Fall 23 HW3.1. Marietta Traffic Authority is concerned about the repeated accidents atthe intersection of Canton and Piedmont Roads. Bayes-inclined city-engineer would like toestimate 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 ofaccidents 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 toassume the Jeffreys' priorT(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 hypothesesHo: 021 USH₁ : 0 <1,based on the posterior, which hypothesis will be favored?

As per the guidelines of Bartleby,solution of only first 3 parts is given.

Answered: Fall 23 HW3.1. Marietta Traffic…

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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