Batch means and spectral variance estimators in Markov chain Monte Carlo

Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases. In addition, for the batch means and overlapping batch means methods we establish conditions ensuring consistency in the mean-square sense which in turn allows us to calculate the optimal batch size up to a constant of proportionality. Finally, we examine the empirical finite-sample properties of spectral variance and batch means estimators and provide recommendations for practitioners.Comment: Published in at http://dx.doi.org/10.1214/09-AOS735 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A study on the statistical convergence of turbulence simulations around a cylinder

The turbulent flow around a circular cylinder at a Reynolds number equal to 3900 is studied by an implicit Large Eddy Simulation performed by means of a discontinuous Galerkin finite element solver. The average velocity field in the wake is evaluated and compared with experimental data from the literature. The focus of the present work is on the estimation of the statistical uncertainty which is related to the use of a finite time window for the averaging operation. This topic represents an open problem for both Direct Numerical Simulations and Large Eddy Simulations in which it is difficult to define a priori the size of the time window which gives statistically converged averaged quantities. Different techniques to estimate this uncertainty are compared in order to get a quantitative criterion for checking the convergence of statistics. In particular, the Non-Overlapping Batch Means and the Batch Means Batch Correlations techniques are applied to the present test case

Estimating population means in covariance stationary process

In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags.Jackknife estimation; ARMA; Longitudinal data; Actual confidence level

Weakly- and Semi-Supervised Panoptic Segmentation

We present a weakly supervised model that jointly performs both semantic- and instance-segmentation -- a particularly relevant problem given the substantial cost of obtaining pixel-perfect annotation for these tasks. In contrast to many popular instance segmentation approaches based on object detectors, our method does not predict any overlapping instances. Moreover, we are able to segment both "thing" and "stuff" classes, and thus explain all the pixels in the image. "Thing" classes are weakly-supervised with bounding boxes, and "stuff" with image-level tags. We obtain state-of-the-art results on Pascal VOC, for both full and weak supervision (which achieves about 95% of fully-supervised performance). Furthermore, we present the first weakly-supervised results on Cityscapes for both semantic- and instance-segmentation. Finally, we use our weakly supervised framework to analyse the relationship between annotation quality and predictive performance, which is of interest to dataset creators.Comment: ECCV 2018. The first two authors contributed equall

On Efficiently Detecting Overlapping Communities over Distributed Dynamic Graphs

Modern networks are of huge sizes as well as high dynamics, which challenges the efficiency of community detection algorithms. In this paper, we study the problem of overlapping community detection on distributed and dynamic graphs. Given a distributed, undirected and unweighted graph, the goal is to detect overlapping communities incrementally as the graph is dynamically changing. We propose an efficient algorithm, called \textit{randomized Speaker-Listener Label Propagation Algorithm} (rSLPA), based on the \textit{Speaker-Listener Label Propagation Algorithm} (SLPA) by relaxing the probability distribution of label propagation. Besides detecting high-quality communities, rSLPA can incrementally update the detected communities after a batch of edge insertion and deletion operations. To the best of our knowledge, rSLPA is the first algorithm that can incrementally capture the same communities as those obtained by applying the detection algorithm from the scratch on the updated graph. Extensive experiments are conducted on both synthetic and real-world datasets, and the results show that our algorithm can achieve high accuracy and efficiency at the same time.Comment: A short version of this paper will be published as ICDE'2018 poste

Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?

Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.Comment: Published in at http://dx.doi.org/10.1214/08-STS257 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org