Results 1 to 3 of 3

Math Help - How to applying the monte carlo method : importance sampling

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    3

    Question How to applying the monte carlo method : importance sampling

    Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate :
    integral(0 to infinity) integral(0 to infinity) 1/(2 * pi * sqrt((1 + x^2 + y^2)^3))dxdy
    Can somebody help me ? Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: How to applying the monte carlo method : importance sampling

    Quote Originally Posted by cristinelm View Post
    Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate :
    integral(0 to infinity) integral(0 to infinity) 1/(2 * pi * sqrt((1 + x^2 + y^2)^3))dxdy
    Can somebody help me ? Thanks in advance.
    More information of why you mention importance sampling. I would first switch to polars, then you are effectivly left with a one dimensional integral, then you need to find a density p(x) such that:

    \frac{r}{2\pi \sqrt{(1 + r^2)^3}\; p(r)}\approx \text{ constant}

    The main consideration for choosing p(x) is that it's cumulative distribution be easily inverted, so that you can easily generate pseudo-random numbers with the required distribution. Which probably means that p(r) should be piecewise polynomial.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2011
    Posts
    3

    Re: How to applying the monte carlo method : importance sampling

    Quote Originally Posted by CaptainBlack View Post
    More information of why you mention importance sampling. I would first switch to polars, then you are effectivly left with a one dimensional integral, then you need to find a density p(x) such that:

    \frac{r}{2\pi \sqrt{(1 + r^2)^3}\; p(r)}\approx \text{ constant}

    The main consideration for choosing p(x) is that it's cumulative distribution be easily inverted, so that you can easily generate pseudo-random numbers with the required distribution. Which probably means that p(r) should be piecewise polynomial.

    CB
    Thanks very much,it was very usefull for me your answer.I have anoather problem now,how can i make a goodness fit test for sample from bivariate cauchy distribution ? Is there any book that i could find some example about goodness fit test for multivariate/bivariate distribution ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Monte Carlo method
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 14th 2010, 10:57 AM
  2. Replies: 3
    Last Post: March 30th 2010, 05:43 AM
  3. Importance sampling in Monte carlo method
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 16th 2010, 10:27 AM
  4. monte carlo importance sampling
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 27th 2008, 07:05 PM
  5. Monte Carlo & Importance Sampling
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 1st 2006, 10:20 AM

Search Tags


/mathhelpforum @mathhelpforum