



\begin{figure}[t!] %
    \begin{center}
    \includegraphics[width=0.5\textwidth]{figures/example.png}
    \end{center}
    \vspace{-.15in}
    \caption{Posteriors of Different Robust Models Fitted with Corrupted Data}	
    \label{fig:example}
    \vspace{-.21in}
\end{figure}


\noindent\textbf{Example: How Good are the Robust Models?}
Figure~\ref{fig:example} presents the posteriors fitted on a corrupted dataset
when applying different \robts on the original model.
The
model $y \sim \mathcal{N}(\beta, 1)$  fits the parameter $\beta$ as the mean of
data $y$. In the dataset, 80\% data points are good (non-noisy) observations
centered at 0, while 20\% are outliers centered at -10, far from the good
observations. We present the posterior distributions of $\beta$ obtained from
original and robust models as different lines on the plot.



We observe that all
robust models are not equally useful: while some (e.g., Reweighting) yield
posteriors that are close to ideal in presence of outliers, some others (e.g.,
Localization) are not too different than the original (non-robust) model.
These observations motivate the need for a systematic study of
\robts.






