The probability integral transform (PIT) converts the stochastic simulator into a deterministic map of distribution-free latent variables and epistemic parameters, and Transitional Markov Chain Monte Carlo (TMCMC) is then employed for posterior inference and model evidence estimation.
Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses remains a major challenge in global sensitivity analysis (GSA). Existing Hilbert--Schmidt Independence Criterion (HSIC)-based approaches are primarily restricted to single-output settings and lack a rigorous de...
Accurately and efficiently estimating the variance of the Maximum Mean Discrepancy (MMD) remains challenging, particularly for unbalanced sample sizes. In this paper, we derive a finite-sample unbiased estimator of the MMD variance. To overcome the traditional $\mathcal{O}(N^2)$ computational bottleneck, we develop a r...
Shi-Jie Zhong, Yikun Yang, Da Gong et al.· 0 citations
In hybrid uncertainty quantification, evaluating how aleatory sensitivities vary under epistemic uncertainty, referred to as conditional Sobol'indices, is typically hindered by the computationally expensive double-loop procedure. Classical Polynomial Chaos Expansion (PCE) provides efficient access to global sensitivity...
We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts. Unlike the squared Maximum Mean Discrepancy (MMD), which discards directional information by squaring the RKHS distance, DKMD integrates the differ...
Shijie Zhong, Jiangfeng Fu· 0 citations
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