Homework Help is Here – Start Your Trial Now!
Math
Statistics
If gene frequencies are in Hardy-Weinberg equilibrium, the genotypes AA, Aa and aa occur with probabilities (1–0)², 20(1-0) and 0². Suppose that on haptoglobin type in a sample of n people, n₁ individuals have genotypes AA, n₂ individuals have genotypes Aa and n3 individuals have genotypes aa: AA n1 Haptoglobin Type Aa n2 aa n3 Thus, (n₁, n2, n3) is multinomial with parameters n and (1 - 0)², 20(1-0) and 0². (a) Write down the likelihood function L(0) of 0. (b) Assume that the prior for is uniform between 0 and 1. Find the posterior

If gene frequencies are in Hardy-Weinberg equilibrium, the genotypes AA, Aa and aa occur with probabilities (1–0)², 20(1-0) and 0². Suppose that on haptoglobin type in a sample of n people, n₁ individuals have genotypes AA, n₂ individuals have genotypes Aa and n3 individuals have genotypes aa: AA n1 Haptoglobin Type Aa n2 aa n3 Thus, (n₁, n2, n3) is multinomial with parameters n and (1 - 0)², 20(1-0) and 0². (a) Write down the likelihood function L(0) of 0. (b) Assume that the prior for is uniform between 0 and 1. Find the posterior

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
See similar textbooks
icon
Related questions
Question
100%
Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!
 
Just do the continued questions!!
a) If gene frequencies are in Hardy-Weinberg equilibrium, the genotypes AA, Aa and aa occur with probabilities (1-0)², 20(1-0) and 0². Suppose that on haptoglobin type in a sample of n people, n₁ individuals have genotypes AA, n₂ individuals have genotypes Aa and n3 individuals have genotypes aa: b) AA n1 Haptoglobin Type Aa n2 Solution: Thus, (n₁, n2, n3) is multinomial with parameters n and (1 - 0)², 20(1-0) and 0². (a) Write down the likelihood function L(0) of 0. (b) Assume that the prior for is uniform between 0 and 1. Find the posterior distribution of given data n₁, n2 and n3. Is this a known distribution? (c) Find the Jeffrey's prior for 0. f(e\n₁, n₂, n3) 0 x L(0)=P(N₁ = n₁, №₂ = n₂, N3 = 13) n! n₁!· n₂! n3! x x aa n3 (1 π₁ (0)=√(1-0)² 2n 0)²″ ¹(20(1 – 0))^²(0)²n ³3 n! n₁!·n₂! n3! n! n₁!·n₂! -n₂! 22xn! n₁!·n₂! n3! 2n 2n (1 – 0)²″ ¹(20(1 – 0))^²(0)²n 3 (1-0) (1 -0 3 ¹(2″ ²0″²(1 – 0)^²) (0)²¹ ³ 2n₁+n₂ n₂+2n3 The Jeffreys prior for the parameter of the continuous probability density function is 2n₁ n₂(-20²+20-1) n3 0²(1-0)² 0² +
Transcribed Image Text:a) If gene frequencies are in Hardy-Weinberg equilibrium, the genotypes AA, Aa and aa occur with probabilities (1-0)², 20(1-0) and 0². Suppose that on haptoglobin type in a sample of n people, n₁ individuals have genotypes AA, n₂ individuals have genotypes Aa and n3 individuals have genotypes aa: b) AA n1 Haptoglobin Type Aa n2 Solution: Thus, (n₁, n2, n3) is multinomial with parameters n and (1 - 0)², 20(1-0) and 0². (a) Write down the likelihood function L(0) of 0. (b) Assume that the prior for is uniform between 0 and 1. Find the posterior distribution of given data n₁, n2 and n3. Is this a known distribution? (c) Find the Jeffrey's prior for 0. f(e\n₁, n₂, n3) 0 x L(0)=P(N₁ = n₁, №₂ = n₂, N3 = 13) n! n₁!· n₂! n3! x x aa n3 (1 π₁ (0)=√(1-0)² 2n 0)²″ ¹(20(1 – 0))^²(0)²n ³3 n! n₁!·n₂! n3! n! n₁!·n₂! -n₂! 22xn! n₁!·n₂! n3! 2n 2n (1 – 0)²″ ¹(20(1 – 0))^²(0)²n 3 (1-0) (1 -0 3 ¹(2″ ²0″²(1 – 0)^²) (0)²¹ ³ 2n₁+n₂ n₂+2n3 The Jeffreys prior for the parameter of the continuous probability density function is 2n₁ n₂(-20²+20-1) n3 0²(1-0)² 0² +
Continue with Question 3 and answer the following: (a) Use the data on the haptoglobin type and compute the MLE Ô for 0 and I(Ô) the Fisher information evaluated at the MLE. (b) Use the normal approximation for posterior distribution to find a 95% credible interval for 0.
Transcribed Image Text:Continue with Question 3 and answer the following: (a) Use the data on the haptoglobin type and compute the MLE Ô for 0 and I(Ô) the Fisher information evaluated at the MLE. (b) Use the normal approximation for posterior distribution to find a 95% credible interval for 0.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 8 steps with 46 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer