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index.Rmd
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---
title: "About LIEB"
site: workflowr::wflow_site
output:
workflowr::wflow_html:
toc: false
editor_options:
chunk_output_type: console
---
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](pairwise_fitting.html) of the Gaussian mixture over pairs of dimensions
2. [Enumerating candidate latent classes](candidate_latent_classes.html) based on the output of the pairwise fits
3. [Pruning the candidate list of latent classes](priors.html) based on computed prior probabilities of each class's mixing weight
4. [Fitting the final model](running_mcmc.html) 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. Navigate to any step's page to learn more.