Fall 23 HW3.1. Marietta Traffic Authority is concerned about the repeated accidents at the intersection of Canton and Piedmont Roads. Bayes-inclined city-engineer would like to estimate the accident rate, even better, find a credible set. A well known model for modeling the number of road accidents in a particular loca- tion/time window is the Poisson distribution. Assume that X represents the number of accidents in a 3 month period at the intersection od Canton and Piedmont Roads. Assume that [X|0] ~ Poi(0). Nothing is known a priori about 0, so it is reasonable to assume the Jeffreys' prior 7(0) = √1(0 < 0 < ∞). In the four most recent three-month periods the following realizations for X are observed: 1, 2, 0, and 2. (a) Compare the Bayes estimator for with the MLE (For Poisson, recall, ÎMLE = X). (b) Compute (numerically) a 95% equitailed credible set. (c) Compute (numerically) a 95% HPD credible set. (d) Numerically find the mode of the posterior, that is, MAP estimator of 0. (e) If you test the hypotheses Ho: 021 H₁ : 0 <1, based on the posterior, which hypothesis will be favored? US
Fall 23 HW3.1. Marietta Traffic Authority is concerned about the repeated accidents at the intersection of Canton and Piedmont Roads. Bayes-inclined city-engineer would like to estimate the accident rate, even better, find a credible set. A well known model for modeling the number of road accidents in a particular loca- tion/time window is the Poisson distribution. Assume that X represents the number of accidents in a 3 month period at the intersection od Canton and Piedmont Roads. Assume that [X|0] ~ Poi(0). Nothing is known a priori about 0, so it is reasonable to assume the Jeffreys' prior 7(0) = √1(0 < 0 < ∞). In the four most recent three-month periods the following realizations for X are observed: 1, 2, 0, and 2. (a) Compare the Bayes estimator for with the MLE (For Poisson, recall, ÎMLE = X). (b) Compute (numerically) a 95% equitailed credible set. (c) Compute (numerically) a 95% HPD credible set. (d) Numerically find the mode of the posterior, that is, MAP estimator of 0. (e) If you test the hypotheses Ho: 021 H₁ : 0 <1, based on the posterior, which hypothesis will be favored? US
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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![Fall 23 HW3.1. Marietta Traffic Authority is concerned about the repeated accidents at
the intersection of Canton and Piedmont Roads. Bayes-inclined city-engineer would like to
estimate the accident rate, even better, find a credible set.
A well known model for modeling the number of road accidents in a particular loca-
tion/time window is the Poisson distribution. Assume that X represents the number of
accidents in a 3 month period at the intersection od Canton and Piedmont Roads.
Assume that [X|0] ~ Poi(0). Nothing is known a priori about 0, so it is reasonable to
assume the Jeffreys' prior
T(0)
1(0 <0<∞).
In the four most recent three-month periods the following realizations for X are observed:
1, 2, 0, and 2.
=
(a) Compare the Bayes estimator for with the MLE (For Poisson, recall, MLE = X).
(b) Compute (numerically) a 95% equitailed credible set.
(c) Compute (numerically) a 95% HPD credible set.
(d) Numerically find the mode of the posterior, that is, MAP estimator of 0.
(e) If you test the hypotheses
Ho: 021 US
H₁ : 0 <1,
based on the posterior, which hypothesis will be favored?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58110eb8-ec30-4c0e-8ae9-9ab7f2632272%2F26ef3663-726b-4e24-b6f9-a0b367db467d%2Fxha1xlt_processed.png&w=3840&q=75)
Transcribed Image Text:Fall 23 HW3.1. Marietta Traffic Authority is concerned about the repeated accidents at
the intersection of Canton and Piedmont Roads. Bayes-inclined city-engineer would like to
estimate the accident rate, even better, find a credible set.
A well known model for modeling the number of road accidents in a particular loca-
tion/time window is the Poisson distribution. Assume that X represents the number of
accidents in a 3 month period at the intersection od Canton and Piedmont Roads.
Assume that [X|0] ~ Poi(0). Nothing is known a priori about 0, so it is reasonable to
assume the Jeffreys' prior
T(0)
1(0 <0<∞).
In the four most recent three-month periods the following realizations for X are observed:
1, 2, 0, and 2.
=
(a) Compare the Bayes estimator for with the MLE (For Poisson, recall, MLE = X).
(b) Compute (numerically) a 95% equitailed credible set.
(c) Compute (numerically) a 95% HPD credible set.
(d) Numerically find the mode of the posterior, that is, MAP estimator of 0.
(e) If you test the hypotheses
Ho: 021 US
H₁ : 0 <1,
based on the posterior, which hypothesis will be favored?
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