If we have a data set consisting of event times $\{t\_1, t\_2, \ldots, t\_N\}$ and would like to model this as a Poisson process with intensity $\lambda$, how do we do it? Intuitively, I would expect that we can calculate the average waiting time $w = \frac{1}{N-1}\sum\_{i=2}^N (t\_i-t\_{i-1})$ and then set $\hat{\lambda} = 1/w$?

Is this correct? If so, how is it justified? Do we have to consider fitting a Poisson distribution to the number of events after doing some sort of binning?