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Smoothness of Metropolis-Hastings algorithm and application to entropy estimation

Didier Chauveau, Pierre Vandekerkhove (2013)

ESAIM: Probability and Statistics

The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent...

Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

Aimé Lachal (2012)

ESAIM: Probability and Statistics

Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci. USA 35 (1949) 605–608], simpler representations may be obtained...

Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

Aimé Lachal (2012)

ESAIM: Probability and Statistics

Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci....

Stochastic algorithm for Bayesian mixture effect template estimation

Stéphanie Allassonnière, Estelle Kuhn (2010)

ESAIM: Probability and Statistics

The estimation of probabilistic deformable template models in computer vision or of probabilistic atlases in Computational Anatomy are core issues in both fields. A first coherent statistical framework where the geometrical variability is modelled as a hidden random variable has been given by [S. Allassonnière et al., J. Roy. Stat. Soc.69 (2007) 3–29]. They introduce a Bayesian approach and mixture of them to estimate deformable template models. A consistent stochastic algorithm has been introduced...

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