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Diffstat (limited to 'finale/project_proposal.tex')
| -rw-r--r-- | finale/project_proposal.tex | 16 |
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} |