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Questions tagged [imprecise-probability]

For questions regarding imprecise probability, which concerns concepts and methods generalizing probability theory beyond real-valued probability measures. It includes extensions of Bayesian methods to reflect uncertainty in degrees of confidence, and covers among other things, upper and lower previsions, interval-valued probability, credal sets, lower envelopes, and Choquet capacities.

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Notation in this imprecise Markov chain upper transition operator definition

In Example 11.6 on p. 270 of Hermans and Škulj's "Stochastic Processes" in Augustin et al.'s Introduction to Imprecise Probabilities, there is a definition of an upper transition operator as $$\...
Mars's user avatar
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5 votes
2 answers
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Simple calculation in imprecise probability urn example

In Miranda and de Cooman's chapter 3, "Structural judgements", in Augustin et al.'s Introduction to Imprecise Probability, example 3.4 on p. 65 shows that independence in the selection (type-...
Mars's user avatar
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4 votes
1 answer
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Why does the natural extension of a lower prevision dominate it?

On p. 48 in Troffaes and de Cooman's Lower Previsions there's a claim that "It is clear that" the natural extension $\underline{E}_\underline{P}$ of lower prevision $\underline{P}$ dominates (42) it, ...
Mars's user avatar
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2 votes
2 answers
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Lower Expectation

Let $X$ be, for simplicity, a finite set (with the discrete topology). Denote with $M(X)$ the set of probability measures on $X$ endowed with the weak topology. For $\mu\in M(X)$ and a (necessarily ...
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