Homework ISC 5228 Fall 2007

  • HW1 For August 30 in class:

    Prepare a five minutes talk about your science background and interest in MCMC methods.
    If you have already ideas about your final project, add another five minutes to include them too.

    Read the book up to chapter 1.4.1 (p.26).

  • HW2 For September 4 (e-mail date):

    Download the program pi_v1.f and run it to obtain a MC estimator of pi relying on one million
    events. Set your seed of the random number generator and record the estimate of pi to six digits.
    E-mail the instructor your estimate and its difference to the analytical pi.

  • HW3 For September 11 (e-mail date):

    Write a random number generator for the Poisson distribution, rmapoisson.f, and integrate this
    subroutine into ForLib. Use your random number generator to generate an empirical, peaked
    cumulative distribution function relying on 10,000 data and plot it together with the exact one.

    Read the book up to chapter 1.6 (p.35).

  • HW4 For September 13 (e-mail date):

    Download and run the program polls.f . The program bootstraps distribution functions, relying
    on data from an early poll of the 1992 US presidential election based on 700 people.
    1. E-mail the plot of all peaked cumulative distributions functions together.
    2. Based this plot, what is a rough estimate of the probability that Clintons wins the election.
    3. Make the answer to the last point precise, by inserting a line in the program, which counts
    explicitly how often Clinton wins. Mail this probabilty too.
    Give probabilities in percent in your e-mails.

    Read the book up to chapter 1.7.3 (p.43). Continue with chapter 1.8 up to the end of chapter 1 (p.47 to 53).

  • For September 20:

    Read chapter 2 up to page 89.

  • HW5 For October 2 (e-mail date):

    Do Assignment a0301_02 of the book. Add reweighting to beta=0.02. Then repeat the simulations for a 4 x 4 lattice, increasing the total statistics to 1,000,000 independent data points for the small lattice. Use reweighting to calculate the energy per spin the old as well as for the new lattice (no error bars yet). Compare with the results from ferdinand.f. For each lattice size e-mail one figure plotting the original and reweighted histograms together, and a table comparing the mean energies per spin (all for both beta values).

    Read chapter 3 (starting p.128) up to page 179.

  • HW6 For October 4 (e-mail date):

    Use binning to get error bars into your mean energy per spin estimates of the previous homework. Perform Gaussian difference tests against the exact results. E-mail a table with all results.

  • For October 14:

    Read chapter 2.7 (jackknife) up to page 109.

  • HW7 For October 19 (e-mail date):

    Produce figure 3.6 of the book using your seed values for the random number generator (5 points).
    Play with reweighting until the peaks take about equal heights. E-mail the beta-value and the figure for that case (5 points).

  • For October 24:

    Read chapter 4. up 4.2.3 (pages 196 to 224).

  • HW8 For October 26 (e-mail date):

    Modify the program from classwork 11, so that it writes the time series for the first 1,000 Metropolis data on a formatted file. Run at a=0.4, a=4 and a=80. In each case make a plot of the time series. E-mail the plots to the instructor together (most important!) with a dicsussion, how the integrated autocorrelation time and acceptance rate relate to the visual impression from the plots (9 points).

  • HW9 For October 31 (e-mail date):

    Conditional probabilities: Find the win probabilities for the two options in the last example of lecture 8 (6 points).

    Read chapter 6 up to page 316.

  • HW10 For November 6 (e-mail date):

    Download and install MPI_STMC.tgz . Then, run the program of Work/2MPI with 4 processes on (a) one CPU and (b) four CPUs. Time each run. Logon first to the CPUs you use, to make sure that nobody else is running. If you cannot find sufficiently empty CPUs, document the load.
    Next, change whatever it takes to reproduce table 6.7 of the book. E-mail the printout of these runs together with the timing above to the instructore

  • HW11 For November 14 (e-mail date):

    The following question was posed to students at the Harvard Medical School: A test for a disease whose prevalence is 1/1000 fails never when the person is infected, but has a false positive rate of 5%. A person is picked randomly from the population at large and tests positive. What is the probability that this person actually has the disease? (Six points.)

  • HW11 For November 20 (e-mail date):

    Continuation of the previous homework: Assume the false positive rates are purely due to chance (i.e., no dependence on conditions of the persons tested). Under the assumptions stated before, how often needs the test to be repeated, so that we are sure with at least 99.9% probability that a person is infected? What is then the expected number of tests needed for a sample of 1000 persons? (Six points.)

  • HW12 For November 27: Read chapter 2.8 (Fitting), p.109-127.

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