AM 207
Monte Carlo
Spring 2013
Pavlos Protopapas
1
Intorduction
Before the actual discovery of the Monte Carlo method, Georges-Louis Leclerc comte de
Buon in 1777 stated a problem involving dropping a needle on a lined surface. Suppose we
have a oor made
AM 207
HM4
Spring 2013
Pavlos Protopapas
Handed out: Saturday March 2, 2013
Due: Saturday, Mar. 9, 2013
Last updated: 2013/03/06, 17:10:57
Instructions:
Upload your answers in a pdf format to the dropbox.
Use the following lenames: AM207 YOURNAME HM4
Y
Solutions to Problem Set 3
AM 207 Sta
March 31, 2013
1
Attribution
Our solutions are based on modications of solutions from students (in particular J.T.B.
Overwelde, Natalie Mashian, and Nicholas Langellier). Thank you for the excellent work.
2
Question 1
AM 207
Gibbs sampling
Spring 2013
Pavlos Protopapas
Last updated: 2013/03/07, 11:01:43
1
Introduction
As we saw already it is not always easy to tune the proposal distribution. The Gibbs sampler
is a procedure for multivariate distributions in which all s
AM 207
HM-X
Spring 2013
noindent Pavlos Protopapas
Handed out: Saturday March 12, 2013
Due: Saturday, Mar. 19, 2013
Last updated: 2013/03/12, 23:27:39
Instructions:
Upload your answers in a pdf format to the dropbox.
Use the following lenames: AM207 YOU
Question 4 (20 points) Suppose we ask individuals to remember the chronological order of world cup
winners. Individuals make a number of mistakes in the ordering of winners that can be captured by simple
probabilistic models, such as Mallows model. To exp
AM 207
HM-X
Spring 2013
Question 1 (25 points) The multivariate normal distribution can be drawn using a Gibbs sampler. Consider a 3-dimensional multivariate normal with mean vector (1, 2, 3), variances each equal to 4, and an
intraclass correlation coeci
Homework 4 Soulutions (Problems 1 and 2)
Problems 3 and 4 are separate.
Boilerplate:
import os
import pymatbridge as pymat
reload(pymat)
from IPython.display import Image
ip = get_ipython()
pymat.load_ipython_extension(ip)
Starting MATLAB on http:/localho
AM 207
2013
Machine Precisions and Uncertainties
Spring
Pavlos Protopapas
Handed out: Jan 1, 2013
1
Precision
Computers are nite. They could do a lot of things but they are limited. A fundamental
design of a computer is how to represent a number in a nite
AM 207
HM5
Spring 2013
Pavlos Protopapas
Handed out: Saturday March 30, 2013
Due: Saturday, April 6, 2013
Last updated: 2013/03/30, 22:26:20
Instructions:
Upload your answers in a pdf format to the dropbox.
Use the following lenames: AM207 YOURNAME HM5
AM 207
HM2
Spring 2013
Pavlos Protopapas
Handed out: Friday Feb. 15, 2013
Due: Friday, Feb. 22, 2013
Instructions:
Upload your answers in a pdf format to the dropbox.
Individual submissions use the following lenames: AM207 YOURNAME HM2
Group submissions
AM 207
Markov Chain Monte Carlo
Spring 2013
Pavlos Protopapas
1
Introduction
Metropolis algorithm is among the top ten most algorithms that are used in science and
engineering in the last twenty years. Metropolis algorithm is one of the algorithms in a
la
AM 207
Numerical Integration
Spring 2013
Pavlos Protopapas
Last update: 2/5/2013
1
Integration
Integrating a function has its history back with the Greeks (doesnt everything?). Archimedes
(287-212 BC) found formulas for the surface areas and volumes of so
AM 207
Simulated Annealing
Spring 2013
Pavlos Protopapas
Handed out: Tuesday Mar. 20, 2012
Last updated: 2013/03/11, 17:22:45
Simulated Annealing is one of the most popular techniques for global optimization. In physical annealing,
a system is rst heated
AM 207
Random Numbers
Spring 2013
Pavlos Protopapas
1
Intorduction
We have introduced the concept of randomly throwing stones or randomly selecting pairs.
In this lecture we will explore how computers generate random numbers.
Randomness means lack of corr
AM 207
HM1
Spring 2013
Pavlos Protopapas
Handed out: Friday Feb. 8, 2013
Due: Saturday, Feb. 15, 2013
Instructions:
Upload your answers in a pdf format to the dropbox.
Use the following lenames: AM207 YOURNAME HM1
Your code should also be uploaded. Use
AM 207
HM3
Spring 2013
Pavlos Protopapas
Handed out: Saturday Feb. 23, 2013
Due: March, March 2, 2013
Instructions:
Upload your answers in a pdf format to the dropbox.
Individual submissions use the following lenames: AM207 YOURNAME HM3
Group submission
Solutions to Problem Set 1
AM 207 Sta
March 11, 2013
1
Question 1
A 64-bit number N can be represented as [(1)s ]x[1.f ]x 2e1023 where the exponent e
has 11 bits, the sign s has 1 bit and the fraction f has 52 bits. In order to maximize N ,
we must maximi
1
Genetic Algorithms: an Introduction
In many physical situations we are interested in the optimal state of
a system, but it is extremely dicult (often impossible) to nd all the
allowed states the system, evaluate them according to some rule, usually by
c
3/5/13
Home wor k2.html
Homework 2
This s olution has been s ourced from s tudent work.
NOTE:Its partly in py thon, partly in Matlab, us ing the ipy thon notebook on the enthought dis tribution updated to
the lates t py thon, and als o us ing, for Matlab