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Abstract: Fluid identification and anisotropic parameters characterization are crucial for shale reservoir exploration and development. However, the anisotropic reflection coefficient equation, based on the transverse isotropy with a vertical axis of symmetry (VTI) medium assumption, involves numerous parameters to be inverted. This complexity reduces its stability and impacts the accuracy of seismic amplitude variation with offset (AVO) inversion results. In this study, a novel anisotropic equation that includes the fluid term and Thomsen anisotropic parameters is rewritten, which reduces the equation's dimensionality and increases its stability. Additionally, the traditional Markov Chain Monte Carlo (MCMC) inversion algorithm exhibits a high rejection rate for random samples and relies on known parameter distributions such as the Gaussian distribution, limiting the algorithm's convergence and sample randomness. To address these limitations and evaluate the uncertainty of AVO inversion, the IADR-Gibbs algorithm is proposed, which incorporates the Independent Adaptive Delayed Rejection (IADR) algorithm with the Gibbs sampling algorithm. Grounded in Bayesian theory, the new algorithm introduces support points to construct a proposal distribution of non-parametric distribution and reselects the rejected samples according to the Delayed Rejection (DR) strategy. Rejected samples are then added to the support points to update the proposal distribution function adaptively. The equation rewriting method and the IADR-Gibbs algorithm improve the accuracy and robustness of AVO inversion. The effectiveness and applicability of the proposed method are validated through synthetic gather tests and practical data applications.