A major concern with the use of non-probability samples is their non-representativeness, which if not accounted properly, may led to large bias in the inference process. The question arising therefore is how to draw inference from such samples, regarding the population that they are believed to represent. In this paper the concept of uncertainty on data generating model, resulting from the lack of knowledge of the sampling design acting in the non-probability sample, is introduced. Furthermore, the reduction of uncertainty due to the availability of extra-sample information is discussed. Finally, the effect of the lack of identifiability on the accuracy of survey estimates is evaluated.