[Yuima-commits] r183 - pkg/yuimadocs/inst/doc/JSS

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

Author: iacus
Date: 2011-09-13 04:03:54 +0200 (Tue, 13 Sep 2011)
New Revision: 183

Modified:
   pkg/yuimadocs/inst/doc/JSS/article.Rnw
Log:
update

Modified: pkg/yuimadocs/inst/doc/JSS/article.Rnw
===================================================================
--- pkg/yuimadocs/inst/doc/JSS/article.Rnw	2011-09-09 08:02:33 UTC (rev 182)
+++ pkg/yuimadocs/inst/doc/JSS/article.Rnw	2011-09-13 02:03:54 UTC (rev 183)
@@ -11,10 +11,13 @@
 
 %% almost as usual
 \author{Alexandre Brouste\\University of Le Mans \And 
-        Stefano M. Iacus\\University of Milan \And 	
-        Hiroki Masuda\\University of Kyushu \And
-        Masaaki Fukasawa\\University of ???\AND
+        Masaaki Fukasawa\\University of Osaka\And
+        Hideitsu Hino\\Waseda University\And
+        Stefano M. Iacus\\University of Milan \AND 	
         Kengo Kamatani\\University of Tokyo \And
+        Koike Yuta\\University of Tokyo\And
+        Hiroki Masuda\\University of Kyushu \AND
+        Ryosuke Nomura\\University of Tokyo\And
         Yusutaka Shimuzu\\University of Osaka \And
         Masayuki Uchida\\University of Osaka \And
         Nakahiro Yoshida\\University of Tokyo 
@@ -531,28 +534,27 @@
 $$\tilde\theta_n=\arg\min_\theta \ell_n({\bf X}_n,\theta)$$
 As an example, we consider the simple model
 \begin{equation}
-\de X_t = -\theta_2  X_t  \de t + \theta_1  \de W_t
+\de X_t = (2-\theta_2  X_t)  \de t + (1+X_t^2)^{\theta_1}  \de W_t
 \label{eq:model1}
 \end{equation}
-with $\theta_1=0.3$ and $\theta_2=0.1$
+with $\theta_1=0.3$ and $\theta_2=0.2$
 <<echo=TRUE, print=FALSE,results=hide>>=
-ymodel <- setModel(drift = "-x*theta2", diffusion = "theta1",
-     time.variable = "t", state.variable = "x", solve.variable = "x")
-n <- 1000
-ysamp <- setSampling(Terminal = (n)^(1/3), n = n)
+ymodel <- setModel(drift="(2-theta2*x)", diffusion="(1+x^2)^theta1")
+n <- 500
+ysamp <- setSampling(Terminal = n^(1/3), n = n)
 yuima <- setYuima(model = ymodel, sampling = ysamp)
 set.seed(123)
-yuima <- simulate(yuima, xinit = 1, true.parameter = list(theta1 = 0.3, theta2 = 0.1))
+yuima <- simulate(yuima, xinit = 1, true.parameter = list(theta1 = 0.2, theta2 = 0.3))
 @
 With the simulated path we can use the function \code{qmle} to estimate the parameters as follows
 <<echo=TRUE, print=FALSE,results=hide>>=
-mle1 <- qmle(yuima, start = list(theta1 = 0.8, theta2 = 0.7), 
-     lower = list(theta1=0.05, theta2=0.05), 
-     upper = list(theta1=0.5, theta2=0.5), method = "L-BFGS-B")
+param.init <- list(theta2=0.5,theta1=0.5)
+mle1 <- qmle(yuima, start =param.init , 
+     lower = list(theta1=0, theta2=0), 
+     upper = list(theta1=1, theta2=1))
 @
 and the estimated coefficients are as follows
 <<echo=TRUE, print=FALSE>>=
-coef(mle1)
 summary(mle1)
 @
 Notice the interface and the output of the \code{qmle} is quite similar to the ones of the standard \code{mle} function of the \pkg{stats4} package of the base \proglang{R} system.
@@ -602,16 +604,15 @@
 In order to perform Bayesian estimation, we need to prepare the prior densities for the parameters.
 For simplicity we use uniform distributions in $[0,1]$
 <<echo=TRUE>>=
-prior <- list(theta2=list(measure.type="code",df="dunif(z,0,1)"), theta1=list(measure.type="code",df="dunif(z,0,1)"))
+prior <- list(theta2=list(measure.type="code",df="dunif(theta2,0,1)"), theta1=list(measure.type="code",df="dunif(theta1,0,1)"))
 @
 Then we call $\tt adaBayes$ as follows
 <<eval=TRUE,echo=TRUE, results=hide>>=
-param.init <- list(theta2=0.5,theta1=0.5)
 bayes1 <- adaBayes(yuima, start=param.init, prior=prior, method="nomcmc")
 @
 and we can compare the adaptive Bayes estimates  with the QMLE estimates
 <<eval=TRUE,echo=TRUE>>=
-bayes1 at coef
+coef(bayes1)
 coef(mle1)
 @
 The argument \code{method="nomcmc"} in \code{adaBayes} performs numerical integration, otherwise MCMC method is used.