The irrelevant information principle for collective probabilistic reasoning

Martin Adamčík; George Wilmers

Displaying similar documents to “The irrelevant information principle for collective probabilistic reasoning”

Entropy-like functionals: conceptual background and some results

Miroslav Katětov (1992)

Commentationes Mathematicae Universitatis Carolinae

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We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy $E$ considered in the author’s previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded.

Limits of Bayesian decision related quantities of binomial asset price models

Wolfgang Stummer, Wei Lao (2012)

Kybernetika

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We study Bayesian decision making based on observations $(X_{n, t} : t \in {0, \frac{T}{n}, 2 \frac{T}{n}, ..., n \frac{T}{n}})$ ( $T > 0, n \in ℕ$ ) of the discrete-time price dynamics of a financial asset, when the hypothesis a special $n$ -period binomial model and the alternative is a different $n$ -period binomial model. As the observation gaps tend to zero (i. e. $n \to \infty$ ), we obtain the limits of the corresponding Bayes risk as well as of the related Hellinger integrals and power divergences. Furthermore, we also give an example for the “non-commutativity” between Bayesian statistical...

Universally typical sets for ergodic sources of multidimensional data

Tyll Krüger, Guido F. Montúfar, Ruedi Seiler, Rainer Siegmund-Schultze (2013)

Kybernetika

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We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below...

About stability of risk-seeking optimal stopping

Raúl Montes-de-Oca, Elena Zaitseva (2014)

Kybernetika

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We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space $X$ . It is supposed that the transition probability $p (\cdot | x)$ , $x \in X$ is approximated by the transition probability $\tilde{p} (\cdot | x)$ , $x \in X$ , and that the stopping rule ${\tilde{f}}_{*}$ , which is optimal for the process with the transition probability $\tilde{p}$ is applied to the process with the transition probability $p$ . We give an upper bound (expressed in term of the total variation distance:...

A note on prediction for discrete time series

Gusztáv Morvai, Benjamin Weiss (2012)

Kybernetika

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Let ${X_{n}}$ be a stationary and ergodic time series taking values from a finite or countably infinite set $𝒳$ and that $f (X)$ is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times $λ_{n}$ along which we will be able to estimate the conditional expectation $E (f (X_{λ_{n} + 1}) | X_{0}, \dots, X_{λ_{n}})$ from the observations $(X_{0}, \dots, X_{λ_{n}})$ in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet...