On a side note, is it ok to do? > which(max(p_x)) and use that instead of numerical integration to get E[X]?
I will try both and report back! Thank you expeRts On Fri, Feb 12, 2016 at 11:29 AM, C W <tmrs...@gmail.com> wrote: > 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.