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Identification of dynamical systems from low-resolution quantized observations presents several challenges because of the limited amount of information available in the data and since proper algorithms have to be designed to handle the error due to quantization. In this article, we consider identification of infinite impulse response models from quantized outputs. Algorithms both for maximum-likelihood estimation and Bayesian inference are developed. Finally, a particle-filter approach is presented for recursive reconstruction of the latent nonquantized outputs from past quantized observations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of identification for a class of nonlinear systems with Hammerstein structure, which is a combination of some basis functions for the static nonlinearity and finite impulse response models for the linear block under quantized output data. Following the empirical Bayes method, we model the impulse response of the system using a Gaussian process whose covariance matrix depends on some suitable kernels. Then, we compute the minimum mean-square error estimation of the impulse response via a special case of Markov Chain Monte Carlo sampling approach, namely, Gibbs sampler. The estimation of the impulse response depends on the kernel hyperparameters, the noise variance and the coefficients of the static nonlinearity. These unknowns are estimated by the marginal likelihood maximization, which is solved via the expectation-conditional maximization algorithm combining the Gibbs sampler. The expectation-conditional maximization method is a variation of the standard expectation-maximization method for solving maximum-likelihood problems. Numerical simulations show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the detection of Least Significant Bits (LSB) steganography in digital media by using hypothesis testing theory. The main goal is threefold: first, it is aimed to design a test whose statistical properties are known, this especially allows the guaranteeing of a false alarm probability. Second, the quantization of samples is studied throughout this paper. Lastly, the use of a linear parametric model of samples is used to estimate unknown parameters and design a test which can be used when no information on cover medium is available. To this end, the steganalysis problem is cast within the framework of hypothesis testing theory and digital media are considered as quantized signals. In a theoretical context where media parameters are assumed to be known, the Likelihood Ratio Test (LRT) is presented. Its statistical performances are analytically established; this highlights the impact of quantization on the most powerful steganalyzer. In a practical situation, when image parameters are unknown, a Generalized LRT (GLRT) is proposed based on a local linear parametric model of samples. The use of such model allows us to establish GLRT statistical properties in order to guarantee a prescribed false-alarm probability. Focusing on digital images, it is shown that the well-known WS (Weighted-Stego) is close to the proposed GLRT using a specific model of cover image. Finally, numerical results on natural images show the relevance of theoretical findings. [Copyright &y& Elsevier]

Abstract: Ordinal categorical time series may be analyzed as censored observations from a suitable latent stochastic process, which describes the underlying evolution of the system. This approach may be considered as an alternative to Markov chain models or to regression methods for categorical time series data. The problem of parameter estimation is solved through a simple pseudolikelihood, called pairwise likelihood. This inferential methodology is successfully applied to the class of autoregressive ordered probit models. Potential usefulness for inference and model selection within more general classes of models are also emphasized. Illustrations include simulation studies and two simple real data applications. [Copyright &y& Elsevier]