Charith Bhagya Karunarathna edited subsection_Several_popular_methods_begin__.tex  over 7 years ago

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\begin{itemize}  \item CAVIARBF \cite{Chen_2015} is a fine-mapping method that uses marginal test statistics for the SNVs and their pairwise association to approximate the Bayesian multivariate regression of phenotypes onto variants that is implemented in BIMBAM \cite{Servin_2007}. However, CAVIARBF is much faster than BIMBAM because it computes Bayes factors using only the SNVs in each causal model. These Bayes factors can be used to calculate the posterior probability of SNVs being causal in the region (the posterior inclusion probability).  \begin{itemize}  \item To compute the probability of SNVs being causal, set of models and their Bayes factors have to be considered. Let $p$ be the total number of SNVs in a candidate region, then the all possible number of causal models is $2^p$. Since it is difficult to compute all To reduce the number of causal  models for large $p$, this approach has to evaluate and save computational time and effort, CAVIARBF imposes  a limitation limit, $L$,  on the number of causal variants in the model. variants.  So, this limitation reduces the number of models to evaluate in the model space, to $ \sum_{i=0}^{L} \dbinom{p}{i} $, where $L$ is the number of causal SNVs in the model. Since there are 2747 SNVs in our data, to keep the computational load down, we considered $L=2$.   \end{itemize}  \item Elastic-net \cite{Zou_2005}: A hybrid regularization and variable selection method that linearly combines the L1 and L2 regularization penalties of the Lasso \cite{Tibshirani_2011} and Ridge \cite{Cessie_1992} methods in multivariate regression. WE CONSIDER ONLY MAIN EFFECTS FOR SNVs IN OUR ELASTIC NET MODELS.