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This question continues exercise sheet 5, question 4. Now there are two machines, each with a different precision of measurement, 71 and 72. They each take a number of measurements with the same known mean μ = 1000. The measurements are x = (₁,...,m) on the first machine can be modelled as a random sample from normal distribution with known mean = 1000 and precision 71 and y = (y₁, yn) on the second machine can be modelled as a random sample from a normal distribution with known mean μ = 1000 and precision 72. The observed data are m= 10, (₁-1000)²=0.12, n = 8 and 1(-1000)² = 0.09. Use independent gamma prior distributions for and 2 with same parameters a and 8 as for r in exercise sheet 5, that is a = 5 and 3 = 0.05. (a) Find the joint posterior density of 71 and 72. (b) What are the marginal posterior distributions for 7 and 7₂?

This question continues exercise sheet 5, question 4. Now there are two machines, each with a different precision of measurement, 71 and 72. They each take a number of measurements with the same known mean μ = 1000. The measurements are x = (₁,...,m) on the first machine can be modelled as a random sample from normal distribution with known mean = 1000 and precision 71 and y = (y₁, yn) on the second machine can be modelled as a random sample from a normal distribution with known mean μ = 1000 and precision 72. The observed data are m= 10, (₁-1000)²=0.12, n = 8 and 1(-1000)² = 0.09. Use independent gamma prior distributions for and 2 with same parameters a and 8 as for r in exercise sheet 5, that is a = 5 and 3 = 0.05. (a) Find the joint posterior density of 71 and 72. (b) What are the marginal posterior distributions for 7 and 7₂?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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This question continues exercise sheet 5, question 4. Now there are two machines, each with a different precision of measurement, 71 and 72. They each take a number of measurements with the same known mean = 1000. The measurements are x = (₁,...,m) on the first machine can be modelled as a random sample from a normal distribution with known mean = 1000 and precision 7₁ and y = (y₁, yn) on the second machine can be modelled as a random sample from a normal distribution with known mean μ = 1000 and precision 72. The observed data are m= 10, ₁(₁-1000)² = 0.12, n = 8 and 1(-1000)² = 0.09. Use independent gamma prior distributions for 1 and 2 with same parameters a and 8 as for r in exercise sheet 5, that is a = 5 and 3 = 0.05. (a) Find the joint posterior density of 71 and 72. (b) What are the marginal posterior distributions for 71 and 72?
Transcribed Image Text:This question continues exercise sheet 5, question 4. Now there are two machines, each with a different precision of measurement, 71 and 72. They each take a number of measurements with the same known mean = 1000. The measurements are x = (₁,...,m) on the first machine can be modelled as a random sample from a normal distribution with known mean = 1000 and precision 7₁ and y = (y₁, yn) on the second machine can be modelled as a random sample from a normal distribution with known mean μ = 1000 and precision 72. The observed data are m= 10, ₁(₁-1000)² = 0.12, n = 8 and 1(-1000)² = 0.09. Use independent gamma prior distributions for 1 and 2 with same parameters a and 8 as for r in exercise sheet 5, that is a = 5 and 3 = 0.05. (a) Find the joint posterior density of 71 and 72. (b) What are the marginal posterior distributions for 71 and 72?
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