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Detecting Markov random fields hidden in white noise. (English) Zbl 1415.62062
Summary: Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds and propose near-optimal tests.

62M05 Markov processes: estimation; hidden Markov models
62G10 Nonparametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M40 Random fields; image analysis
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