Scnditignal inference and maximum likelihood in a capture-recapture model
A capture-recapture model is used to illustrate the use of sufficient statistics to factor the joint likelihood function into parts suitable for inferences, valid in samples of any size, on various subsets of the parameters. An assessment is made of the information ignored by confining attention to these parts of the likelihood function. The appropriate application of maximum likelihood estimation is illustrated as providing reasonably accurate approximations to these inferences. Although there are practical examples of this approach in the statistical literature, general awareness of the logical principles involved does not seem widespread. This paper illustrates and explains these logical principles in a more complex situation