English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the coherent theory of (epistemic) uncertainty ofWalley, in which beliefs are represented through sets of probabilitydistributions, and we focus on the problem of modeling prior ignorance about acategorical random variable. In this setting, it is a known result that a stateof prior ignorance is not compatible with learning. To overcome this problem,another state of beliefs, called \emph{near-ignorance}, has been proposed.Near-ignorance resembles ignorance very closely, by satisfying some principlesthat can arguably be regarded as necessary in a state of ignorance, and allowslearning to take place. What this paper does, is to provide new and substantialevidence that also near-ignorance cannot be really regarded as a way out of theproblem of starting statistical inference in conditions of very weak beliefs.The key to this result is focusing on a setting characterized by a variable ofinterest that is \emph{latent}. We argue that such a setting is by far the mostcommon case in practice, and we provide, for the case of categorical latentvariables (and general \emph{manifest} variables) a condition that, ifsatisfied, prevents learning to take place under prior near-ignorance. Thiscondition is shown to be easily satisfied even in the most common statisticalproblems. We regard these results as a strong form of evidence against thepossibility to adopt a condition of prior near-ignorance in real statisticalproblems.

Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance