Trojani, Fabio Piatti, Alberto 2006-10-19 It is well known that a state of prior ignorance is not compatible with learning, at least in a coherent theory of (epistemic) uncertainty. What is less widely known, is that there is another state of beliefs, called near-ignorance, that resembles ignorance very closely by satisfying some principles that can arguably be regarded as necessary in a state of ignorance, and that allows learning to take place. What this thesis does is to provide new and substantial evidence that also near-ignorance cannot be really regarded as a way out of the problem of starting statistical inference in conditions of very weak beliefs. The key to this result is focusing on a setting characterized by a variable of interest that is latent. We argue that such a setting is by far the most common case in practice. In the first part of the thesis we provide, for the case of categorical latent variables (and general manifest variables) a condition that, if satisfied, prevents learning to take place under prior near-ignorance. This condition is shown to be easily satisfied even in the most common statistical problems. We regard these results as a strong form of evidence against the possibility to adopt a condition of prior near-ignorance in real statistical problems. In the second part of the thesis we propose a slightly modified framework that allows learning to take place under a very weak specification of prior knowledge. The proposed approach is a first preliminary attempt to reconcile latent variables with a very weak specification of prior knowledge. application/pdf https://localhost:5000/ark:/12658/srd1318179 https://susi.usi.ch/global/documents/318179 https://susi.usi.ch/documents/318179/files/2006ECO004.pdf eng info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:rero-006-108300 info:eu-repo/semantics/altIdentifier/ark/12658/srd1318179 info:eu-repo/semantics/openAccess License undefined Prior near ignorance Latent variables Learning info:eu-repo/classification/udc/33 Learning under prior ignorance http://purl.org/coar/resource_type/c_db06