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This article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive (AR) processes in the presence of outliers. The number and locations of the piecewise AR segments, as well as the orders of the respective AR processes, are assumed to be unknown. In addition, each piece may contain an unknown number of innovational and/or additive outliers. The minimum description length (MDL) principle is applied to compare various segmented AR fits to the data. The goal is to find the “best” combination of the number of segments, the lengths of the segments, the orders of the piecewise AR processes, and the number and type of outliers. Such a “best” combination is implicitly defined as the optimizer of an MDL criterion. Since the optimization is carried over a large number of configurations of segments and positions of outliers, a genetic algorithm is used to find optimal or near‐optimal solutions. Numerical results from simulation experiments and real data analyses show that the procedure enjoys excellent empirical properties. 

We present a new method to estimate the boundary of extended sources in high-energy photon lists and to quantify the uncertainty in the boundary. This method extends the graphed seeded region growing method developed by M. Fan et al. Here, we describe how an unambiguous boundary of a centrally concentrated astronomical source may be defined by first spatially segmenting the photon list, then forcibly merging the segments until only two segments—an extended source and its background—remain, and finally constructing a boundary as the connected outer edges of the Voronoi tessellation of the photons included in the source segment. The resulting boundary is then modeled using Fourier descriptors to generate a smooth curve, and this curve is bootstrapped to generate uncertainties. We apply the method to photon event lists obtained during the observations of galaxies NGC 2300 and Arp 299. We demonstrate how the derived extent and enclosed flux of NGC 2300 obtained with Chandra and XMM-Newton are comparable. We also show how complex internal structure, as in the case of Arp 299, may be subsumed to construct a compact boundary of the object. 

In this paper, we propose a new framework to detect adversarial examples motivated by the observations that random components can improve the smoothness of predictors and make it easier to simulate the output distribution of a deep neural network. With these observations, we propose a novel Bayesian adversarial example detector, short for BATER, to improve the performance of adversarial example detection. Specifically, we study the distributional difference of hidden layer output between natural and adversarial examples, and propose to use the randomness of the Bayesian neural network to simulate hidden layer output distribution and leverage the distribution dispersion to detect adversarial examples. The advantage of a Bayesian neural network is that the output is stochastic while a deep neural network without random components does not have such characteristics. Empirical results on several benchmark datasets against popular attacks show that the proposed BATER outperforms the state-of-the-art detectors in adversarial example detection.