Learning about a Categorical Latent Variable under Prior Near-Ignorance

Details Learning about a Categorical Latent Variable under Prior Near-Ignorance Learning about a Categorical Latent Variable under Prior Near-Ignorance

2007-05-29

arxiv.org/abs/0705.4312v1

Proc. 5th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2007) pages 357-364

Mathematics

Probability

15 LaTeX pages

Scientific paper

It is well known that complete 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 a state similar to full ignorance, that Walley calls near-ignorance, that permits learning to take place. In this paper we 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, and we show, for the case of categorical latent variables (and general manifest variables) that there is a sufficient condition that, if satisfied, prevents learning to take place under prior near-ignorance. This condition is shown to be easily satisfied in the most common statistical problems.

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