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[R-gregmisc-users] SF.net SVN: r-gregmisc: [1243] trunk/PathwayModeling/thesispaper
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From: <wa...@us...> - 2008-02-07 17:10:33
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Revision: 1243
http://r-gregmisc.svn.sourceforge.net/r-gregmisc/?rev=1243&view=rev
Author: warnes
Date: 2008-02-07 09:10:27 -0800 (Thu, 07 Feb 2008)
Log Message:
-----------
Slides for Myriad visit
Modified Paths:
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trunk/PathwayModeling/thesispaper/slides.tex
Added Paths:
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trunk/PathwayModeling/thesispaper/figures/MSR16.pdf
Added: trunk/PathwayModeling/thesispaper/figures/MSR16.pdf
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Property changes on: trunk/PathwayModeling/thesispaper/figures/MSR16.pdf
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Modified: trunk/PathwayModeling/thesispaper/slides.tex
===================================================================
--- trunk/PathwayModeling/thesispaper/slides.tex 2008-02-05 21:38:08 UTC (rev 1242)
+++ trunk/PathwayModeling/thesispaper/slides.tex 2008-02-07 17:10:27 UTC (rev 1243)
@@ -3,10 +3,7 @@
\mode<presentation>
{
\usetheme{Warsaw}
- % or ...
-
\setbeamercovered{transparent}
- % or whatever (possibly just delete it)
}
%\setbeameroption{show notes}
@@ -20,7 +17,6 @@
% \documentclass[doublespacing]{elsart}
\usepackage{graphicx}
\usepackage[nogin]{Sweave}
-\usepackage[numbers]{natbib} \bibliographystyle{plainnat}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{yfonts}
@@ -32,18 +28,20 @@
\usepackage{makeidx}
\usepackage{dchem}
\usepackage{color}
+\usepackage[numbers]{natbib}
+\bibliographystyle{plainnat}
\newcommand{\deriv}[2]{\ensuremath{\frac{\mathrm{d} #1}{\mathrm{d} #2}}}
\title{Statistical Modeling of Biochemical Pathways}
-\author{Robert B. Burrows\inst{1} \and Gregory R. Warnes\inst{2,3} }
+\author{Gregory R. Warnes\inst{1,2,3} }
\institute{
\inst{1}%
- New England Biometrics\\
- North Scituate, RI
+ Biostatistics and Computational Biology \\
+ University of Rochester
\and
\inst{2}%
- Biostatistics and Computational Biology \\
+ Center for Biodefense Immune Modeling \\
University of Rochester
\and
\inst{3}%
@@ -56,37 +54,56 @@
$ $Id$ $
}
-%\begin{abstract}
-%The usefulness of Markov chain Monte Carlo methods for the modeling
-%of biochemical reactions is examined. With simulated data, it is
-%shown that mechanistic models can be fit to sequences of enzymatic
-%reactions. These methods have the advantages of being relatively easy
-%to use and producing probability distributions for the model
-%parameters rather than point estimates.
-%Three Markov chain Monte Carlo algorithms are used to fit models to
-%data from a
-%sequence of 4 enzymatic reactions. The algorithms
-%are evaluated with respect to
-%the goodness-of-fit of the fitted models and the time to completion.
-%It is shown that the algorithms produce essentially the same
-%parameter distributions but the time to completion varies.
-%\end{abstract}
-
\frame{
\maketitle
}
+%%\section[Abstract]{}
+%%\begin{abstract}
+%\frame{
+% \frametitle{Abstract}
+% \small
+% We examine the usefulness of Bayesian statistical methods for
+% the modeling of biochemical reactions. With simulated data, it is
+% shown that these methods can effectively fit mechanistic models of
+% sequences of enzymatic reactions to experimental data. This
+% approach has the advantages of being flexible, relatively easy to use,
+% and producing full probability distributions for the model parameters
+% rather than point estimates, thus allowing more informative inferences
+% (including relationships between parameters) to be drawn. Further,
+% these methods perform well even when the mechanistic model leads
+% to multiple solution regions, high parameter correlations, and other
+% 'unfriendly' behavior.
+
+% The presentation will include a brief overview of Bayesian statistical
+% methods for those unfamiliar with these techniques, as well as a brief
+% discussion of the computational methods utilized.
+%}
+%%\end{abstract}
+
\section[Outline]{}
\frame{
\frametitle{Outline}
- \tableofcontents
+
+% \tableofcontents
+
+ \begin{columns}
+ \begin{column}{0.5\textwidth}
+ \tableofcontents[sections={1-4}]
+ \end{column}
+ \begin{column}{0.5\textwidth}
+ \tableofcontents[sections={5-8}]
+ \end{column}
+ \end{columns}
+
}
\section{Overview}
+\subsection{Goal}
\frame{
\frametitle{Overview}
- \begin{block}{Goal:}
+ \begin{block}{Goal: Model Biochemical Pathways}
Estimate key rate parameters of biological pathways, e.g
\includegraphics[width=0.75\textwidth]{figures/glycolysis}
@@ -95,16 +112,87 @@
changes, and understand the system.
\end{block}
}
+
+\subsection{Components}
\frame{
\frametitle{Overview}
- \begin{block}{Method:}
- ``Wrap'' standard deterministic mathematical model
- within a Bayesian statistical model
+ \begin{block}{Combine 3 components:}
+ \begin{tabular}{ll}
+ Biochemistry & Biochemical components \& relationships \\
+ Mathematical Model & Strucure of relationships between components \\
+ Bayesian Statistics & Relationship between previous information, \\
+ & model and measured data \\
+ \end{tabular}
+
+% \begin{block}{Method:}
+% \begin{center}
+% ``Wrap'' standard deterministic mathematical model describing a
+% biochemical pathway within a Bayesian statistical model
+% \end{center}
\end{block}
+
}
+\subsection{Intro to Bayesian Statistics}
+\frame{
+ \frametitle{Intro to Bayesian Statistics (1/2)}
+ \begin{enumerate}
+ \item Based on Decision Theory
+ \item Modeling Process:
+ \begin{enumerate}
+ \item Costruct a model for observed data: {\color{blue} ``Likelihood'':
+ $L(\mathit{Data}|\theta)$ }
+ \item Describe current information about model parameters:
+ { \color{green} ``Prior distribution'' $\pi(\theta)$ }
+ \item Run experiment \& collect data
+ \item Apply Bayes Rule $\to$ {\color{red}``Posterior distribution''}
+
+\begin{equation}\label{BayesRule}
+{\color{red}\pi(\theta|\mathit{Data})} = \frac{{\color{blue}L(\mathit{Data}|\theta)} {\color{green}\pi(\theta)}}{\int {L(\mathit{Data}|\theta) \pi(\theta)}d\theta}
+\end{equation}
+
+ \item Draw conclusions using Posterior
+ \end{enumerate}
+ \end{enumerate}
+}
+
+\frame{
+ \frametitle{Intro to Bayesian Statistics (2/2)}
+ \begin{itemize}
+ \item Strengths
+ \begin{itemize}
+ \item Very flexible
+ \item Consistent with human thinking
+ \item Allows inclusion of existing domain knowledge
+ \end{itemize}
+ \item Weaknesses
+ \begin{itemize}
+ \item Characterization of ``current information'' can be
+ controversial
+ \item Computationaly expensive
+ \item Less popular than Frequentist statistics
+ \end{itemize}
+ \end{itemize}
+}
+
+
+
\section{Evaluation Approach}
+
\frame{
+ \frametitle{Overview}
+ \begin{block}{Goal: Model Biochemical Pathways}
+ Estimate key rate parameters of biological pathways, e.g
+
+ \includegraphics[width=0.75\textwidth]{figures/glycolysis}
+
+ in order to estimate rate parameters, predict responses to
+ changes, and understand the system.
+ \end{block}
+}
+
+
+\frame{
\frametitle{Evaluation Approach}
\begin{enumerate}
\item{Create artificial model}
@@ -124,7 +212,7 @@
R3 \yields R4 \yields R5 \yields sink \end{reaction}
Chemical Equations:
- \begin{chemarray*} \small
+ \begin{chemarray*}
source &\yields^{k_1}& R1\\
R1 + E1 &\eqbm^{k_2}_{k_3}& R1E1 \yields^{k_4} R2 + E1\\
R2 + E2 &\eqbm^{k_5}_{k_6}& R2E2 \yields^{k_7} R3 + E2\\
@@ -324,7 +412,43 @@
}
\frame{
- \frametitle{Convergence Rates}
+\begin{block}{What is Markov Chain Monte Carlo?}
+
+\textcolor{blue}{Markov Chain Monte Carlo (MCMC)} is a technique for
+generating \textcolor{red}{dependent} samples (a Markov Chain) from a
+distribution without needing the \textcolor{blue}{normalizing constant}.
+
+\end{block}
+\begin{block}{When is MCMC useful?}
+
+\textcolor{blue}{MCMC} is useful when it is \textcolor{red}{difficult} to
+\textcolor{blue}{simulate} from the target distribution, such as when the
+\textcolor{blue}{normalizing constant} is difficult or impossible to
+compute and \textcolor{blue}{rejection sampling} is not possible.
+
+Examples:
+\begin{itemize}
+ \item Sampling from \textcolor{blue}{Bayesian Posterior Distributions}
+ \item Computing \textcolor{blue}{Maximum-Likelihood tests for intractable
+ likelihoods}
+\end{itemize}
+
+\end{block}
+
+}
+
+\frame{
+\frametitle{MCMC In pictures}
+\begin{center}
+\includegraphics[height=0.75\textheight]{MCMC-Picture}
+\hfill
+\includegraphics[height=0.75\textheight]{MCMC-Histogram}
+\end{center}
+}
+
+
+\frame{
+ \frametitle{Convergence Rates (1/2)}
\begin{center}
Mean Squared Residuals \\
~
@@ -343,6 +467,16 @@
\end{center}
}
+\frame{
+ \frametitle{Convergence Rates (2/2)}
+ \begin{center}
+ \includegraphics[scale=0.5]{figures/MSR16}
+ \end{center}
+
+
+}
+
+
\section{Results}
\frame{
\frametitle{Results}
@@ -377,22 +511,77 @@
\end{center}
}
-\section[]{References}
+\section{Acknowledgments}
\frame{
- \frametitle{For More Information}
- \begin{itemize}
- \item Greg Warnes \
+ \frametitle{Acknowledgments}
+
+ Robert "Bing" Burrows, Ph.D., who was primarily responsible for work
+ described here passed away unexpectedly on December 27, 2006.
+
+\begin{quote}
+\tiny
+ BURROWS, ROBERT BERNARD, II, 63, of North Scituate [Rhode Island],
+ died Wednesday, December 27, 2006. He was a long time resident of
+ Lexington, MA before moving to Rhode Island in 2001. After
+ graduating from Lexington High School, Dr. Burrows earned his
+ Bachelor of Arts from Northeastern University, a Ph.D. in
+ Biochemistry from the Massachusetts Institute of Technology, and a
+ Master of Science in Statistics from the University of Rhode Island.
+ He was a self-employed Research Biochemist and previously worked for
+ the Boston Biomedical Research Institute. He leaves his sister Ellen
+ Conner and her husband Donald of Coventry, his dearest friend Sally
+ Glanz of North Scituate and many cousins. (\emph{The Providence Journal/Evening
+ Bulletin} 2006 Dec. 31; Sec. B5)
+\end{quote}
+}
+
+\section[]{Reference \& Contact Information}
+\frame{
+ \frametitle{Reference \& Contact Information}
+ \begin{block}{Manuscript}
+ Burrows~RB, Warnes~GR, Hanumara~RC, ``Statistical Modeling of Biochemical Pathways'',
+ \emph{IET Systems Biology}, IET Syst. Biol. 1, 353 (2007)
+ \end{block}
+ \begin{block}{Contact Information}
\begin{itemize}
- \item Email: \texttt{wa...@bs...}
- \item Personal Web Page: \texttt{http://www.warnes.net}
- \item Research Web Page: \texttt{http://research.warnes.net}
+ \item Email: \texttt{gr...@wa...}
+ \item Personal Web Page: \texttt{http://www.warnes.net}
+ \item CBIM Web Page: \texttt{https://cbim.urmc.rochester.edu}
+ \item UR Biostat Web Page \texttt{http://www.urmc.rochester.edu/smd/biostat}
\end{itemize}
- \item Robert Burrows
- \begin{itemize}
- \item Email: \texttt{rb...@ne...}
- \item Web Page: \texttt{http://www.nebiometrics.com}
- \end{itemize}
- \end{itemize}
+ \end{block}
}
+%%\bibliography{./refs}
+%\begin{thebibliography}{99}
+% \bibitem{Oates02}%1
+% Oates,~P.J., 2002, Polyol pathway and diabetic peripheral
+% neuropathy, \emph{Int. Rev. Neurobiol.},
+% \textbf{50}, 325--392.
+% \bibitem{Gilks95} %5
+% Gilkes,~W.R., Richardson,~S., and Spiegelhalter,~D.J. (Ed.),
+% \emph{Markov Chain Monte Carlo in Practice} (Boca Raton, FL:
+% Chapman \& Hall/CRC)
+% \bibitem{R}%9
+% R Development Team, \emph{R: A Language and Environment for
+% Statistical Computing}, http://www.r-project.org (accessed 7 Nov 06)
+% \bibitem{Michaelis13} %10
+% Michaelis, L. and Menten, M.L., 1913, Die kinetic der
+% invertinwirkung, \emph{Biochem. Zeit.}, \textbf{49},
+% 333--369.
+% \bibitem{Hydra}%13
+% Warnes, G.R., Hydra {MCMC} {L}ibrary,
+% http://www.sourceforge.net/projects/hydra-mcmc
+% \bibitem{Warnes00} %14
+% Warnes, G.R., 2000, The {N}ormal {K}ernel {C}oupler: {A}n adaptive
+% {M}arkov chain {M}onte {C}arlo method for efficiently sampling
+% from multi-modal distributions, thesis, University of Washington.
+% \bibitem{projo}%16
+% OBITUARIES-SCITUATE-BURROWS. \emph{The Providence Journal/Evening
+% Bulletin} 2006 Dec. 31; Sec. B5
+%\end{thebibliography}
+
+
+
+
\end{document}
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