## Using the tdistribution in ecological models and Bayesian updating of the parameter

Our simplest statistical model involving a normal random variable was

Y = m + X, where m is unknown and to be estimated and X was a normally distributed random variable. A more complicated version, in which Yis constrained to be positive, is log(Y) = log(m) + X. However, ecological or evolutionary data are often non-normal, with tails that are fatter than normal. This suggests that we might work with the model

Y = m + r„, where Tv is a random variable following a t-distribution with v degrees of freedom. (Alternatively, of course, we might work with log(Y) = log(m) + Tv.) Carpenter et a/. (1999) used such an approach in development of a model for the eutrophication of a lake. Furthermore, we know that as v !i, Tv!X, so that by applying Bayesian methods, we can allow the data to tell us the kind of error distribution to use (see Gelman et a/. (1995) pp. 350-361).

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