deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 5021c6d..abe22be 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\item Sample $50$ cases and $50$ controls from all $1500$ individuals.  \item 2630 out of 4000 SNVs were polymorphic.  \item 8 out of 13 risk SNVs were polymorphic.  \end{itemize}  \end{enumerate}  \item Several popular methods 
...
\item Suitable for effects in one direction.   \item \citeNP{Price_2010} found the VT approach had high power to detect the association between rare variants and disease trait in their simulations.  \end{itemize}  \item We used VTWOD function in RVtests R package.  \item C-alpha \cite{Neale_2011}: Test the variance of the effect size for variants in a specific genomic window (No effect, increase or decrease risk).  \begin{itemize}  \item Sensitive to risk and protective variants in the same gene. 
...
\begin{itemize}  \item CAVIARBF \cite{Chen_2015} Fine mapping method using marginal test statistics for the SNVs and their pairwise association. Approximates the Bayesian multivariate regression implemented in BIMBAM \cite{Servin_2007}. CAN YOU DESCRIBE HOW BIMBAM MODELS ALL POSSIBLE COMBINATIONS OF 1,2,3 etc. SNVS AND THEIR INTERACTION TERMS? THEN SAY THAT, TO KEEP THE COMPUTATIONAL LOAD DOWN, WE CONSIDERED ALL POSSIBLE COMBINATIONS OF SNVS UP TO PAIRS ONLY.  \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 models for large $p$, this approach has a limitation on the number of causal variants in the model. So, this limitation reduces the number of models to evaluate in the model space, to $ \sum_{i=0}^{l} \sum_{i=0}^{L}  \dbinom{p}{i} $, where $l$ $L$  is the number of causal SNVs in the model. Since there are 2630 SNVs in our data, to keep the computational load down, we considered $l=2$. $L=2$.    \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.