Uncertainty-based analysis for non-probability samples

The use of non-probability samples is becoming increasingly important due to their availability at relatively low cost. The main limitation is that their use involves some form of arbitrary selection of units into the sample. As a consequence, inclusion probabilities are unknown, and it is not possible to apply weights, as suggested by probability randomisation theory, to remove selection bias and to make inference on finite population parameters. As a matter of fact, the lack of knowledge of the sampling design generating the non-probability sample produces uncertainty about the data generation model. In this talk the concept of uncertainty is discussed. A measure of uncertainty is introduced and its asymptotic proprieties are evaluated.