Bayesian inference in the framework of uncertainty theory

Anshui Li1, Waichon Lio2
1School of Mathematics, Physics and Information, Shaoxing University, Shaoxing, 312000, China
2School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China

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Tài liệu tham khảo

Berger JO (2013) Statistical decision theory and Bayesian analysis. Springer, New York

Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. Chapman & Hall, Toronto

Jin T, Yang X, Xia H, Ding H (2021) Reliability index and option pricing formulas of the first-hitting time model based on the uncertain fractional-order differential equation with caputo type. Fractals 29(01):2150012

Li A, Xia Y (2024) Parameter estimation of uncertain differential equations with estimating functions. Soft Comput 28(1):77–86

Lio W, Kang R (2023) Bayesian rule in the framework of uncertainty theory. Fuzzy Opt Decision Making 22(3):337–358

Lio W, Liu B (2018) Residual and confidence interval for uncertain regression model with imprecise observations. J Intell Fuzzy Syst 35(2):2573–2583

Lio W, Liu B (2020) Uncertain maximum likelihood estimation with application to uncertain regression analysis. Soft Comput 24(13):9351–9360

Liu B (2007) Uncertainty theory. Springer, Berlin

Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

Liu Y, Liu B (2022) Residual analysis and parameter estimation of uncertain differential equations. Fuzzy Opt Decision Making 21(4):513–530

Meng X, Yang L, Mao Z, del Águila Ferrandis J, Karniadakis GE (2022) Learning functional priors and posteriors from data and physics. J Comput Phys 457:111073

Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press, Massachusetts

Tian C, Jin T, Yang X, Liu Q (2022) Reliability analysis of the uncertain heat conduction model. Comput Math Appl 119:131–140

Tran BH, Rossi S, Milios D, Filippone M (2022) All you need is a good functional prior for Bayesian deep learning. J Mach Learn Res 23(74):1–56

Yang X, Liu B (2019) Uncertain time series analysis with imprecise observations. Fuzzy Opt Decision Making 18(3):263–278

Yao K, Liu B (2018) Uncertain regression analysis: an approach for imprecise observations. Soft Comput 22(17):5579–5582

Ye T, Liu B (2022) Uncertain hypothesis test with application to uncertain regression analysis. Fuzzy Opt Decision Making 21(2):157–174

Ye T, Liu B (2023) Uncertain hypothesis test for uncertain differential equations. Fuzzy Opt Decision Making 22(2):195–211

Ye T, Liu B (2023) Uncertain significance test for regression coefficients with application to regional economic analysis. Commun Stat-Theory Methods 52(20):7271–7288

Zhou H, Ibrahim C, Zheng WX, Pan W (2022) Sparse bayesian deep learning for dynamic system identification. Automatica 144:110489