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Asymptotic behaviour of a BIPF algorithm with an improper target

Claudio Asci, Mauro Piccioni (2009)

Kybernetika

The BIPF algorithm is a Markovian algorithm with the purpose of simulating certain probability distributions supported by contingency tables belonging to hierarchical log-linear models. The updating steps of the algorithm depend only on the required expected marginal tables over the maximal terms of the hierarchical model. Usually these tables are marginals of a positive joint table, in which case it is well known that the algorithm is a blocking Gibbs Sampler. But the algorithm makes sense even...

Asymptotic equipartition properties for simple hierarchical and networked structures

Kwabena Doku-Amponsah (2012)

ESAIM: Probability and Statistics

We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...

Asymptotic equipartition properties for simple hierarchical and networked structures

Kwabena Doku-Amponsah (2012)

ESAIM: Probability and Statistics

We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...

Asymptotic Feynman–Kac formulae for large symmetrised systems of random walks

Stefan Adams, Tony Dorlas (2008)

Annales de l'I.H.P. Probabilités et statistiques

We study large deviations principles for N random processes on the lattice ℤd with finite time horizon [0, β] under a symmetrised measure where all initial and terminal points are uniformly averaged over random permutations. That is, given a permutation σ of N elements and a vector (x1, …, xN) of N initial points we let the random processes terminate in the points (xσ(1), …, xσ(N)) and then sum over all possible permutations and initial points, weighted with an initial distribution. We prove level-two...

Asymptotic properties of harmonic measures on homogeneous trees

Konrad Kolesko (2010)

Colloquium Mathematicae

Let Aff(𝕋) be the group of isometries of a homogeneous tree 𝕋 fixing an end of its boundary. Given a probability measure on Aff(𝕋) we consider an associated random process on the tree. It is known that under suitable hypothesis this random process converges to the boundary of the tree defining a harmonic measure there. In this paper we study the asymptotic behaviour of this measure.

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