We can estimate the period *t* tha=
t has elapsed if we know =CE=BB and the number of events *a* that have =
occurred in time *t*. The mathematics are exactly the same as the es=
timate for =CE=BB. The reader =
may like to verify that, by using a prior of *p*(*t)* =3D 1/ *t* we obtain a posterior distribution: *t<=
/em> =3D Gamma(1/=CE=BB**,=CE=B1**) which is the same result we would obtain if we were trying to predict fo=
rward (i.e. determine a distribution of variability of) the time required t=
o observe **a* events given =CE=BB =3D 1/=CE=B2. Also, if we can reasonably describe our prior belief =
of the elapsed period t with a Gamma(b,a) distribution, the posterior is given by a Gamma(~~b/ (1 + b=CE=BB),~~*=CE=B1** + **a*) distribution.

Note that here we use the parameterizatio=
n Gamma(b, a) *where* *<=
em>b* *=3D Scale and* *a =3D* *Shape,=
*whereas in other sections of ModelAssist we might report a three=
-parameter version of the Gamma distribution.

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