Solutions to some exercises from Bayesian Data Analysis,
third edition, by Gelman, Carlin, Stern, and Rubin
22 Aug 2014
These solutions are in progress. For more information on either the solutions or the book (published by CRC), check the website, http:/
Statistics 201C Homework 4 Solution
1. (a) Given X1 , . . . , Xi1 , denote the distinct values of them by cfw_xc , c = 1, . . . , Ki1 , each
Ki1
value with sample size ni1,c , where c=1
ni1,c = i 1. Then we have
E(Ki |Ki1 ) = E(E(Ki |Ki1 )|X1 , . . . , Xi
2.4 Shrinkage Estimation of Variance
Introduction to gene expression
DNA, gene, RNA, protein, central dogma
Typical data:
microarray data, RNA-Seq data
1
DNA
DNA (Deoxyribonucleic acid) is a
molecule to store genetic
information of a living organism.
DN
Problem Set 2 Solutions
Statistics 201C Homework 1 Solution
1. (a) We know Y fX,Y (x, y)dx is normally distributed. Let Z N (0, 22 ) and independent
of X. Then we have Y = aX + Z. It follows that
EY = aEX + EZ = a
and
V ar Y = a2 V ar X + V ar Z = a2 12 +
Stats C180/236 Problem Set 3
(Datasets can be downloaded from the course Moodle site)
1. Gelman et al.: chapter 3, problem 13.
2. The standard linear regression model can be written in matrix notation as Y = X + U ,
where Y is the n1 vector of response va
Statistics 201C Homework 3 Solution
1. The posterior distribution for with known :
n
1
T 1
T 1
p(|y, ) exp ( 0 ) 0 ( 0 ) +
(yi ) (yi )
.
2
i=1
(1)
For the second part in Equation (1):
n
i=1
(yi )T 1 (yi )
= tr[1
n
i=1
= tr[1
n
i=1
= tr[1
n
i=1
= tr[1
n
(y