The counting process is a function that is incremented by 1 each time a new event arrives. Clearly, fewer events occurred in the treatment group than in the control group. If these are login events, it means the new code contains a bug that prevents some users from logging in successfully.
This is a common situation when dealing with event timestamps. As another example, if events correspond to bugs or crashes, we want to know whether these events accumulate faster in the treatment than in the control group.Furthermore, we would like to answer the question ASAP to prevent further disruption of service. This requires the sequential testing techniques introduced in Part 1.
Time non-homogeneous Poisson process
Our data for each treatment group are implementations of a one-dimensional point process, that is, a sequence of timestamps. Since the rate at which events arrive is time-varying (in treatment and control), we model the point process as a time-nonuniform Poisson point process. This point process is defined by the intensity function λ: ℝ →[0∞)Thenumberofeventsintheinterval[0t)denotedN
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