1. Yn~p(y | 0) = h(y) exp{0¹y (0)} for yy with y მს(0) (a) Show that E(y |0) = {(0) = 20 Let y₁,.. not depending on 0. Also, let have prior p(0 | Yo, A) = h(yo, A) exp{0¹yo - X(0)} with yo Y. (b) Show that Yo E{{(0)} = + constant and and use E{§(0)|y1:n} = Write [Hints: For part (a), take the derivative of fp(y | 0)dy = 1 w.r.t. and apply Leibniz rule. For part (b), first prove the prior expectation result. Note that the integration is now w.r.t. 0, not y. yo + ny X+n Ə(0) ᎧᎾ + constant. 1 მს(0) = { {Yo vo - (10 - 150(0))} Yo 5 exp{0¹y₁ − Av(0)} = (yo - X² 1³6(0)) exp{0¹ Yo — Av(0)}. 20 For the posterior expectation result, simply appeal to conjugacy.]
1. Yn~p(y | 0) = h(y) exp{0¹y (0)} for yy with y მს(0) (a) Show that E(y |0) = {(0) = 20 Let y₁,.. not depending on 0. Also, let have prior p(0 | Yo, A) = h(yo, A) exp{0¹yo - X(0)} with yo Y. (b) Show that Yo E{{(0)} = + constant and and use E{§(0)|y1:n} = Write [Hints: For part (a), take the derivative of fp(y | 0)dy = 1 w.r.t. and apply Leibniz rule. For part (b), first prove the prior expectation result. Note that the integration is now w.r.t. 0, not y. yo + ny X+n Ə(0) ᎧᎾ + constant. 1 მს(0) = { {Yo vo - (10 - 150(0))} Yo 5 exp{0¹y₁ − Av(0)} = (yo - X² 1³6(0)) exp{0¹ Yo — Av(0)}. 20 For the posterior expectation result, simply appeal to conjugacy.]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Need accurate and clear handwriting.
![iid
1.
Let y1,..., yn * p(y | 0) = h(y) exp{0™y – v(0)} for y € Y with y
not depending on 0.
đ (0)
(a) Show that E(y | 0) = (0) =
Also, let 0 have prior p(0 | yo:A) = h(yo, A) exp{0"yo – Ab(0)} with yo E ).
(b) Show that
Уо + пy
E{{(0)} =
Yo
+ constant
E{{(0) | y1:n}
+ constant.
and
A+n
[Hints: For part (a), take the derivative of S p(y | 0)dy = 1 w.r.t. 0 and apply
Leibniz rule. For part (b), first prove the prior expectation result. Note that the
integration is now w.r.t. 0, not y.
1
Write
yo - A
дө
d (0)
exp{0"yo - Ab(0)} = (yo – x-
) exp{0"yo - Ap(0)}.
and use
For the posterior expectation result, simply appeal to conjugacy.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42ba5f8f-83a4-4ffb-a789-b4db00d273a0%2F1941ff62-83bd-4dbd-b4be-db98c7ec9811%2F0je1jgh_processed.png&w=3840&q=75)
Transcribed Image Text:iid
1.
Let y1,..., yn * p(y | 0) = h(y) exp{0™y – v(0)} for y € Y with y
not depending on 0.
đ (0)
(a) Show that E(y | 0) = (0) =
Also, let 0 have prior p(0 | yo:A) = h(yo, A) exp{0"yo – Ab(0)} with yo E ).
(b) Show that
Уо + пy
E{{(0)} =
Yo
+ constant
E{{(0) | y1:n}
+ constant.
and
A+n
[Hints: For part (a), take the derivative of S p(y | 0)dy = 1 w.r.t. 0 and apply
Leibniz rule. For part (b), first prove the prior expectation result. Note that the
integration is now w.r.t. 0, not y.
1
Write
yo - A
дө
d (0)
exp{0"yo - Ab(0)} = (yo – x-
) exp{0"yo - Ap(0)}.
and use
For the posterior expectation result, simply appeal to conjugacy.]
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