The general theory for making maximum likelihood (model-based) inference from sample survey data is presented in Breckling et al. (1994). We present an overview of this theory and use this to create a model-based approach to analysing sparse, clustered data. The ideas contained within Breckling et al. (1994) are expanded by creating a model not dissimilar to the final model proposed, but simple enough to give an idea of the possibilities of modelling this situation in a frequentist framework and also an indication of where some of the complexities underlying the problem arise. In itself this section presents an interesting and stand alone extension to Breckling et al. (1994). We then explore some of the literature on modelling oil-pools, a situation involving continuous measurements which poses similar problems to those needing to be addressed in the discrete clustered case. This gives us a critical insight into how to create a likelihood which includes a sampling proportional to size strategy. The main work of the thesis is in the synthesis of these ideas into a model which gives a more efficient estimate of overall population totals than the design-based estimates proposed by Thompson (1990). This model is predictably complex and despite critical insights into simplifying the problem, such as finessing the spatial component of the clusters, we necessarily use Bayesian methodology to make inference from the sample. The estimates produced prove to be more efficient than the design-based estimates and the model is a success.