Suppose the posterior distribution Tpost has a pdf k(0|x1,... , xn), 0 E R. Given c1, c2 > 0, consider the ss function L(0, a) such that Ī(0, a) = Sa(0 – a), 0 > a, lc2(a – 0), 0 < a. cove that the Bayesian estimator 0 with respect to L is the quantile of the posterior distribution.
Suppose the posterior distribution Tpost has a pdf k(0|x1,... , xn), 0 E R. Given c1, c2 > 0, consider the ss function L(0, a) such that Ī(0, a) = Sa(0 – a), 0 > a, lc2(a – 0), 0 < a. cove that the Bayesian estimator 0 with respect to L is the quantile of the posterior distribution.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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![2. Suppose the posterior distribution Tpost has a pdf k(0|x1, ... , Xn), 0 E R. Given c1, c2 > 0, consider the
loss function L(0, a) such that
L(0, a) =
Sa (0 – a), 0 > a,
|c2(a – 0), 0 < a.
Prove that the Bayesian estimator 0 with respect to L is the quantile of the posterior distribution.
Ci+c2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6e05a3e-dd95-40ef-9f0f-346e495ffe3c%2Fe19a96d3-5d21-425c-b930-47c053a3b36c%2Fv85gbkb_processed.png&w=3840&q=75)
Transcribed Image Text:2. Suppose the posterior distribution Tpost has a pdf k(0|x1, ... , Xn), 0 E R. Given c1, c2 > 0, consider the
loss function L(0, a) such that
L(0, a) =
Sa (0 – a), 0 > a,
|c2(a – 0), 0 < a.
Prove that the Bayesian estimator 0 with respect to L is the quantile of the posterior distribution.
Ci+c2
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