  A novel adaptive Markov chain Monte Carlo algorithm is presented. The
algorithm utilizes sparsity in the partial correlation structure of a density
to efficiently estimate the covariance matrix through the Cholesky factor of
the precision matrix. The algorithm also utilizes the sparsity to sample
efficiently from both MALA and Metropolis Hasting random walk proposals.
Further, an algorithm that estimates the partial correlation structure of a
density is proposed. Combining this with the Cholesky factor estimation
algorithm results in an efficient black-box AMCMC method that can be used for
general densities with unknown dependency structure. The method is compared
with regular empirical covariance adaption for two examples. In both examples,
the proposed method's covariance estimates converge faster to the true
covariance matrix and the computational cost for each iteration is lower.
