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作者：Iyer, Srikanth K.; Thacker, Debleena
作者单位：Indian Institute of Science (IISC) - Bangalore; Indian Statistical Institute; Indian Statistical Institute Delhi
摘要：We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function n f(center dot), where n is an element of N, and f is a probability density function on R-d. A vertex located at x connects via directed edges to other vertices that are within a cut-off distance r(n)(x). We prove strong law results for (i) the critical cut-off function so that almost surely, the graph does not contain any node wi...
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作者：Burnashev, Marat V.; Tchamkerten, Aslan
作者单位：Russian Academy of Sciences; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time tau(l) of a given level l with a stopping time eta defined over the noisy observation process. Main results are upper and lower bounds on the minimum mean absolute deviation in f(eta) E vertical bar eta - tau(l)vertical bar which become tight as l -> infinity. Interestingly, in this regime the estimation error does not get smaller if we a...
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作者：Neal, Peter; Roberts, Gareth; Yuen, Wai Kong
作者单位：University of Manchester; University of Warwick; Brock University
摘要：We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous target densities. The main result is a weak convergence result as the dimensionality d of the target densities converges to infinity. In particular, when the proposal variance is scaled by d(-2), the sequence of stochastic processes formed by the first compone...
