cosmetic change

vignettes/Optimalgo.Rmd

@@ -203,7 +203,7 @@ grlnlbeta(c(3, 4), x) #test
 hist(x, prob=TRUE)
 lines(density(x), col="red")
 curve(dbeta(x, 3, 3/4), col="green", add=TRUE)
-legend("topleft", lty=1, col=c("red","green"), leg=c("empirical", "theoretical"))
+legend("topleft", lty=1, col=c("red","green"), legend=c("empirical", "theoretical"), bty="n")
 ```
 
 ## Fit Beta distribution
@@ -253,18 +253,23 @@ Results are displayed in the following tables:
 (4) the log-transformed parametrization with the (true) gradient (`-G` stands for gradient).
 
 ```{r, results='asis', echo=FALSE}
-kable(unconstropt[, grep("G-", colnames(unconstropt), invert=TRUE)], digits=3)
+kable(unconstropt[, grep("G-", colnames(unconstropt), invert=TRUE)], digits=3,
+      caption="Unconstrained optimization with approximated gradient")
 ```
 
 ```{r, results='asis', echo=FALSE}
-kable(unconstropt[, grep("G-", colnames(unconstropt))], digits=3)
+kable(unconstropt[, grep("G-", colnames(unconstropt))], digits=3,
+      caption="Unconstrained optimization with true gradient")
 ```
 
 ```{r, results='asis', echo=FALSE}
-kable(expopt[, grep("G-", colnames(expopt), invert=TRUE)], digits=3)
+kable(expopt[, grep("G-", colnames(expopt), invert=TRUE)], digits=3,
+      caption="Exponential trick optimization with approximated gradient")
 ```
+
 ```{r, results='asis', echo=FALSE}
-kable(expopt[, grep("G-", colnames(expopt))], digits=3)
+kable(expopt[, grep("G-", colnames(expopt))], digits=3,
+      caption="Exponential trick optimization with true gradient")
 ```
 
 
@@ -343,7 +348,7 @@ grlnlNB <- function(x, obs, ...)
 ## Random generation of a sample
 
 ```{r, fig.height=4, fig.width=4}
-#(1) beta distribution
+#(2) negative binomial distribution
 n <- 200
 trueval <- c("size"=10, "prob"=3/4, "mu"=10/3)
 x <- rnbinom(n, trueval["size"], trueval["prob"])
@@ -352,8 +357,8 @@ hist(x, prob=TRUE, ylim=c(0, .3))
 lines(density(x), col="red")
 points(min(x):max(x), dnbinom(min(x):max(x), trueval["size"], trueval["prob"]), 
        col = "green")
-legend("topleft", lty = 1, col = c("red", "green"), 
-       leg = c("empirical", "theoretical"))
+legend("topright", lty = 1, col = c("red", "green"), 
+       legend = c("empirical", "theoretical"), bty="n")
 ```
 
 ## Fit a negative binomial distribution
@@ -404,19 +409,23 @@ Results are displayed in the following tables:
 (3) the log-transformed parametrization without specifying the gradient,
 (4) the log-transformed parametrization with the (true) gradient (`-G` stands for gradient).
 
-```{r, results='asis', echo=FALSE}
-kable(unconstropt[, grep("G-", colnames(unconstropt), invert=TRUE)], digits=3)
+```{r, echo=FALSE}
+kable(unconstropt[, grep("G-", colnames(unconstropt), invert=TRUE)], digits=3,
+      caption="Unconstrained optimization with approximated gradient")
 ```
 
 ```{r, results='asis', echo=FALSE}
-kable(unconstropt[, grep("G-", colnames(unconstropt))], digits=3)
+kable(unconstropt[, grep("G-", colnames(unconstropt))], digits=3,
+      caption="Unconstrained optimization with true gradient")
 ```
 
 ```{r, results='asis', echo=FALSE}
-kable(expopt[, grep("G-", colnames(expopt), invert=TRUE)], digits=3)
+kable(expopt[, grep("G-", colnames(expopt), invert=TRUE)], digits=3,
+      caption="Exponential trick optimization with approximated gradient")
 ```
 ```{r, results='asis', echo=FALSE}
-kable(expopt[, grep("G-", colnames(expopt))], digits=3)
+kable(expopt[, grep("G-", colnames(expopt))], digits=3,
+      caption="Exponential trick optimization with true gradient")
 ```
 
 
@@ -436,16 +445,15 @@ We can simulate bootstrap replicates using the `bootdist` function.
 b1 <- bootdist(fitdist(x, "nbinom", method = "mle", optim.method = "BFGS"), 
                niter = 100, parallel = "snow", ncpus = 2)
 summary(b1)
-plot(b1)
-abline(v = trueval["size"], h = trueval["mu"], col = "red", lwd = 1.5)
+plot(b1, trueval=trueval)
 ```
 
 
 
 # Conclusion
 
 Based on the two previous examples, we observe that all methods converge to the same
-point. This is rassuring.  
+point. This is reassuring.  
 However, the number of function evaluations (and the gradient evaluations) is
 very different from a method to another.
 Furthermore, specifying the true gradient of the log-likelihood does not