\relax \@writefile{toc}{\contentsline {chapter}{\numberline {8}General model framework}{113}} \@writefile{toc}{\contentsline {author}{Ning Sun and Hongyu Zhao}{113}} \@writefile{lof}{\addvspace {10pt}} \@writefile{lot}{\addvspace {10pt}} \@writefile{toc}{\contentsline {section}{\numberline {8.1}Introduction}{113}} \@writefile{toc}{\contentsline {section}{\numberline {8.2}METHODS}{114}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.2.1}Model Specification}{115}} \@writefile{lof}{\contentsline {figure}{\numberline {8.1}{\ignorespaces The hierarchical structure of the misclassification model discussed in this paper. The unknown parameters are in the ovals, and the known parameters are in the rectangles.}}{116}} \newlabel{fig:heiarchical}{{8.1}{116}} \newlabel{eq:sysmodel}{{8.1}{116}} \newlabel{eq:mis0}{{8.3}{117}} \newlabel{eq:mis3}{{8.6}{117}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.2.2}MCMC algorithm for statistical inference}{118}} \newlabel{eq:sigma}{{8.7}{118}} \newlabel{eq:beta}{{8.8}{118}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.2.3}Data analysis and simulation set-up}{119}} \@writefile{lof}{\contentsline {figure}{\numberline {8.2}{\ignorespaces The activities of five transcription factors vary over 18 time points. Two of the five transcription factors share similar variation, which may lead to identifiable problem of the model. However, our results show that the slight difference between the TF activities prevents the problem.}}{120}} \newlabel{fig:beta}{{8.2}{120}} \@writefile{toc}{\contentsline {section}{\numberline {8.3}Simulation Results}{121}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.3.1}Convergence diagnosis of the MCMC procedure}{121}} \@writefile{lof}{\contentsline {figure}{\numberline {8.3}{\ignorespaces The posterior distributions for the model parameters $\beta _t$ and $\sigma _t^{2}$ at $t$ = 4. The standard deviations of these posterior distributions are 0.075, 0.078, 0.092, 0.077, 0.091, and 0.027, respectively.}}{121}} \newlabel{fig:mcmcrun}{{8.3}{121}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.3.2}Misspecification of the model parameters $p$, $q$, and $\pi _X$}{122}} \@writefile{lof}{\contentsline {figure}{\numberline {8.4}{\ignorespaces The false positive and false negative rates of the inferred network. The X-axis is the standard deviation in the gene expression data, while the Y-axis is either the false positive rate or false negative of the posterior network with respect to the true regulatory network in the cell cycle. Different lines correspond to different levels of quality of the protein-DNA binding data.}}{123}} \newlabel{fig:fpfn}{{8.4}{123}} \@writefile{lof}{\contentsline {figure}{\numberline {8.5}{\ignorespaces The effects of the misspecification of the model parameters $p$, $q$, and $\pi _X$ on the inferred network. The standard deviation of the simulated gene expression data is 0.2. The real values of parameters ($p$,$q$) or $\pi _X$ are indicated in the title of each plot. In the first three plots, the true value of $\pi _X$ is 0.46, but ($p$,$q$) are specified as (0.9,0.9), (0.8,0.8), (0.7,0.7), (0.6,0.6), (0.5,0.5), (0.4,0.4), (0.3,0.3), (0.2,0.2), (0.1,0.1), (0.05, 0.05), (0.01,0.01), and (0.05, 0.4). For the last plot, the values of (p, q) are (0.1,0.1), but $\pi _X$ is specified at various levels: 0.1, 0.2, 0.3, 0.4, 0.46, 0.5, 0.6, 0.7, 0.8, and 0.9.}}{124}} \newlabel{fig:sensitivity}{{8.5}{124}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.3.3}Effect of the number of experiments used in the inference}{125}} \@writefile{toc}{\contentsline {section}{\numberline {8.4}Application to Yeast Cell Cycle Data}{125}} \@writefile{toc}{\contentsline {section}{\numberline {8.5}Summary}{125}} \@writefile{lot}{\contentsline {table}{\numberline {8.1}{\ignorespaces The estimates of the regulation activities of the transcription factors and $\sigma $ based on our model.}}{126}} \newlabel{tab:estimates}{{8.1}{126}} \@writefile{lof}{\contentsline {figure}{\numberline {8.6}{\ignorespaces The effect of sample size on the inferred network. The number besides each symbol indicates the number of the time points used in the simulated gene expression data. 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