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Extra resources for An Introduction to the Philosophy of Mind
One way of dealing with populations that cluster or are territorial is to use a probability density function (pdf) that is more able to deal with this than is the binomial. The negative binomial is a ﬂexible candidate (see below). In practice, however, design-based methods (Chapter 10) are usually used in preference to maximum likelihood methods for these surveys. Design-based methods do not rely on any assumptions about animal distribution. The Horvitz–Thompson estimator proper was developed for design-based sampling theory and it is directly applicable here because the inclusion probability (Pc ) is known (from the design).
19) Maximum likelihood estimation The description above begs the question of how to estimate the unknown inclusion probabilities. They can be factorized into a probability of the animal (cluster) being in the covered region (Pc ) and a probability that it is detected, given that it is in the covered region (Pa ). The coverage probability Pc is conventionally treated as known (it is determined by the survey design), but Pa must be estimated from the observed distances. In this book we focus on estimation by maximum likelihood.
The negative binomial is a ﬂexible candidate (see below). In practice, however, design-based methods (Chapter 10) are usually used in preference to maximum likelihood methods for these surveys. Design-based methods do not rely on any assumptions about animal distribution. The Horvitz–Thompson estimator proper was developed for design-based sampling theory and it is directly applicable here because the inclusion probability (Pc ) is known (from the design). 21) in this case; the diﬀerence between the two methods lies in the estimation of variance.