2018/07/21 by Mohammad Motamed, Motamed, Mohammad, Daniel Appelö +1 · 1 citation
Computer Science · Mathematics · #35L53 #60J22 #62F15 #62P30 #65M32 #86A15 #Advanced Statistical Methods and Models #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1807.09682
openalex publication_date 2018/07/21 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
We present a Bayesian framework based on a new exponential likelihood\nfunction driven by the quadratic Wasserstien metric. Compared to conventional\nBayesian models based on Gaussian likelihood functions driven by the\nleast-squares norm (L2 norm), the new framework features several advantages.\nFirst, the new framework does not rely on the likelihood of the measurement\nnoise and hence can treat complicated noise structures such as combined\nadditive and multiplicative noise. Secondly, unlike the normal likelihood\nfunction, the Wasserstein-based exponential likelihood function does not\nusually generate multiple local extrema. As a result, the new framework\nfeatures better convergence to correct posteriors when a Markov Chain Monte\nCarlo sampling algorithm is employed. Thirdly, in the particular case of signal\nprocessing problems, while a normal likelihood function measures only the\namplitude differences between the observed and simulated signals, the new\nlikelihood function can capture both the amplitude and the phase differences.\nWe apply the new framework to a class of signal processing problems, that is,\nthe inverse uncertainty quantification of waveforms, and demonstrate its\nadvantages compared to Bayesian models with normal likelihood functions.\n