\chapter{Conclusion}
\label{ch:conc}


 
In this paper, the main focus was on using the RJMCMC for model selection in solving for the regression coefficients in a  standard linear model, however, the selection of predictors is not known. We were given a large number of predictors and were required to select an appropriate subset to obtain the optimal model.  In this problem, we focused on the first $n$ predictors, a subset, of a total number of predictors, $m$.

It was found that by using RJMCMC algorithm to perform the required selection implicitly by simulating from the posterior distribution of $\mathbf{b}_n$, under the density, $f(\mathbf{b}_n|\mathbf{y})$.  Although the computations times were relatively high in comparison to other programs/homeworks, the method was able to calculate the coefficients for the model
\begin{equation}
y = \sum^n_{i=1}x_i b_i + \epsilon
\end{equation}
