# Direct parametrization of Cholesky decomposition of spatial covariance matrix

In spatial data analysis, a simple way to model the covariance stucture between spatial observations is via a covariance function like $cov(y_i,y_j) = C e^{-rD_{ij}}$, based on some (euclidean) distance matrix $D$. Bayesian parameter estimation via MCMC would require repeatedly inverting the changing covariance matrix, which is computationally impossible for large N.

Is there a kind of standard solution to this problem? Is it possible to directly parametrize the Cholesky decomposition in term of the parameters, to circumvent the matrix inversion?