Apply the Kuo-Mallick model to predictor selection in the nodal involvement data using a uniform prior on \(k\) between the extremes \(k=0.5\) and \(k=4\). So the variance in the normal prior for \(\beta_{j}\) is

\[V_{j}=k(1.18)^{2}, \quad k \sim U(0.5,4)\]
How does this affect the posterior model probabilities for \(\left\{x_{1}, x_{2}, x_{3}\right\}\) and \(\left\{x_{1}, x_{2}, x_{3}, x_{4}\right\}\).