Last updated: 2019-07-17

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The Limited Information Empirical Bayes (LIEB) methodology was designed for Gaussian mixture models where the behavior of each component in the mixture is dictated by a latent class \(h_m\) which has the form \(h_m=(h_{[1]},\,h_{[2]},\ldots,h_{[D]})\) where \(h_{[d]} \in\{-1,\,0,\,1\}\) for \(d\in\{1,\ldots,D\}\), where \(D\) is the dimension of the data. For even moderate dimensions, this model becomes computationally intractible to fit directly because the number of candidate latent classes is \(3^D\). The LIEB procedure rigorously circumvents this computational challenge, providing the user with the likely latent classes and fitting the model in an empirical Bayesian hierarchical framework with Markov Chain Monte Carlo (MCMC).

LIEB occurs in 4 major steps:

  1. Pairwise fitting of the Gaussian mixture over pairs of dimensions
  2. Enumerating candidate latent classes based on the output of the pairwise fits
  3. Pruning the candidate list of latent classes based on computed prior probabilities of each class’s mixing weight
  4. Fitting the final model using MCMC

This analysis can be tricky, because some parts (e.g., Steps 1 and 3) require low memory but can be parallelized. Meanwhile, Steps 2 and 4 cannot be parallelized, and Step 2 in particular can require high memory. To be efficient when running an analysis with LIEB, we recommend splitting the steps up accordingly.

Each step of LIEB has its own page. We walk through a complete analysis of a simulated dataset throughout these 4 pages. Though the simple analysis provided here can be run on your personal laptop, in practice with real genomic datasets, one will need access to a computing cluster. We assume the user knows how to request multiple cores for parallel jobs or more memory for high-memory tasks. Navigate to any step’s page to learn more.