1
Course 12.425. Problem Set 6. Due Thursday Dec. 6, 2007.
For all problems be sure to show your work including all steps taken.
1. Atmospheric Escape
Note: this is the same problem given in Problem Set 5, but with a correction to b. We assume your answer
1
Course 12.425. Problem Set 1. Due 20 Sept. 2007
1. How long would it take for a spacecraft to get from Earth to the nearest star with an exoplanet?
List any assumptions you made and show your calculation.
2. Properties of known exoplanets. From the Extr
1
Course 12.425. Problem Set 3. Due 25 Oct. 2007.
1. Star and Planet Radii.
a. The smallest star is a so-called M9 dwarf star which has a radius 0.09Rsun and a mass 0.08Msun . How does
Jupiter compare in radius and mass to such a star?
b. How can a star b
1
Course 12.425. Problem Set 2. Due 2 Oct. 2007.
1. The Stellar Magnitude System.
a. Derive the stellar magnitude formula given below, using the fact that ve magnitudes is a factor of 100.
mb ma = 2.5 log10
Fb
.
Fa
(1)
b. If the planet-star ux ratio is 10
1
Course 12.425. Problem Set 4. Due 1 Nov. 2007.
1. Planet Albedos and Related Questions
a. Which body in our solar system has the highest albedo?
b. One analogy for the brightness ratio of an Earth-twin is: looking for a rey 6 feet away from a searchligh
1
Course 12.425. Problem Set 5. Due Tuesday 20 Nov. 2007.
For all problems be sure to show your work including all steps taken.
1. Exoplanet Detection: Direct Imaging vs. Radial Velocity
In class we discussed the planet candidate 2M1207 discovered by dire
Examples of State-space models (cont.)
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
Novemeber 27, 2007
revised November 30, 2009
Lecture 22
State-space models. ML estimation. DSGE models.
Examples of State-space
Gibbs Sampling
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
December 11, 2007
Lecture 26
MCMC: Gibbs Sampling
Last time, we introduced MCMC as a way of computing posterior moments and probabilities. The
idea was
Acceptance-Rejection Method (AR)
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
Novemeber 29, 2007
Lecture 25
MCMC: Metropolis Hastings Algorithm
A good reference is Chib and Greenberg (The American Statistician 19
State-Space Models
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
Novemeber 15, 2007
revised November 24, 2009
Lecture 21
Filtering. State space models. Kalman lter.
State-Space Models
In this lecture we consider s
Dierences between Bayesian and Frequentist Approaches
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
Novemeber 29, 2007
revised December 3, 2009
Lecture 23-24
Intro to Bayes approach. Reasons to be Bayesian
Many id
Multi-dimensional Random Walk
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
Novemeber 1, 2007
Lecture 20
Cointegration
We think, or at least we cannot reject the null hypothesis, that many macro series have unit r
Breaks
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 30, 2007
revised November 3, 2009
Lecture 19
Breaks and Cointegration
The goal of this lecture is to analyze and test for another type of non-stationari
Local to Unity Asymptotics
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 25, 2007
Lecture 18
More Non-Stationarity
We have seen that theres a discrete dierence between stationarity and non-stationarity. Wh
Review from last time
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 23, 2007
revised October 22, 2009
Lecture 17
Unit Roots
Review from last time
Let yt be a random walk
yt = yt +
t
, = 1
where t is a mart
Introduction
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 18, 2007
Lecture 16
Empirical Processes
Introduction
References: Hamilton ch 17, Chapters by Stock and Andrews in Handbook of Econometrics vol 4
E
Summary of FAVAR
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 16, 2007
revised October, 2012 Lecture 15
Factor Models Part 2
Summary of FAVAR
Take the same model as last time:
xit =i (L)ft + i (L)xit1 + v
Motivation
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 11, 2007
revised October 13, 2009
Lecture 14
Factor Models
Motivation
Last time, we discussed structural VARs. One of our main concerns was that sho
1. Goals & Assumptions
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
October 4, 2007
revised October, 2012
Lecture 12-13
Structural VARs
1. Goals & Assumptions
This lecture is about applied Macroeconomics. This is
Notation and some Linear Algebra
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
September 27, 2007
revised October 5, 2009
Lecture 11
VARs
Notation and some Linear Algebra
Let
p
yt =
aj ytj + et
(1)
j=1
where yt an
Introduction
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
September 2, 2007
revised October, 2012
Lecture 9
Bootstrap
The goal oof this lecture is to cover the basics for bootstrap procedures. This lecture is NOT
Wold Decomposition Theorem
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
September 25, 2007
Corrected October, 2012 Lecture 10
Introduction to VARs
Wold Decomposition Theorem
Theorem 1 (Wold decomposition). Let yt
1. What are Weak Instruments?
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
Novemeber 13, 2007
corrected September 2012
Lecture 7-8
Weak IV.
This lecture extensively uses lectures given by Jim Stock as a part of m
Review
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
September 18, 2007
revised September 21, 2009
Lecture 4
Spectrum
Review
Recall the spectrum is
eij j
S() =
j=
note that j = j , so S() is real valued and
S() =0
Spectrum Estimation
1
14.384 Time Series Analysis, Fall 2007
Professor Anna Mikusheva
Paul Schrimpf, scribe
September 20, 2007
revised September 22, 2009
Lecture 5
Spectrum Estimation and Information Criteria
Spectrum Estimation
Same setup as last time. W
Introduction to
Materials S i
M t i l Science & E i
Engineering
i
Chapter 20
20.
M GNE
MAGNETIC PROPERTIES
O E
E
How do we measure the magnetic properties?
What
Wh t are th atomic reasons f magnetism?
the t i
for
ti ?
How are magnetic materials classified
CONCEPT CHECK
QUESTIONS AND ANSWERS
Chapter 2
Atomic Structure and Interatomic Bonding
Concept Check 2.1
Question: Why are the atomic weights of the elements generally not integers? Cite two
reasons.
Answer: The atomic weights of the elements ordinarily a
FORMULAS & CONVERSION FACTORS: INTRO MATERIALS SCIENCE Universal gas constant R = 8.314 J/mol.K ; Related to k and NA by R = NA . k Boltzmann constant k = 1.38x10-23 J/atom.K = 8.62x10-5 eV/atom.K Avogadros number NA = 6.023x1023 molecules/mol . Conversio