Hi Peter, Great, let me try that and get back to you on my findings in a few hours! :)
On Fri, Feb 12, 2016 at 11:09 AM, peter dalgaard <pda...@gmail.com> wrote: > I don't see here FAQ 7.31 comes in either (for once!...) > > However, either the density is unnormalized and the integral is not 1, or > the integral is 1 and it is normalized. The one in the picture clearly does > not integrate to one. You can fit a rectangle of size 0.1 by 1e191 under > the curve so the integral should be > 1e190 . > > As depicted, I don't see why a plain integral from .5 to 1.5 shouldn't > work. > > -pd > > On 12 Feb 2016, at 16:57 , C W <tmrs...@gmail.com> wrote: > > > 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. > > -- > Peter Dalgaard, Professor, > Center for Statistics, Copenhagen Business School > Solbjerg Plads 3, 2000 Frederiksberg, Denmark > Phone: (+45)38153501 > Office: A 4.23 > Email: pd....@cbs.dk Priv: pda...@gmail.com > > [[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.
