Applied Statistics - Week 2

Overview:
  • Calculation of means, RMS, and their uncertainties
  • The use of Monte Carlo techniques
    Program files can be found at: /scrx/hep/petersen/AS09/Week2/
    Copy by: cp -r /scrx/hep/petersen/AS09/Week2/ ~/AS09/.

    Anvendt Statistik - Week 2

    Pi estimate

    Pi estimate is a simple illustration of the use of Monte Carlo, in this case for determining the value of pi. At the same time it illustrates the calculation of mean and width, and the uncertainty on these.

    In the directory PiEstimate (cd PiEstimate) you will find the relevant C++ program, which you should first take a look at (emacs PiEstimate &), then compiles (make) and run (./PiEstimate).
    The program takes random pairs of uniformly distributed numbers within a unit square, and determins which fraction of these lies within the unit circle, from which pi can be evaluated.

    N dimentional ball:

    Again using Monte Carlo, one is this time faced with the problem of determing the hyper volume of an N dimensional hyperbal, that is a unit ball in N dimensional space.
    Given knowledge of pi (for example from previous exercise), one can now get a precisely eough estimate in order to guess at which (simple) fraction should accompany the expected pi^something R^N behavior.

    More to be added, if found necessary. Last updated 6th of September 2009.