9. Consider the time series yt on t = 1, . . . , T counts of coal-mining disasters from Carlin et al. (1992a). The series runs from 1851 to 1962, and a lower rate of disasters is suggested from the late nineteenth century by simple plots. Carlin et al. consider a change point model 

where γ1 = γ2 with independent gamma priors on γ1 and γ2 and a discrete uniform prior for τ on (1, . . . , N). So γ1 ∼ Ga(a1, b1) and γ2 ∼ Ga(a2, b2) where a1 and a2 are known constants and an additional gamma prior stage is put on b1 and b2 , namely b1 ∼ Ga(g1, h1)
and b2 ∼ Ga(g2, h2). One possible expression of such a model is as

where the Vj are known and I (u) = 1 if u is true. Consider this model and a two change point model defined by

yi~ Po(1) yi~Po(2) 1>T,