But (theoretical) correctness, asymptotic exactness and dimension independence aren’t necessarily useful things… I would love it if someone could prove that, given a random sequence, you can construct a pseudo-marginal mcmc scheme that is exact for an arbitrary distribution that is coupled with the random sequence for an arbitrary time T (in expectation, maybe)… It would be one hell of a companion to the paper that Geoff Nicholls, Colin Fox and Alexis Muir-Watt wrote!

Éric

Fully endorsing the risk of mixing the message and the speaker, I love the contrast.

truncnorm=function(a,b,mu,sigma){
u0] = qnorm(pnorm((a-mu)/sigma)*(1-u[foo>0])+u[foo>0]*pnorm((b-mu)/sigma))
u[foo<=0] =-qnorm(pnorm(-(a-mu)/sigma)*(1-u[foo<=0])-u[foo<=0]*pnorm(-(b-mu)/sigma))
return(mu+sigma*u)
}

> truncnorm(8,9,0,1)
[1] 8.0414
> truncnorm(8,9,0,1)
[1] 8.0414
> truncnorm(8,9,0,1)
[1] 8.209536
> truncnorm(8,9,0,1)
[1] 8.125891
> truncnorm(8,9,0,1)
[1] 8.076571
> truncnorm(8,9,0,1)
[1] Inf

Compare it:

> sum(is.finite(rtnorm(10000,0,1,8,9)))
[1] 10000

Ok, so I vectorized the original code from this post and did some investigation:

truncnorm=function(a,b,mu,sigma){
u0] = qnorm(pnorm((a-mu)/sigma)*(1-u[foo>0])+u[foo>0]*pnorm((b-mu)/sigma))
u[foo<=0] =-qnorm(pnorm(-(a-mu)/sigma)*(1-u[foo<=0])-u[foo 100000-sum(is.finite(truncnorm(rep(8,100000),rep(9,100000),rep(0,100000),rep(1,100000))))
[1] 9166
> system.time(truncnorm(rep(8,100000),rep(9,100000),rep(0,100000),rep(1,100000)))
user system elapsed
0.08 0.00 0.08
> system.time((rtnorm(100000,0,1,8,9)))
user system elapsed
0.11 0.03 0.14

Clearly, the iCDF is faster. However, it is quite astonishing how fast the A-R sampler is.

Here’s what I wrote a few years ago about a similar book:

the point of the comic-book format seems to be to allow a punchy, power-point sort of delivery. The picture conveys essentially no content, which would suggest that the entire contents of a 222-page comic book could be presented in a 10-page pamphlet of text. The remaining 212 pages are essentially a reader-friendly trick to get students to turn the pages. It’s the printed analogy to a power-point presentation.

So . . . let’s take the customers’ word for it that these cartoon guides are good. If so, this suggests that the useful content of a typical introductory statistics book can be captured in 10 pages. And, if this is the case, it in turn suggests that textbook writers could do a better job with those other 212 pages. Maybe it would be better to have a 10-page textbook and 212 pages of examples? Presumably a good textbook author could do better than those silly cartoons.