Bayes Theorem and Diseases/Machines
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Confused on how to apply Bayes Th. to this problem.
You have a machine that can identify a disease in 75% of cases, and in 95% of cases the machine is able to correctly indicate that a person does NOT have a disease. What is the probability of a machine incorrectly saying a person has a disease when they do not, and what is the probability of the machine incorrectly saying a person does not have a disease when they actually do?
MY WORK:
Assume M stands for the machines predictability.
Assume D stands for a person having the disease.
P(M)=0.75 which means the machine correctly predicts 75% of the time, P(M')=0.25 which means the machine incorrectly predicts 25% of the time.
P(M|D')=0.95 meaning a person does not have a disease and the prediction is positive.
I need to first find P(M'|D) is the probability of a person having the disease but the prediction is wrong. I then need to find P(M'|D') which is person not having disease and prediction is wrong.
I am stuck here. Is my thought process correct? Do I not need to have information of P(D) to proceed?
machine-learning bayes-theorem
asked Sep 10 at 18:59
Anju Baker
82
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up vote
1
down vote
favorite
Confused on how to apply Bayes Th. to this problem.
You have a machine that can identify a disease in 75% of cases, and in 95% of cases the machine is able to correctly indicate that a person does NOT have a disease. What is the probability of a machine incorrectly saying a person has a disease when they do not, and what is the probability of the machine incorrectly saying a person does not have a disease when they actually do?
MY WORK:
Assume M stands for the machines predictability.
Assume D stands for a person having the disease.
P(M)=0.75 which means the machine correctly predicts 75% of the time, P(M')=0.25 which means the machine incorrectly predicts 25% of the time.
P(M|D')=0.95 meaning a person does not have a disease and the prediction is positive.
I need to first find P(M'|D) is the probability of a person having the disease but the prediction is wrong. I then need to find P(M'|D') which is person not having disease and prediction is wrong.
I am stuck here. Is my thought process correct? Do I not need to have information of P(D) to proceed?
machine-learning bayes-theorem
asked Sep 10 at 18:59
Anju Baker
82
1
I don't see the need for Bayes' Theorem or conditional probabilities. Why aren't the answers by definition $100%-95%=5%$ for the first question and $100%-75%=25%$ for the second? Am I misunderstanding what you mean by the first sentence of the second paragraph? If so, could you please clarify what you do mean?
– joriki
Sep 10 at 19:18
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Confused on how to apply Bayes Th. to this problem.
You have a machine that can identify a disease in 75% of cases, and in 95% of cases the machine is able to correctly indicate that a person does NOT have a disease. What is the probability of a machine incorrectly saying a person has a disease when they do not, and what is the probability of the machine incorrectly saying a person does not have a disease when they actually do?
MY WORK:
Assume M stands for the machines predictability.
Assume D stands for a person having the disease.
P(M)=0.75 which means the machine correctly predicts 75% of the time, P(M')=0.25 which means the machine incorrectly predicts 25% of the time.
P(M|D')=0.95 meaning a person does not have a disease and the prediction is positive.
I need to first find P(M'|D) is the probability of a person having the disease but the prediction is wrong. I then need to find P(M'|D') which is person not having disease and prediction is wrong.
I am stuck here. Is my thought process correct? Do I not need to have information of P(D) to proceed?
machine-learning bayes-theorem
asked Sep 10 at 18:59
Anju Baker
82
Confused on how to apply Bayes Th. to this problem.
You have a machine that can identify a disease in 75% of cases, and in 95% of cases the machine is able to correctly indicate that a person does NOT have a disease. What is the probability of a machine incorrectly saying a person has a disease when they do not, and what is the probability of the machine incorrectly saying a person does not have a disease when they actually do?
MY WORK:
Assume M stands for the machines predictability.
Assume D stands for a person having the disease.
P(M)=0.75 which means the machine correctly predicts 75% of the time, P(M')=0.25 which means the machine incorrectly predicts 25% of the time.
P(M|D')=0.95 meaning a person does not have a disease and the prediction is positive.
I need to first find P(M'|D) is the probability of a person having the disease but the prediction is wrong. I then need to find P(M'|D') which is person not having disease and prediction is wrong.
I am stuck here. Is my thought process correct? Do I not need to have information of P(D) to proceed?
machine-learning bayes-theorem
machine-learning bayes-theorem
asked Sep 10 at 18:59
Anju Baker
82
asked Sep 10 at 18:59
Anju Baker
82
asked Sep 10 at 18:59
Anju Baker
82
asked Sep 10 at 18:59
Anju Baker
82
asked Sep 10 at 18:59
Anju Baker
82
82
1
I don't see the need for Bayes' Theorem or conditional probabilities. Why aren't the answers by definition $100%-95%=5%$ for the first question and $100%-75%=25%$ for the second? Am I misunderstanding what you mean by the first sentence of the second paragraph? If so, could you please clarify what you do mean?
– joriki
Sep 10 at 19:18
add a comment |Â
1
I don't see the need for Bayes' Theorem or conditional probabilities. Why aren't the answers by definition $100%-95%=5%$ for the first question and $100%-75%=25%$ for the second? Am I misunderstanding what you mean by the first sentence of the second paragraph? If so, could you please clarify what you do mean?
– joriki
Sep 10 at 19:18
1
1
I don't see the need for Bayes' Theorem or conditional probabilities. Why aren't the answers by definition $100%-95%=5%$ for the first question and $100%-75%=25%$ for the second? Am I misunderstanding what you mean by the first sentence of the second paragraph? If so, could you please clarify what you do mean?
– joriki
Sep 10 at 19:18
I don't see the need for Bayes' Theorem or conditional probabilities. Why aren't the answers by definition $100%-95%=5%$ for the first question and $100%-75%=25%$ for the second? Am I misunderstanding what you mean by the first sentence of the second paragraph? If so, could you please clarify what you do mean?
– joriki
Sep 10 at 19:18
add a comment |Â
1 Answer
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oldest
votes
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0
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I think you are going astray because your interpretation of the problem statement is a bit off. When the problem states:
You have a machine that can identify a disease in 75% of cases
This is conditional on the disease being present, i.e., $P(M|D) = 0.75; P(M'|D) = 0.25.$
Then, you won't need need $P(D)$ to answer the two questions that were posed - they can be determined by thinking through what $P(M'|D')$ and $P(M'|D)$ represent.
answered Sep 10 at 19:21
E. Tucker
364
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
I think you are going astray because your interpretation of the problem statement is a bit off. When the problem states:
You have a machine that can identify a disease in 75% of cases
This is conditional on the disease being present, i.e., $P(M|D) = 0.75; P(M'|D) = 0.25.$
Then, you won't need need $P(D)$ to answer the two questions that were posed - they can be determined by thinking through what $P(M'|D')$ and $P(M'|D)$ represent.
answered Sep 10 at 19:21
E. Tucker
364
add a comment |Â
up vote
0
down vote
accepted
I think you are going astray because your interpretation of the problem statement is a bit off. When the problem states:
You have a machine that can identify a disease in 75% of cases
This is conditional on the disease being present, i.e., $P(M|D) = 0.75; P(M'|D) = 0.25.$
Then, you won't need need $P(D)$ to answer the two questions that were posed - they can be determined by thinking through what $P(M'|D')$ and $P(M'|D)$ represent.
answered Sep 10 at 19:21
E. Tucker
364
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
I think you are going astray because your interpretation of the problem statement is a bit off. When the problem states:
You have a machine that can identify a disease in 75% of cases
This is conditional on the disease being present, i.e., $P(M|D) = 0.75; P(M'|D) = 0.25.$
Then, you won't need need $P(D)$ to answer the two questions that were posed - they can be determined by thinking through what $P(M'|D')$ and $P(M'|D)$ represent.
answered Sep 10 at 19:21
E. Tucker
364
I think you are going astray because your interpretation of the problem statement is a bit off. When the problem states:
You have a machine that can identify a disease in 75% of cases
This is conditional on the disease being present, i.e., $P(M|D) = 0.75; P(M'|D) = 0.25.$
Then, you won't need need $P(D)$ to answer the two questions that were posed - they can be determined by thinking through what $P(M'|D')$ and $P(M'|D)$ represent.
answered Sep 10 at 19:21
E. Tucker
364
answered Sep 10 at 19:21
E. Tucker
364
answered Sep 10 at 19:21
E. Tucker
364
answered Sep 10 at 19:21
E. Tucker
364
364
add a comment |Â
add a comment |Â
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1
I don't see the need for Bayes' Theorem or conditional probabilities. Why aren't the answers by definition $100%-95%=5%$ for the first question and $100%-75%=25%$ for the second? Am I misunderstanding what you mean by the first sentence of the second paragraph? If so, could you please clarify what you do mean?
– joriki
Sep 10 at 19:18