Estimating the parameters of a Poisson / gamma density Suppose that y}, "-1931 are a random sample from the Poisson/gamma density yiaab) = where a :> 0 and b > 0. This density is an appropriate model for observed counts that show more dispersion than predicted under a Poisson model. Suppose that {(1,5) are assigned the noninformative prior proportional to 1/{ab)2. If we transform to the real-valued parameters 61 2 loge and 6'2 2 log I), the posterior density is proportional to {_yiF+ a} if] 19 t? d t 9(1' 2! aa)oc Dcaltl'zrfl F{a)ytl (b+1):9ri+aj 1i: 1 where a : exp{6'1} and b : exp{92}. Use this framework to model data collected by Gilchrist (1984). in which a series of 33 insect traps were set across sand dunes and the numbers of different insects caught over a xed time were recorded. The number of insects of the taxa Staphyiaoidea caught in the traps is shown here. 25023134303 21106003011 50120021110 By computing the posterior density on a gridj simulate 1000 draws from the joint posterior densityr of (61,92). From the simulated sample. nd 90% interval estimates for the parameters a and b