Just as a quick note, sometimes there is a more quick way to estimate the parameter of a Poisson model from data than a generalised linear model (via e.g. R’s glm function). This is the case when the expected mean λ is just a straight line that starts at 0 at time 0: $$\lambda(t) = gt.$$ This can model for example the number n(t) of a steadily produced mRNA species in a cell after the enhancer becomes active for the first time: the sum of two Poisson-distributed values with means λ_{1} (already existing number), λ_{2} (production during next time slice) is also Poisson-distributed with mean $$\lambda_1+\lambda_2$$

In this case the maximum likelihood or Bayesian estimate (they are the same, assuming no particular prior knowledge) for g is simply

$$ g=\frac{\sum{n}}{\sum{t}} $$

This is because the probability of a single Poisson event with λ=gt is Continue reading