Fast Computation of Posterior Mode in Multi-Level Hierarchical Models

Part of Advances in Neural Information Processing Systems 21 (NIPS 2008)

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Liang Zhang, Deepak Agarwal


Multi-level hierarchical models provide an attractive framework for incorporating correlations induced in a response variable organized in a hierarchy. Model fitting is challenging, especially for hierarchies with large number of nodes. We provide a novel algorithm based on a multi-scale Kalman filter that is both scalable and easy to implement. For non-Gaussian responses, quadratic approximation to the log-likelihood results in biased estimates. We suggest a bootstrap strategy to correct such biases. Our method is illustrated through simulation studies and analyses of real world data sets in health care and online advertising.