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Download a pdf copy of this help file here |
|
Download a pdf copy of this help file here |
For a Poisson process, we can estimate the period t that has elapsed
if we know l
and the number of events a
that have occurred in time t. The maths turns out to be exactly
the same as the estimate for l.
The reader may like to verify that, by using a prior of p(t) = 1/
t we obtain a posterior distribution: t = Gamma(a,1/l)
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 l
= 1/b.
Also, if we can reasonably describe our prior belief with a Gamma(a,b)
distribution, the posterior is given by a Gamma(a + a, b/ (1 +
b l))
distribution.
