Bayesian Estimation of the Precision Matrix with Monotone Missing Data

Abstract. This research paper stands for the estimation of the precision matrix of the normal matrix with monotone missing data. We explicitly provide maximum and expectation a posteriori estimators. For this purpose, we basically use an extension of the Wishart distribution, that is, the Riesz distribution on symmetric matrices. We prove that some of the latter distributions may be presented using Gaussian samples with missing data. An algorithm for generating this distribution is illustrated. Therefore we prove that the inverse Riesz model extends the conjugate property of the inverseWishart one. This allows us to determine the desired Bayesian estimators. Besides, we propose an estimator of the precision matrix based on the notion of the Cholesky decomposition. Finally, we test the performance of the estimators by means of the mean squared error.