Sampling with auxiliary information and repulsion

Matthieu Wilhelm
EPFL, Lausanne, Suisse

Date(s) : 14/05/2018   iCal
10 h 30 min - 11 h 30 min

In this talk, random sampling will be discussed in several different settings. First, sampling in finite population is discussed, in view of three principles: overrepresentation, restriction and randomization. We argue that those principles should be kept in mind when designing a survey and we give rationale for their use. When auxiliary information is available, and under some reasonable model, it is possible to optimize the sampling design while keeping the design unbiasedness properties of the Horvitz-Thompson estimator of the total (or the mean) of the variable of interest. In particular, we highlight the role of balanced sampling when the assumed model is linear in terms of the auxiliary variables.
Sometimes, no auxiliary information is available but a correlation between close units exists. This can be the case if the variable of interest varies smoothly across the units, for instance for a survey in real time or a spatial survey. We show that a repulsive sampling design is appropriate in this case. We then introduce a class of sampling design in finite population that allows us to control the spreading between units.
In a second part, we consider sampling in a Euclidean space, where the variable of interest is a function and we aim at computing the integral (or the mean) of this function on some bounded domain. In the case of a one dimensional function, we develop a family of sampling processes that allows us to continuously tune the repulsion between units.
Finally, if time permits, we will discuss the application of determinantal point processes for the purpose of sampling.



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