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.
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
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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.
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