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Comment: reworded this for clarify

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We can estimate the period t that has elapsed if we know λ and the number of events a that have occurred in time t. The maths turns out to be mathematics are exactly the same as the estimate for λ. The reader may like to verify that, by using a prior of p(t) = 1/ t we obtain a posterior distribution: t = Gamma(0,1/λ,α) which is the same result we would obtain if we were trying to predict forward (i.e. determine a distribution of variability of) the time required to observe a events given λ = 1/β. Also, if we can reasonably describe our prior belief of the elapsed period t with a Gamma(0,b,a) distribution, the posterior is given by a Gamma(0,b/ (1 + bλ),α + a) distribution.

Note that here we use the parameterization Gamma(b, a)  where b = Scale and a = Shape, whereas in other sections of ModelAssist we might report a three-parameter version of the Gamma distribution