[Pomp-commits] r242 - pkg/inst/doc

[noreply at r-forge.r-project.org]

Author: kingaa
Date: 2010-05-17 18:19:35 +0200 (Mon, 17 May 2010)
New Revision: 242

Modified:
   pkg/inst/doc/intro_to_pomp.Rnw
   pkg/inst/doc/intro_to_pomp.pdf
Log:
- minor edits to intro vignette


Modified: pkg/inst/doc/intro_to_pomp.Rnw
===================================================================
--- pkg/inst/doc/intro_to_pomp.Rnw	2010-05-17 13:55:35 UTC (rev 241)
+++ pkg/inst/doc/intro_to_pomp.Rnw	2010-05-17 16:19:35 UTC (rev 242)
@@ -143,12 +143,12 @@
 \end{equation}
 In these equations, $\alpha$ and and $\beta$ are $2\times 2$ constant matrices.
 $\xi_{t}$ and $\varepsilon_{t}$ are mutually-independent families of i.i.d.\ bivariate standard normal random variables.
-$\sigma$ is a lower-triangular matrix such that $\sigma\sigma^T$ is the variance-covariance matrix of $X_{t+1}\vert X_{t}$.
-We'll assume that each component of $X$ is measured independently and with the same error, $\tau$, so that the variance-covariance matrix of $Y_{t}\vert X_{t}$ has $\tau^2$ on the diagonal and zeros elsewhere.
+$\sigma$ is a lower-triangular $2\times 2$ matrix such that $\sigma\sigma^T$ is the variance-covariance matrix of $X_{t+1}\vert X_{t}$.
+We'll assume that each component of $X$ is measured independently and with the same error, $\tau$, so that the variance-covariance matrix of $Y_{t}\vert X_{t}$ is just $\tau^2$ times the identity matrix.
 
 Given a data set, one can for this model obtain exact maximum likelihood estimates of the parameters using the Kalman filter.
 We will demonstrate this below.
-Here, we'll approach this model as we would a more complex model for which no such exact estimator is available.
+Here, however, for pedagogical reasons, we'll approach this model as we would a more complex model for which no such exact estimator is available.
 
 \section{Defining a partially observed Markov process in \pomp.}
 
@@ -165,7 +165,7 @@
 For this simple model, all this is easy enough.
 More generally, it will be difficult to do some of these things.
 Depending on what we wish to accomplish, however, we may not need all of these capabilities and in particular,
-\textbf{to use any particular one of the algorithms in \pomp, we never need to specify all these.}
+\textbf{to use any particular one of the algorithms in \pomp, we need never specify \emph{all} these.}
 For example, to simulate data, all we need is \ref{it:rproc} and \ref{it:rmeas}.
 To run a particle filter (and hence to use iterated filtering, \code{mif}), one needs \ref{it:rproc} and \ref{it:dmeas}.
 To do MCMC, one needs \ref{it:dproc} and \ref{it:dmeas}.
@@ -663,11 +663,11 @@
 \end{equation*}
 In the continuous-time case, this is the vectorfield
 \begin{equation*}
-  x\,\mapsto\,\lim_{{\Delta}{t}\,\to\,0}\,\frac{\expect{X_{t+{\Delta}{t}}\;\vert\;X_{t}=x,\theta}}{{\Delta}{t}}.
+  x\,\mapsto\,\lim_{{\Delta}{t}\,\to\,0}\,\expect{\frac{X_{t+{\Delta}{t}}-X_{t}}{{\Delta}{t}}\;\Big{\vert}\;X_{t}=x,\theta}.
 \end{equation*}
 Our discrete-time bivariate autoregressive process has the deterministic skeleton
 \begin{equation}\label{eq:ou-skel}
-  X_{t} = \alpha\,X_{t-1}
+  x\,\mapsto\,\alpha\,x,
 \end{equation}
 which can be implemented in the \R\ function
 <<ou2-skeleton-def,echo=T>>=

Modified: pkg/inst/doc/intro_to_pomp.pdf
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