conclusion.tex

\section{Conclusion}
\frame{\tableofcontents[currentsection]}

\begin{frame}{Further Results of CSE}
\begin{itemize}
    \item Can study \textbf{power, False Discovery Rate (FDR)}, and \textbf{bias of bounded estimators}.
    \item Theory also holds for \textbf{Generalized Linear Models (GLMs)} after conditioning on covariates.
    \begin{itemize}
        \item E.g. logistic regression.
    \end{itemize}
    \item \textbf{Quasi-convexity} results for the Tilt-Bound/Inverted Tilt-Bound simplify computations to checking vertices.
    \item See pre-print for details.
\end{itemize} 
\end{frame}

\begin{frame}{Computational Tricks}
    \begin{itemize}

    \item Adaptive simulation/grid sizing (dramatic overall cost reduction!).

    \item Correlated simulations (dramatic sampling reduction!). 
    \begin{itemize}
        \item \textbf{BoTorch} uses a similar (more advanced) trick.
        \item Thanks to \textbf{Prof. Art Owen} for the idea!
    \end{itemize}
    
    \item How to perform \textbf{1 trillion simulations} of a complex Bayesian design? 
    \begin{itemize}
        \item \textbf{Integrated Nested Laplace Approximation (INLA)}.
        \item Our INLA code is \textbf{1 million times faster} than standard MCMC packages.
        \item Similar accuracy in most cases.
    \end{itemize}

    \end{itemize}
\end{frame}

\begin{frame}{Remarks}
\begin{itemize}
    \item Proof-by-simulation is \textbf{general, powerful, and robust}.
    \item Continuous Simulation Extension converts
        simulations at finite points
        into guarantees over \textbf{regions}.

    \item Practical advantage: CSE analyzes the design 
        \textbf{as represented in code}. Robust to:
        \begin{itemize}
            \item Approximations.
            \item Theoretical uncertainties with convergence of algorithms
        \end{itemize}
    \item With the right software, method is \textbf{tractable}!
\end{itemize} 
\end{frame}

\begin{frame}{End Goals}
%\begin{itemize}
%    \item We hope these tools can streamline innovation in trial design
%    \item Objective proofs should help improve regulatory consistency
%    \item Reducing the time and human capital cost of validating new procedures is good for everyone
%    \item Speculatively: this might pave the way to use ``black-box" statistical procedures. Our guarantees would apply, as long as the model class assumption is trusted.
%\end{itemize}
\begin{itemize}
    \item Streamline innovation in trial design.
    \item Improve regulatory consistency with objective proofs.
    \item Reduce time and human capital cost of validating new procedures.
    \item Speculatively: enable new ``black-box" statistical procedures.
\end{itemize}
\end{frame}