Hi Bert, Yay fantasyland!
In all seriousness, You are referring to this? https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f In particular, you mean this: .Machine$double.eps ^ 0.5? Thanks! On Fri, Feb 12, 2016 at 10:53 AM, Bert Gunter <bgunter.4...@gmail.com> wrote: > You are working in fantasyland. Your density is nonsense. > > Please see FAQ 7.31 for links to computer precision of numeric > calculations. > > > Cheers, > Bert > Bert Gunter > > "The trouble with having an open mind is that people keep coming along > and sticking things into it." > -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) > > > On Fri, Feb 12, 2016 at 7:36 AM, C W <tmrs...@gmail.com> wrote: > > Hi David, > > > > This is the Gaussian looking distribution I am trying to integrate. > > > https://drive.google.com/file/d/0B2xN0-A6iTB4NThIZ2tYdGxHc00/view?usp=sharing > > > > Notice the unnormalized density goes up as high as 2.5*101^191. > > > > I tried to create small intervals like > >> seq(0.5, 1.3, by = 10^(-8)) > > > > but that doesn't seem to be good enough, as we know, it should integrate > to > > 1. > > > > On Thu, Feb 11, 2016 at 3:32 PM, David Winsemius <dwinsem...@comcast.net > > > > wrote: > > > >> > >> > On Feb 11, 2016, at 11:30 AM, C W <tmrs...@gmail.com> wrote: > >> > > >> > Hi David, > >> > > >> > My real function is actually a multivariate normal, the simple toy 1-d > >> normal won't work. > >> > > >> > But, you gave me an idea about restricting the bounds, and focus > >> integrating on that. I will get back to you if I need any further > >> assistance. > >> > >> You'll probably need to restrict your bounds even more severely than I > did > >> in the 1-d case (using 10 SD's on either side of the mean) . You might > need > >> adequate representation of points near the center of your > hyper-rectangles. > >> At least that's my armchair notion since I expect the densities tail off > >> rapidly in the corners. You can shoehorn multivariate integration around > >> the `integrate` function but it's messy and inefficient. There are other > >> packages that would be better choices. There's an entire section on > >> numerical differentiation and integration in CRAN Task View: Numerical > >> Mathematics. > >> > >> -- > >> David. > >> > >> > >> > > >> > Thank you so much! > >> > > >> > On Thu, Feb 11, 2016 at 2:06 PM, David Winsemius < > dwinsem...@comcast.net> > >> wrote: > >> > > >> > > On Feb 11, 2016, at 9:20 AM, C W <tmrs...@gmail.com> wrote: > >> > > > >> > > I want to do numerical integration w.r.t. mu: P(mu) × N(mu, 0.00001) > >> > > > >> > > Because the variance is small, it results in density like: > 7.978846e+94 > >> > > > >> > > Is there any good suggestion for this? > >> > > >> > So what's the difficulty? It's rather like the Dirac function. > >> > > >> > > integrate( function(x) dnorm(x, sd=0.00001), -.0001,0.0001) > >> > 1 with absolute error < 7.4e-05 > >> > > >> > > >> > -- > >> > David. > >> > > >> > > > >> > > Thanks so much! > >> > > > >> > > > >> > > On Thu, Feb 11, 2016 at 9:14 AM, C W <tmrs...@gmail.com> wrote: > >> > > > >> > >> Wow, thank you, that was very clear. Let me give it some more runs > >> and > >> > >> investigate this. > >> > >> > >> > >> On Thu, Feb 11, 2016 at 12:31 AM, William Dunlap < > wdun...@tibco.com> > >> > >> wrote: > >> > >> > >> > >>> Most of the mass of that distribution is within 3e-100 of 2. > >> > >>> You have to be pretty lucky to have a point in sequence > >> > >>> land there. (You will get at most one point there because > >> > >>> the difference between 2 and its nearest neightbors is on > >> > >>> the order of 1e-16.) > >> > >>> > >> > >>> seq(-2,4,len=101), as used by default in curve, does include 2 > >> > >>> but seq(-3,4,len=101) and seq(-2,4,len=100) do not so > >> > >>> curve(..., -3, 4, 101) and curve(..., -2, 4, 100) will not show > the > >> bump. > >> > >>> The same principal holds for numerical integration. > >> > >>> > >> > >>> > >> > >>> Bill Dunlap > >> > >>> TIBCO Software > >> > >>> wdunlap tibco.com > >> > >>> > >> > >>> On Wed, Feb 10, 2016 at 6:37 PM, C W <tmrs...@gmail.com> wrote: > >> > >>> > >> > >>>> Dear R, > >> > >>>> > >> > >>>> I am graphing the following normal density curve. Why does it > look > >> so > >> > >>>> different? > >> > >>>> > >> > >>>> # the curves > >> > >>>> x <- seq(-2, 4, by=0.00001) > >> > >>>> curve(dnorm(x, 2, 10^(-100)), -4, 4) #right answer > >> > >>>> curve(dnorm(x, 2, 10^(-100)), -3, 4) #changed -4 to -3, I get > wrong > >> > >>>> answer > >> > >>>> > >> > >>>> Why the second curve is flat? I just changed it from -4 to -3. > >> There is > >> > >>>> no density in that region. > >> > >>>> > >> > >>>> > >> > >>>> Also, I am doing numerical integration. Why are they so > different? > >> > >>>> > >> > >>>>> x <- seq(-2, 4, by=0.00001) > >> > >>>>> sum(x*dnorm(x, 2, 10^(-100)))*0.00001 > >> > >>>> [1] 7.978846e+94 > >> > >>>>> x <- seq(-1, 4, by=0.00001) #changed -2 to -1 > >> > >>>>> sum(x*dnorm(x, 2, 10^(-100)))*0.00001 > >> > >>>> [1] 0 > >> > >>>> > >> > >>>> What is going here? What a I doing wrong? > >> > >>>> > >> > >>>> Thanks so much! > >> > >>>> > >> > >>>> [[alternative HTML version deleted]] > >> > >>>> > >> > >>>> ______________________________________________ > >> > >>>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, > see > >> > >>>> https://stat.ethz.ch/mailman/listinfo/r-help > >> > >>>> PLEASE do read the posting guide > >> > >>>> http://www.R-project.org/posting-guide.html > >> > >>>> and provide commented, minimal, self-contained, reproducible > code. > >> > >>>> > >> > >>> > >> > >>> > >> > >> > >> > > > >> > > [[alternative HTML version deleted]] > >> > > > >> > > ______________________________________________ > >> > > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > >> > > https://stat.ethz.ch/mailman/listinfo/r-help > >> > > PLEASE do read the posting guide > >> http://www.R-project.org/posting-guide.html > >> > > and provide commented, minimal, self-contained, reproducible code. > >> > > >> > David Winsemius > >> > Alameda, CA, USA > >> > > >> > > >> > >> David Winsemius > >> Alameda, CA, USA > >> > >> > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
