adding questions to objective

1 files changed, 15 insertions, 1 deletions

diff --git a/finale/project_proposal.tex b/finale/project_proposal.tex
index c92bb36..912b281 100644
--- a/finale/project_proposal.tex
+++ b/finale/project_proposal.tex
@@ -1,4 +1,4 @@
-\documentclass[10pt]{article}
+\documentclass[8pt]{article}
 \usepackage{fullpage, amsmath, amssymb, amsthm}
 
 \title{Regression Analysis with Network data}
@@ -64,4 +64,18 @@ $$
 
 \subsection*{Objectives}
 
+\begin{itemize}
+\item Try a Bayesian approach to estimate these parameters. Use the posterior
+predictive distribution to obtain confidence intervals for the edge parameters.
+Validate this with bootstrapping. How does this perform in different networks?
+Can you intuitively link certain node-level/graph-level properties with the
+resulting variance on the estimated parameter?
+\item Do the previous observations correspond with the theoretical result, given
+by the Fisher information matrix: $$\hat \beta \sim \mathcal{N}(\beta,
+I{(\theta)}^{-1})$$ where $I(\theta) = - \left(\frac{\partial^2\log
+\mathcal{L}}{\partial \theta^2} \right)^{-1}$
+\item Are there networks in which the Fisher information matrix is singular?
+What happens to the estimation of $\beta$ in this case?
+\end{itemize}
+
 \end{document}