Prediction of Unseen Proportions in Urn Models with Restricted Sampling

Imagine an urn with colored balls but with an unknown composition i.e. you do not know what are the specific colors in the urn nor their relative proportions. The urn could be composed by infinitely many colors and to learn about its composition you have been sampling balls with replacement from it. In this extended abstract we will construct exact confidence intervals for the proportion in the urn of the so far unobserved colors when there is an upper-bound m for the additional number of samples permitted from the urn. The research is motivated by a variety of situations of practical interest. For instance, the different colors in the urn could represent different solutions to a particular binding site problem in a random RNA pool, or the number of different species of bacteria present in a sample of soil or the gut of a person with a digestive disorder.