Typos in section 2.2
jhaeberl opened this issue · 3 comments
In 2.2, the following code yields 0.125 which is in fact smaller than 0.137 obtained when using theta = 0.8, not larger as claimed in the text.
theta <- runif(100, min=0.7, max=0.9)
estimated_means <- rbinom(n=100, size=10, prob=theta)/10
sd(estimated_means)
At the bottom of section 2.2.3 it should be B(84,24) , not B(83,23).
Corrected, many thanks!
I think the issue with describing the sd=0.125 in section 2.2 is still there ("... but not as small as when we assumed that θ was a point value ...")
Thanks for catching these mistakes. I have rewritten the section like this:
The higher standard deviation is now coming from the uncertainty associated with the
$\theta$ parameter. To see this, assume a "tighter" PDF for$\theta$ , say$\theta \sim \mathit{Uniform}(0.3,0.8)$ , then the variability in the estimated means would again be smaller, but not as small as when we assumed that$\theta$ was a point value:
theta<-runif(100,min=0.3,max=0.8)
estimated_means<-rbinom(n=100,size=10,prob=theta)/10
sd(estimated_means)
In other words, the greater the uncertainty associated with the parameter
$\theta$ , the greater the variability in the data.
I have now also corrected the end of section 2.2.3.