In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. We also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack" R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation

在贝叶斯模型校准中，似然函数的评估通常涉及找到协方差矩阵的逆和行列式。当使用马尔可夫链蒙特卡罗（MCMC）方法从后验中进行采样时，可能需要成千上万的可能性评估。在本文中，我们证明可以利用协方差矩阵的结构，从而在实践中节省大量时间。我们还导出了两个简单的方程式，用于在这种情况下近似协方差矩阵的逆，可以在近二次时间内计算出它们。这些策略的实际意义通过一个简单的数值案例研究得到了证明，并且“嘎嘎” [R包裹。对于具有1000行的协方差矩阵，应用这些策略进行一百万次似然评估，与朴素的实现相比，可将速度提高大约4000