6 Poisson Counts and the Gaussian Approximation
In many applications the data begin with simple event counts. The natural model is then Poisson, while the Gaussian description should be treated as an asymptotic approximation rather than as the starting point.
Three ideas matter here:
- the mean and variance of a Poisson variable are equal;
- at large expected counts the distribution approaches a normal shape;
- the quality of the approximation should be checked numerically, not assumed.
6.0.1 Companion notebook
The notebook for this chapter runs a tiny toy study: repeated Poisson draws and a comparison between empirical summary statistics and the theoretical expectation.