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Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-t-distributed measurement noise.

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Linear signal estimation based on sample covariance matrices (SCMs) can perform poorly if the training data are limited and the SCMs are ill-conditioned. Diagonal loading (DL) may be used to improve robustness in the face of limited training data. This paper introduces two leave-one-out cross-validation schemes for choosing the DL factor. One scheme repeatedly splits the training data with respect to time, while the other repeatedly splits the out-of-training data with respect to space.

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Abstract

We consider the problem of selecting and ordering a subset of N' out of N observations to be presented to a human being in the context of a binary hypothesis testing problem. We restrict our attention to i.i.d. Gaussian observations. We propose an extension of the approximate subset sum algorithm,and show that it can be used to solve the problem with polynomial complexity. Furthermore, we show that the solution yields near optimal detection performance when compared to the case where all N observations are optimally processed.

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In many problems of signal processing, an important task is the classification of data. A group of methods that has attracted much interest for this purpose are the nonparametric Bayesian methods, and in particular, those based on the Dirichlet process. A useful metaphor for various generalizations of the Dirichlet process has been the Chinese restaurant process. Often the task of classification must be carried out in a sequential manner, and to that end the concepts from Bayesian non-parametrics cannot be applied straightforwardly.

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We propose sequential Monte Carlo (SMC) methods for state-space models. The latent processes represent correlated mixtures of fractional Gaussian processes embedded in white Gaussian noises and the observed data are nonlinear functions of the latent states.

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