution a natural choice to describe them, but their distribution is clearly overdispersed relative to the Poisson. We saw in Chapter 1 that this feature can be accommodated by using a mixture of Poisson distributions with means λ_{1}, λ_{2}, …, λ
_{m}
. The choice of mean is made by a second random process, the parameter process. The mean λ_{
i
} is selected with probability δ
_{
i
}, where i = 1, 2,…, m and
∑
i
=
1
m
δ
i
=
1
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.