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Homework MCMC Fall 2008
- Unless noted otherwise, each homework counts ten points:
- HW1 For September 04 (in class 5 points):
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).
- HW3 For September 17 (e-mail date):
A Harvard Professor has fed fish oil to 3,500 heart patients over a few
years (presumably sponsored by the powerful fish oil industry).
The mortality rate was 27% compared to 29% in a control group of
3,500 patients, which did not take fish oil. The benefits of fish oil
made considerable noise in some news ,
but Prof. Manousakis at FSU doubts that they are
statistically relevant.
Perform a bootstrap simulation of 10,000 such studies and report
the percentage of studies in which fish oil is not beneficial
(e-mail also your program). Voice then your opinion about Prof
Manousakis' suspicion. Compare with HEP Physics, where a discovery
is defined by a five sigma deviation from the zero hypothesis.
Solution: fishoil.f ,
Read the book up to chapter 2.5 (p.89).
- HW4 For October 1 (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). Solutions (download and install in STMC/homework):
1001a_rwght.tgz ,
1001b_rwght.tgz .
Read chapter 3, starting p.128 up to page 179.
- HW5 For October 15 (e-mail date):
Read the following pdf file mcmc_Cv.pdf .
Complete Table 3.17 of the file (assignments a0305_02 to a0305_04
of STMC1new from classwork) and e-mail the completed table.
Read chapter 2.7 (jackknife) up to page 109.
- HW6 For October 25 (e-mail date):
Read chapter 3, section 3.3.4.5 again.
Integrate the routines of
AddLibFortran.tgz into STMC1new/Libs/Fortran and the folder
3d3qPotts.tgz into STMC1new/Homework.
Use your personal random number seeds. Run the programs on the
preset 8^3 lattice and determine the equal heights double-peak
histogram. Then iterate the calculation to lattices
of size 12^3, 16^3, 20^3 and 24^3 with the statistics
preset in mc.par. Simulate always at the equal-heights temperature
estimate from the previous lattice. Finally, plot all equal
heights histograms together and e-mail this plot.
Typical solution: 3d3q_ehgts.pdf.
Read chapter 3, section 3.3.4.5 again.
- HW7 For November 10 (e-mail date):
This homework is a competition. First prize 10 points, second prize
9 points, third prize 8 points and all others up to seven points.
To produce more data, you are encouraged to join in teams up to
three. Each student of a team will get the full number of points
according to the position of the team.
Take the programs from classwork 14. Change to the critical temperature
of the 2D Ising model as given in this
mc.par file. Start with L=20 of LxL
lattices, increase L in steps of 20 and calculate reliable (!)
estimates of tau_int on as large lattices as you can get to. You
should use the nsw option of the production program and the NSKIP,
NSTEP options of the analysis program when you get to large lattices,
where you have to increase the production statistics beyond the one
preset in the mc.par file. At the end date mail a table with three
columns: L, tau_int, error bar.
Read chapter 4 up to 4.2, p.227.
- HW8 For November 10 (e-mail date, 6 points):
Secure the equal heights beta values and their error bars from HW6.
Fit these values to the form beta(L)=beta_c+const/L^3. E-mail your
estimate of beta_c (with error bars) and a plot of the fit.
Read chapter 2.7, p.103 to 2.8, p.127.
- HW9 For November 17 (e-mail date, 10 points):
These data sets are results for HW7:
HW7Eakins.txt and
HW7Wu.txt . Fit each of them to the form
const L^z and report z. Make a table of Gaussian difference
tests between the two data sets.
Read chapter 5.1, p.236 to 267. Read chapters 6 and 7.
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