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国际不确定性的量化期刊
影响因子: 3.259 5年影响因子: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.2019027745
pages 395-414

WASSERSTEIN METRIC-DRIVEN BAYESIAN INVERSION WITH APPLICATIONS TO SIGNAL PROCESSING

Mohammad Motamed
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico
Daniel Appelo
Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado

ABSTRACT

We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstein metric. Compared to conventional Bayesian models based on Gaussian likelihood functions driven by the least-squares norm (L2 norm), the new framework features several advantages. First, the new framework does not rely on the like-lihood of the measurement noise and hence can treat complicated noise structures such as combined additive and multiplicative noise. Second, unlike the normal likelihood function, the Wasserstein-based exponential likelihood function does not usually generate multiple local extrema. As a result, the new framework features better convergence to correct posteriors when a Markov Chain Monte Carlo sampling algorithm is employed. Third, in the particular case of signal processing problems, although a normal likelihood function measures only the amplitude differences between the observed and simulated signals, the new likelihood function can capture both amplitude and phase differences. We apply the new framework to a class of signal processing problems, that is, the inverse uncertainty quantification of waveforms, and demonstrate its advantages compared to Bayesian models with normal likelihood functions.

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