written here as LAGPS[O, A], the resulting estimated predictive probability mass functions being shown in Scollnik's Figure 3. The first set of priors was gamma[2, 0.25] for 0, where the gamma[oa, d] distribution has density O3xK-c. exp(-3x)/F(o), and uniform[O, 1] for A. The second set had the same gamma distribution for 0, and for A it had the probability density {exp(0.5[1-(1-A)-2])}/(1A)3, corresponding to a negative exponential distribution with rate 0.5 for the (index of dispersion 1). The mass functions are remarkably similar, raising the question as to how different the results for standard maximum likelihood (ML) would be. (Janardan, Kerster, and Schaeffer [1979] fitted these data using moments, obtaining an excellent fit.) The social behavior of the isopods would plausibly lead to a deficiency in the single-bug class and a corresponding inflation of the other classes. Perhaps the simplest model for this is obtained by taking a basic Poisson[A] distribution, applying a factor of w to the unit class, and scaling all others by the corresponding factor to produce a probability distribution (abbreviated as PS1[w, A]). (Cole [1946] had proposed some rather more complicated ad hoc models.) These two models, LAGPS and PSI, when fitted by ML (all the non-Bayesian fits described below use ML) to the quoted data give results shown in the third and fourth columns of Table 1. The fit for LAGPS[0, A] is obviously very good, with a chi-squared value of 13.4 with 13 d.f. (grouping to at least unity from the smallest class upwards, if necessary repeatedly) and a P-value of 0.41. (A negative binomial fit is very similar.) The PS1[w, A] fit is equally obviously very bad (chi-squared of 386 with 7 d.f.), so that this simplest model is not acceptable; moreover, the estimate of w, the factor by which the unit class is supposed to be reduced is 2.5, with a standard error of 0.6, which is not at all consistent with the model in context. The alternative, very similar model for which all the transferred probability from the unit class is placed in the zero class fits almost as badly. For LAGPS, comparisons of the ML estimates with the two sets of Bayesian procedure estimates are shown in Table 2 (extracted from Scollnik's Figure 3), using the headings of Mean and SD for