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The Commission formed a Sub-Commission on Zodiacal Light, presided over by Prof. Issei Yamamoto. The constitution of a sub-commission on the light of the night sky and kindred phenomena was proposed, but left in abeyance, pending the Stockholm Meeting. Dr Jean Dufay kindly consented to write, at the president’s request, a paper on the present state of the problem of the light of the night sky, which is printed with this Report.
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 nonparametric estimate of the entropy for these iterative densities. This theoretical study can be viewed as a building block for a more general MCMC evaluation tool grounded on such estimates.
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