Merge pull request #182 from markovmodel/fig4cap2

Figure 4 caption

Author: thempel

manuscript/manuscript.tex

@@ -424,10 +424,12 @@ \subsection{MSM estimation and validation}
 \includegraphics{figure_4}
 \caption{Example analysis of the conformational dynamics of a pentapeptide backbone:
 (a)~The convergence behavior of the implied timescales associated with the four slowest processes.
+The solid lines refer to the maximum likelihood result while the dashed lines show the ensemble mean computed with a Bayesian sampling procedure~\cite{ben-rev-msm}.
+The black line (marking equality of timescale and lag time) with grey area indicates the timescale horizon below which the MSM cannot resolve processes.
+As implied timescales are well-converged at $\tau=0.5$~ns, this lag time is chosen for subsequent MSM estimation.
 (b)~Chapman-Kolmogorov test computed using an MSM estimated with lag time $\tau=0.5$~ns assuming~5 metastable states.
-The solid lines in (a) refer to the maximum likelihood result while the dashed lines show the ensemble mean computed with a Bayesian sampling procedure~\cite{ben-rev-msm}.
-The black line indicates where implied timescales are equal to the lag time,
-whereas the grey area indicates all implied timescales faster than the lag time.
+Predictions from this model agree with higher lag time estimates within confidence intervals.
+Implied timescales convergence as well as a passing Chapman-Kolmogorov test are a necessary condition in MSM validation.
 In both panels, the (non-grey) shaded areas indicate~$95\%$ confidence intervals computed with the aforementioned Bayesian sampling procedure.}
 \label{fig:its-and-ck}
 \end{figure}