Sampling and sampling algorithms for finite populations

The aim of this course is to examine methods of selecting samples for extrapolation to the whole population. We begin by presenting a number of applications where sampling is necessary. We then show how extrapolation can be justified using a sampling design, a model or both. After a brief review of the most classical methods (simple random sampling, stratification), we explain the advantages and difficulties of unequal probability sampling. We show how these methods can be implemented. We then develop algorithms for selecting balanced samples. Finally, we present methods for obtaining a spatially spread sample. We then return to the examples to show how the sampling designs can be optimized.