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.