-
作者：Monard, Francois; Nickl, Richard; Paternain, Gabriel P.
作者单位：University of California System; University of California Santa Cruz; University of Cambridge
摘要：We consider the statistical inverse problem of recovering a function f : M -> R, where M is a smooth compact Riemannian manifold with boundary, from measurements of general X-ray transforms I-a(f) of f, corrupted by additive Gaussian noise. For M equal to the unit disk with flat geometry and a = 0 this reduces to the standard Radon transform, but our general setting allows for anisotropic media M and can further model local attenuation effects-both highly relevant in practical imaging problems...
-
作者：Enikeeva, Farida; Harchaoui, Zaid
作者单位：Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; University of Washington; University of Washington Seattle
摘要：We consider the problem of detecting a change in mean in a sequence of high-dimensional Gaussian vectors. The change in mean may be occurring simultaneously in an unknown subset components. We propose a hypothesis test to detect the presence of a change-point and establish the detection boundary in different regimes under the assumption that the dimension tends to infinity and the length of the sequence grows with the dimension. A remarkable feature of the proposed test is that it does not req...
-
作者：Truquet, Lionel
作者单位：Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：A primary motivation of this contribution is to define new locally stationary Markov models for categorical or integer-valued data. For this initial purpose, we propose a new general approach for dealing with time-inhomogeneity that extends the local stationarity notion developed in the time series literature. We also introduce a probabilistic framework which is very flexible and allows us to consider a much larger class of Markov chain models on arbitrary state spaces, including most of the l...
-
作者：Deligiannidis, George; Bouchard-Cote, Alexandre; Doucet, Arnaud
作者单位：University of Oxford; University of British Columbia
摘要：Nonreversible Markov chain Monte Carlo schemes based on piecewise deterministic Markov processes have been recently introduced in applied probability, automatic control, physics and statistics. Although these algorithms demonstrate experimentally good performance and are accordingly increasingly used in a wide range of applications, geometric ergodicity results for such schemes have only been established so far under very restrictive assumptions. We give here verifiable conditions on the targe...
-
作者：Drton, Mathias; Fox, Christopher; Kaeufl, Andreas; Pouliot, Guillaume
作者单位：University of Washington; University of Washington Seattle; University of Copenhagen; University of Chicago; University of Augsburg; University of Chicago; Universite de Montreal; Polytechnique Montreal
摘要：Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and bidirected edges that indicate possible correlations among noise terms. Using this graphical representation, we determine the maximum likelihood threshold, that is, the minimum sample size at which the likelihood function of a Gaussian structural equation mod...
-
作者：Petersen, Alexander; Mueller, Hans-Georg
作者单位：University of California System; University of California Santa Barbara; University of California System; University of California Davis
摘要：Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of Frechet regression. This is a general approach to regression when responses are complex random objects in a metric space and predictors are in R-p, achieved by extending the classical concept of a Frechet mean to the notion of a conditional Frechet mean. We devel...
-
作者：Cao, Xuan; Khare, Kshitij; Ghosh, Malay
作者单位：State University System of Florida; University of Florida
摘要：Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying variables. A variety of priors have been developed in recent years...
-
作者：Fan, Zhou; Johnstone, Iain M.
作者单位：Yale University; Stanford University
摘要：We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedu...
-
作者：Gerber, Mathieu; Chopin, Nicolas; Whiteley, Nick
作者单位：University of Bristol; Institut Polytechnique de Paris; ENSAE Paris
摘要：We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost sure weak convergence of measures output from Kitagawa's [J. Comput. Graph. Statist. 5 (1996) 1-25] stratified resampling method. Carpenter, Ckiffird and Fearnhead's [IEE Proc. Radar Sonar Navig. 146 (1999) 2-7] systematic resampling method is similar in structure but can fail to converge ...
-
作者：Lauritzen, Steffen; Uhler, Caroline; Zwiernik, Piotr
作者单位：University of Copenhagen; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Pompeu Fabra University
摘要：We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof that the maximum likelihood estimator (MLE) for such distributions exists based on n >= 2 observations, irrespective of the underlying dimension. Slawski and Hein [Linear Algebra Appl. 473 (2015) 145-179], who first proved this result, also provided empirica...
