Samples from the posterior distribution of two parameters, μ and σ, were obtained using a statisticalsoftware package. Using these samples the following numerical summaries were produced.node meansdmuMC error 2.5% 5.0% median 95.0% 97.5% start sample0.6636 1.459 0.02027 -2.217 -1.845 0.6573 3.056 3.565 1000 5001sigma 59.79 20.67 0.3235 31.78 37.89 55.96 78.14 109.4 1000 5001(a) Write down an estimate of the posterior mean and 95% equal-tailed credible interval for o.Comment on the shape of the posterior distribution for o.(b)Was the simulation run for long enough? Justify your answer.(c) Suppose the simulation is run for a further 50000 iterations.(1) Is the width of the credible interval for o likely to increase, decrease or stay roughly thesame? Justify your answer.(11) Is the MC error for o likely to increase, decrease or stay roughly the same? Justify youranswer.

The given numerical summaries are, node mean sd MC error 2.50% 5% median 95.00% 97.50% start…

Answered: Samples from the posterior distribution…

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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Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. Ho: H=H H₁: Hy > H₂ ỌC. Ho: H=H2 H₁: H₁ H₂ The test statistic, t, is. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. -C OB. Ho: ₁2/₂ H₁ H₁ H₂ OD. Ho. Hy#t H₁: H₁ H₂ O A. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. O B. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women…
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