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作者：Frazier, D. T.; Martin, G. M.; Robert, C. P.; Rousseau, J.
作者单位：Monash University; Universite PSL; Universite Paris-Dauphine; University of Oxford
摘要：Approximate Bayesian computation allows for statistical analysis using models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on the rate at which the posterior distribution concentrates on sets containing the true parameter, the limiting shape of the posterior distribution, and the asymptotic distribution of the posterior mean. These results hold under given rates for the tolerance ...
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作者：Shively, T. S.; Walker, S. G.
作者单位：University of Texas System; University of Texas Austin; University of Texas System; University of Texas Austin
摘要：We show that the Bayes factor for testing whether a subset of coefficients are zero in the normal linear regression model gives the uniformly most powerful test amongst the class of invariant tests discussed in Lehmann & Romano (2005) if the prior distributions for the regression coefficients are in a specific class of distributions. The priors in this class can have any elliptical distribution, with a specific scale matrix, for the subset of coefficients that are being tested. We also show un...
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作者：Fokianos, K.; Pitsillou, M.
作者单位：University of Cyprus
摘要：We introduce the matrix multivariate auto-distance covariance and correlation functions for time series, discuss their interpretation and develop consistent estimators for practical implementation. We also develop a test of the independent and identically distributed hypothesis for multivariate time series data and show that it performs better than the multivariate Ljung-Box test. We discuss computational aspects and present a data example to illustrate the method.
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作者：Li, Wentao; Fearnhead, Paul
作者单位：Newcastle University - UK; Lancaster University
摘要：We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont et al. (2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increas...
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作者：Green, Peter J.; Thomas, Alun
作者单位：University of Technology Sydney; Utah System of Higher Education; University of Utah
摘要：We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure. We prove the equivalence of this property to an exponential family assumption, and discuss identifiability, modelling, inferential and computational implications.
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作者：Jung, Sungkyu; Lee, Myung Hee; Ahn, Jeongyoun
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Cornell University; Weill Cornell Medicine; University System of Georgia; University of Georgia
摘要：We consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The proposed estimator is show...
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作者：Li, Wentao; Fearnhead, Paul
作者单位：Newcastle University - UK; Lancaster University
摘要：Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. We present results on the asymptotic variance of estimators obtained using approximate Bayesian computation in a large data limit. Our key assumption is that the data are summarized by a fixed-dimensional summary statistic that obeys a cen...
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作者：Yu, C.; Hoff, P. D.
作者单位：University of Washington; University of Washington Seattle; Duke University
摘要：Commonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average, but their actual coverage rate for a given group will be above or below the nominal rate, depending on the group mean. While correct coverage for a given group can be achieved with a standard t-interval, this approach is not adaptive to the available information about the distribution of group-specific means. In this article we construct confidence intervals that ...
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作者：Picard, Franck; Reynaud-Bouret, Patricia; Roquain, Etienne
作者单位：Centre National de la Recherche Scientifique (CNRS); VetAgro Sup; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We propose a continuous testing framework to test the intensities of Poisson processes that allows a rigorous definition of the complete testing procedure, from an infinite number of hypotheses to joint error rates. Our work extends procedures based on scanning windows by controlling the familywise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way. We introduce the p-value process on which the decision rule is based. Our method is applied in neuroscienc...
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作者：Diaz, I.; Savenkov, O.; Ballman, K.
作者单位：Cornell University; Weill Cornell Medicine
摘要：We consider estimation of an optimal individualized treatment rule when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying the expected time to occurrence of an event of interest. We use semiparametric efficiency theory to construct estimators with properties such as double robustness. We propose two estimators of the optimal rule, which arise from considering two loss functions aimed at directly estimating the conditional treatme...
