Revision: 1060
http://svn.sourceforge.net/r-gregmisc/?rev=1060&view=rev
Author: warnes
Date: 2007-03-01 14:42:15 -0800 (Thu, 01 Mar 2007)
Log Message:
-----------
Correct spelling error
Modified Paths:
--------------
trunk/PathwayModeling/thesispaper/discussion.Snw
Modified: trunk/PathwayModeling/thesispaper/discussion.Snw
===================================================================
--- trunk/PathwayModeling/thesispaper/discussion.Snw 2007-03-01 22:38:28 UTC (rev 1059)
+++ trunk/PathwayModeling/thesispaper/discussion.Snw 2007-03-01 22:42:15 UTC (rev 1060)
@@ -4,42 +4,43 @@
$Id$
\end{verbatim}
-We are interested in assessing the usefulness of Markov chain Monte Carlo
-(MCMC) methods for the fitting of models of metabolic pathways. Fitting
-metabolic pathway models can be difficult because pathways are described by sets
-of reaction rate equations with overlapping sets of parameters. We have
-found that the MCMC algorithms handle this situation well, and produce
-reasonable joint probability densities for the model parameters.
-This output can be used for the estimation of confidence intervals
-for the parameters and the detection of correlations and multimodality.
-Thus MCMC compares favorably with maximum likelyhood methods that
-produce point estimates of the parameters and nonlinear regression
-methods that find approximations of the parameters and their variances.
+We are interested in assessing the usefulness of Markov chain Monte
+Carlo (MCMC) methods for the fitting of models of metabolic
+pathways. Fitting metabolic pathway models can be difficult because
+pathways are described by sets of reaction rate equations with
+overlapping sets of parameters. We have found that the MCMC algorithms
+handle this situation well, and produce reasonable joint probability
+densities for the model parameters. This output can be used for the
+estimation of confidence intervals for the parameters and the
+detection of correlations and multimodality. Thus MCMC compares
+favorably with maximum likelihood methods that produce point estimates
+of the parameters and nonlinear regression methods that find
+approximations of the parameters and their variances.
-MCMC methods and Bayesian statistics are
-particularly useful for modeling networks of biological reactions. These
-networks typically are modeled by large numbers of parameters and
-frequentist methods require at least as many observations as there are
-parameters to fit a model. In contrast, Bayesian methods incorporate our
-prior knowledge of the system and use the experimental data to refine
-the estimates (Figure~\ref{converged}). Thus the model fitting procedure
-described here lends itself to iterative experimentation where the
-experimental results, even if they consit of a single datum, can be
-used to update the prior for the next experiment.
+MCMC methods and Bayesian statistics are particularly useful for
+modeling networks of biological reactions. These networks typically
+are modeled by large numbers of parameters and frequentist methods
+require at least as many observations as there are parameters to fit a
+model. In contrast, Bayesian methods incorporate our prior knowledge
+of the system and use the experimental data to refine the estimates
+(Figure~\ref{converged}). Thus the model fitting procedure described
+here lends itself to iterative experimentation where the experimental
+results, even if they consit of a single datum, can be used to update
+the prior for the next experiment.
-The models used here have the form of the Hill function,
-$\frac{x^n}{\theta^n+x^n}$, with an exponent of 1. This form was chosen
-because the functions exhibit two of the characteristics of
-enzyme-catalyzed reactions: linearity at low concentrations of substrate
-and saturability. This, of course, is also the form of the
-Michaelis-Menten equation. These functions have the reactant
-concentrations as the independent variables since they are quantities that
-are relatively easy to measure. A drawback with these models is that they
-describe irreversible reactions whereas most enzymatic reactions are
-reversible. We have tried using a model of reversible reactions, the
-Haldane equation, but it does not fit the data from a perturbation
-equation very well. It can be used with MCMC simulation for multiple
-steady states, a situation we will continue to examine.
+The models used here have the form of the Hill function,
+$\frac{x^n}{\theta^n+x^n}$, with an exponent of 1. This form was
+chosen because the functions exhibit two of the characteristics of
+enzyme-catalyzed reactions: linearity at low concentrations of
+substrate and saturability. This, of course, is also the form of the
+Michaelis-Menten equation. These functions have the reactant
+concentrations as the independent variables since they are quantities
+that are relatively easy to measure. A drawback with these models is
+that they describe irreversible reactions whereas most enzymatic
+reactions are reversible. We have tried using a model of reversible
+reactions, the Haldane equation, but it does not fit the data from a
+perturbation equation very well. It can be used with MCMC simulation
+for multiple steady states, a situation we will continue to examine.
Three algorithms from the Hydra library were used. Two of the algorithms,
the component-wise Metropolis and the all-components Metropolis
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
