Charles University, Faculty of Mathematicsand Physics
Prague, Czech Republic
16-19 July 2007


Alberto Piatti, Marco Zaffalon, Fabio Trojani, Hutter Marcus

Learning about a Categorical Latent Variable under Prior Near-Ignorance


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.

Keywords. Prior near-ignorance, latent and manifest variables, observational processes, vacuous beliefs, imprecise probabilities.

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Authors addresses:

Alberto Piatti
Galleria 2, Via Cantonale, CH-6928 Manno

Marco Zaffalon
Galleria 2
CH-6928 Manno

Fabio Trojani
Rosenbergstr. 52
CH-9000 St.Gallen

Hutter Marcus
Marcus Hutter, Assoc. Prof.
RSISE, Room B259, Building 115
Australian National University
Corner of North and Daley Road
Canberra ACT 0200, Australia

E-mail addresses:

Alberto Piatti
Marco Zaffalon
Fabio Trojani
Hutter Marcus

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