ABSTRACT
In this chapter, experimental designs are considered for the situation where the data are thought to come from Poisson distributions. The chapter starts with a consideration of the Poisson distribution, and then examines means of designing experiments. A theorem is given that tells how a locally D-optimal design can be obtained for many parameter sets. For such parameter sets, designs can be obtained directly without having to perform any numerical optimisation. This is a distinct advantage. When the postulated parameter vector does not meet the requirements of the theorem, numerical optimisation is required, and several examples are given of this. The problem of separation that can arise for small designs can occur for the Poisson distribution as well as the binomial distribution, and the use of MPL estimators to get around this problem is described. Only D-optimality and IMSE-optimality are considered.
