Limits of Learning about a Categorical LatentVariable under Prior Near-Ignorance

In this paper, we consider the coherent theory of (epistemic) uncertainty ofWalley, in whichbeliefs are represented through sets of probability distributions, and we focus on the problemof modeling prior ignorance about a categorical random variable. In this setting, it isa known result that a state of prior ignorance is not compatible with learning. To overcomethis problem, another state of beliefs, called near-ignorance, has been proposed.Near-ignorance resembles ignorance very closely, by satisfying some principles that canarguably be regarded as necessary in a state of ignorance, and allows learning to take place.What this paper does, is to provide new and substantial evidence that also near-ignorancecannot be really regarded as a way out of the problem of starting statistical inference inconditions of very weak beliefs. The key to this result is focusing on a setting characterizedby a variable of interest that is latent.[...]