A Bayesian Framework for Multivariate Multifractal Analysis

Multifractal analysis has become a reference tool for signal and image processing. Grounded in the quantification of local regularity fluctuations, it proven useful an increasing range applications, yet so far involving only univariate data (scalar valued time series or single channel images). Recently theoretical ground multivariate multifractal been devised, showing potential quantifying transient higher-order dependence beyond linear correlation among collections data. However, accurate estimation parameters associated with model remains challenging, especially small sample size This work studies original Bayesian framework estimation, combining novel generic statistical model, Whittle-based likelihood approximation augmentation strategy allowing parameter separability. careful design enables efficient procedures to be constructed two relevant choices priors using Gibbs sampling strategy. Monte Carlo simulations, conducted on synthetic signals images various sizes settings, demonstrate significant performance improvements over state art, at moderately larger computational cost. Moreover, we show relevance proposed real-world modeling important application drowsiness detection from multichannel physiological signals.