Likelihood and all that © 2006

Previous chapters have introduced all the ingredients you need to define a model — mathematical functions to describe the deterministic patterns and probability distributions to describe the stochastic patterns — and shown how to use these ingredients to simulate simple ecological systems. However, you need to learn not only how to construct models but also how to estimate parameters from data, and how to test models against each other. You may be wondering by now how one actually does this. In general, to estimate the parameters of a model we have to find the parameters that make that model fit the data best. To compare among models we have to figure out which one fits the data best, and decide if one or more models fit sufficiently much better than the rest that we can declare them the winners. Our goodness-of-fit metrics will be based on the likelihood, the probability of seeing the data we actually collected given a particular model — which in this case will mean both the general form of the model and the specific parameter values.