hw1 - STA 414S/2104S: Homework #1 Due Feb.11, 2010 at 1 pm...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
STA 414S/2104S : Homework #1 Due Feb.11, 2010 at 1 pm Late homework is penalized at 20% deduction per day. You are welcome to discuss your work on this homework with your classmates. You are required to write up the work on your own, using your own words, and to provide your own computer code. Answers to the computational questions must be submitted in two parts. The first part presents your conclusions and supporting evidence in a report, written in paragraphs and sentences (not point form) that does not include computer code . This part may include tables and figures. The second part is a complete, and annotated, file showing the computer code that you used to obtain the results discussed in the first part. It is important to include readable code, since everyone’s answers will be based on different training and test samples. 1. Likelihood and Bayesian inference in the linear model: Suppose that the n × 1 vector Y follows a normal distribution with mean and variance σ 2 I : Y N ( Xβ,σ 2 I ) i.e. that f ( y | β,σ 2 ) = 1 ( 2 πσ ) n exp {- 1 2 σ 2 ( y - ) T ( y - ) } . (a) The maximum likelihood estimates ( ˆ β, ˆ σ 2 ) are defined to be the values of β and σ 2 that simultaneously maximize the likelihood function, or more conveniently the log-likelihood function ( β,σ 2 ) = log f ( y | β,σ 2 ) .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

hw1 - STA 414S/2104S: Homework #1 Due Feb.11, 2010 at 1 pm...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online