Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S0~U(.49,.51) M+ 0 = .80 C+0 = .10 In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc.M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Sydney. Call that Bayes factor Bc:s Out of n = 20 trials, the psychic predicts k = 10 flips correctly. With that information, which one of these statements is true? Вс.м < 1 Вм:s <1 Bc:s < 1 Bc.s Всм х Вм:S You won't need to calculate anything, just think about what each part of the formula means, and which values must be bigger than which other values.
Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S0~U(.49,.51) M+ 0 = .80 C+0 = .10 In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc.M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Sydney. Call that Bayes factor Bc:s Out of n = 20 trials, the psychic predicts k = 10 flips correctly. With that information, which one of these statements is true? Вс.м < 1 Вм:s <1 Bc:s < 1 Bc.s Всм х Вм:S You won't need to calculate anything, just think about what each part of the formula means, and which values must be bigger than which other values.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:Suppose I flip a fair coin n =
20 times. A psychic tries to predict the outcome before each flip. Three
researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who
thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who
thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the
psychic's success rate is 10%.
Specifically:
S+ 0 ~ U(.49, .51)
M + 0 = .80
C0 = .10
%3D
In all cases, assume the number of successful predictions follows a binomial distribution with success
rate 0. Usek for the number of successes and n for the number of trials.
Given all that:
Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over
Morgan. Call that Bayes factor Bc:M
Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over
Sydney. Call that Bayes factor BM:S
Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over
Sydney. Call that Bayes factor Bc:s
Out of n = 20 trials, the psychic predicts k = 10 flips correctly.
%3D
With that information, which one of these statements is true?
Всм < 1
BM:S <1
BC:s < 1
BC:S
Вс.м X Вм:S
You won't need to calculate anything, just think about what each part of the formula means, and
which values must be bigger than which other values.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman