1. Suppose that we have N observations denoted by x = (x1,..., N), from an autoregressive (AR) model of order 1. Therefore data is generated by the process, xt = axt-1 + Et, t = 2,..., N, where Et~ (iid) N (0,7-¹). Suppose that we specify a prior distributions for a: a ~ N(0, 0a), and a gamma prior for T: T~ Gamma (a, B). (a) Calculate the full posterior conditional distribution of 7. (b) Calculate the full posterior conditional distributions of a.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
1. Suppose that we have N observations denoted by x=
an autoregressive (AR) model of order 1. Therefore data is generated by
the process,
(x1,..., IN), from
Xt = axt-1 + Et, t= 2, ..., N,
(iid)N(0, T-1). Suppose that we specify a prior distributions
N(0, oa), and a gamma prior for T: T ~
where &t ~
for a: a ^
Gamma(a, B).
(a) Calculate the full posterior conditional distribution of T.
(b) Calculate the full posterior conditional distributions of a.
Transcribed Image Text:1. Suppose that we have N observations denoted by x= an autoregressive (AR) model of order 1. Therefore data is generated by the process, (x1,..., IN), from Xt = axt-1 + Et, t= 2, ..., N, (iid)N(0, T-1). Suppose that we specify a prior distributions N(0, oa), and a gamma prior for T: T ~ where &t ~ for a: a ^ Gamma(a, B). (a) Calculate the full posterior conditional distribution of T. (b) Calculate the full posterior conditional distributions of a.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman