A Bayesian approach is proposed to estimate unknown parameters in stochastic dynamic equations (SDEs). The Fokker–Planck equation from statistical physics method is adopted to calculate the quasi-stationary probability density function. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings (MH) algorithm is proposed to obtain Bayesian estimates of unknown parameters in SDEs. Three simulation studies of SDEs are conducted to investigate the performance of the proposed methodologies. Empirical results evidence that the proposed method performs well in the sense that Bayesian estimates of unknown parameters are quite close to their corresponding true values and their corresponding standard divinations are quite small, and the computational accuracy of normalization parameters strongly affects the accuracy of the proposed Bayesian estimates.

中文翻译：

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通过 Fokker-Planck 方程对随机动力学方程进行贝叶斯估计

提出了一种贝叶斯方法来估计随机动态方程 (SDE) 中的未知参数。采用统计物理方法中的 Fokker-Planck 方程计算准平稳概率密度函数。提出了一种结合 Gibbs 采样器和 Metropolis-Hastings (MH) 算法的混合算法来获得 SDE 中未知参数的贝叶斯估计。对 SDE 进行了三项模拟研究，以研究所提出方法的性能。经验结果表明，所提出的方法在未知参数的贝叶斯估计非常接近其相应的真实值并且其相应的标准占卜非常小的意义上表现良好，