STAT 135 Solutions to Homework 6
Spring 2015
Problem 1
In the oneway ANOVA balanced design with I groups and J observations per group, the observations are modeled
as Yij N ( + i , 2 ) and independent. We saw that
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18
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Ch 9 Problem 39 continued
thereisstrongevidenceagainstthenullhypothesis.Datasuggeststhatthereisatemporal
trendintheincidenceofbites.
Note:Youcanalsolookatthepvaluetodeterminewhetherornotyourejectthenull
hypothesis.Sincepvalue=1.31*1014 <0.05=,werejectthen
STAT 135, Midterm exam, Spring 2016, H. Pitters
NAME (IN CAPS):
SID number and SECTION:
Show your work or provide a brief explanation for
all answers. This quiz is closed books. You are
allowed to use the notes you took during class, a
calculator and extr
SOME NEW IDEAS ON FRACTIONAL FACTORIAL
DESIGN AND COMPUTER EXPERIMENT
A Thesis
Presented to
The Academic Faculty
by
Heng Su
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy in the
H. Milton Stewart School of Industrial and Sy
arXiv:1607.06903v2 [stat.ME] 30 Aug 2016
Asymptotic Properties of Approximate Bayesian
Computation
David T. Frazier, Gael M. Martin, Christian P. Robertand Judith Rousseau
August 31, 2016
Abstract
Approximate Bayesian computation (ABC) is becoming an acce
Model surgery: joining and splitting models with
Markov melding
Robert J. B. Goudie, Anne M. Presanis, David Lunn,
Daniela De Angelis and Lorenz Wernisch
arXiv:1607.06779v2 [stat.ME] 2 Sep 2016
September 5, 2016
MRC Biostatistics Unit, Cambridge, UK
Abstr
Reciprocal Graphical Models for Integrative
Gene Regulatory Network Analysis
arXiv:1607.06849v1 [stat.ME] 22 Jul 2016
Yang Ni1 , Yuan Ji2 , and Peter M
uller3
1
Department of Statistics and Data Sciences, The University of Texas at
Austin
2
Program for Co
Integrative genetic risk prediction using nonparametric
empirical Bayes classification
arXiv:1607.06976v2 [stat.ME] 25 Aug 2016
Sihai Dave Zhao1
1
Department of Statistics, University of Illinois at UrbanaChampaign
August 29, 2016
Abstract
Genetic risk p
arXiv:1607.06565v1 [stat.ME] 22 Jul 2016
Controlling for Latent Homophily in Social
Networks through Inferring Latent Locations
Cosma Rohilla Shalizi
Edward McFowland III
Last LATEXd July 25, 2016
Abstract
Social influence cannot be identified from purely
Solutions
HW
2
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11
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STAT 135, 2. Midterm exam, Spring 2017, H. Pitters
NAME (IN CAPS):
SID number and SECTION:
Please write your answers on the exam sheets. Show
your work or provide a brief explanation for all answers. This quiz is closed books. You are allowed
to use a cal
STAT 135 Solutions to Homework 1: 25 points
Spring 2015
Problem 1: 5 points
Let X1 , X2 be iid continuous random variables, with cumulative probability distribution F (x) = P (Xi x).
1. Show that P (X2 > X1 ) = E(F (X1 )
Z
Z
x2
P (X1 < X2 ) =
f (x1 , x2 )
HW 7 Solutions
STAT 135 Fall 2015
April 6, 2015
Problem 1
2
2
N (x , x ) and Y N (y , y ). To get the shortest CI, we need to minimize the variance of X Y which is,
X
mn
n
2
x
mn
+
y2
n .
Now lets take the derivative of this variance with respect to n an
STAT 135 Solutions to Homework 6
Spring 2015
Problem 1. Suppose that under H0 a measurement X N (0, 2 ) and that
under H1 , X N (1, 2 ), and that the prior probabilities of H0 and H1 are
equal: P (H0 ) = P (H1 ). For = 1 and x [0, 3], plot and compare (i)
STAT 135 Solutions to Homework 2: 30 points
Spring 2015
Problem 1: 10 points
Suppose X1 , X2 are independent samples from a Bernoulli distribution B(p), and let T = X1 + X2 .
1. Show that T Bin(2, p)
Note that we can consider each Xi as the outcome (1 = s
STAT 135 Solutions to Homework 3: 30 points
Spring 2015
The objective of this Problem Set is to study the Stein Phenomenon (1955). Suppose that = (1 , 2 , . . . , n )
consists of n unknown parameters, with n 3. We wish to estimate these parameters with n
STAT 135 Solutions to Homework 1
Spring 2015
Problem 1
Let X1 , ., Xn be iid Poisson random variables with rate . We want to test the hypothesis H0 : = 1 against
H1 : = 1.21. Let denote the TypeI error probability and denote the TypeII error probability
HW 9 solutions
STAT 135 Fall 2015
April 23, 2015
Problem 1
Part 1.
We will assume a null hypothesis
H0 = pi1 = pi2 = pi3 = pi4 for all i, where i are the word combo categories. The alternative is that
this is not the case. We add all the test statistics f
STAT 135, Concepts of Statistics
Helmut Pitters
Linear regression
Department of Statistics
University of California, Berkeley
April 20, 2017
Linear regression.
Example (Growth of Kalama children)
How (fast) do children grow?
In context of nutritional stud
STAT 135, Concepts of Statistics
Helmut Pitters
Comparing two populations  matched samples
Department of Statistics
University of California, Berkeley
April 17, 2017
Review: Covariance and correlation.
Example: comparing production methods
Often in stati
Problem 27
To show that the procedure will generate a simple random sample of size n, we need to show every possible
1
. i.e. if N = n + 1, we need show that this procedure can generate a
(Nn )
1
sample of size n with probability n+1 .
sample occurs with
Solutions
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Plot for Experiment 1: Toss thumbtack 20 times and plot loglikelihood.
PI < seq(from = 0, to = 1, by = 0.001)
log_likelihood < 12*log(PI) + 8*log(1PI)
plot(PI, log_likelihood, type = "l",
main = expression(paste("Experiment 1: loglik(",pi, ")"),
xlab
arXiv:1607.06801v3 [stat.ME] 27 Oct 2016
Highdimensional regression adjustments in
randomized experiments
Stefan Wager*
Wenfei Du*
Jonathan Taylor*
Robert Tibshirani*
*
Department of Statistics, Stanford University
Stanford Graduate School of Business
Disease Mapping with Generative Models
Feifei Wang1, , Jian Wang1, , Alan E. Gelfand2, , and Fan Li2,
arXiv:1607.07002v1 [stat.ME] 24 Jul 2016
1
Guanghua School of Management, Peking University, Beijing 100871, P. R. China
2
Department of Statistical Scie
A Statistical Model for the Analysis of Beta Values in DNA
Methylation Studies
Leonie Weinhold1 , Simone Wahl2 , Matthias Schmid1
1
Department of Medical Biometry, Informatics and Epidemiology
University of Bonn, SigmundFreudStr. 25, D53127 Bonn, Germa