# Thread: Stats - bayes theory

1. ## Stats - bayes theory

D1: .50
D2: .50

Suppose also that medical research has established the probability associated with each of three symptoms (denoted S1, S2, and S3) that may accompany the two diseases. That is, suppose that, given diseases D1 and D2, the probabilities that the patient will have symptoms S1, S2, or S3 are as follows: P(S1│D1) = .25; P(S2│D1) = .15; P(S3│D1) = .65; P(S1│D2) = .10; P(S2│D2) = .15; P(S3│D2) = .20.

2. Originally Posted by desire150
D1: .50
D2: .50

Suppose also that medical research has established the probability associated with each of three symptoms (denoted S1, S2, and S3) that may accompany the two diseases. That is, suppose that, given diseases D1 and D2, the probabilities that the patient will have symptoms S1, S2, or S3 are as follows: P(S1│D1) = .25; P(S2│D1) = .15; P(S3│D1) = .65; P(S1│D2) = .10; P(S2│D2) = .15; P(S3│D2) = .20.
Yes, and the question is?

CB

3. I followed the Bayes theory and this is the answers I got. Of course they are wrong.

b. The patient has symptom S2. D1 0.04 and D2 0.06 (3 pts)

c. The patient has symptom S3. D1 0.833 and D2 0.166 (3 pts)

d. For a patient with symptom S1 in part (a), we also find symptom S3. The posterior probabilities are: D1 0.4839 and D2 0.5161 (3 pts)

4. I still don't understand the question. Are you simply meant to find the Probability a person has Symptoms 1, 2 and 3?

5. Originally Posted by desire150
I followed the Bayes theory and this is the answers I got. Of course they are wrong.

b. The patient has symptom S2. D1 0.04 and D2 0.06 (3 pts)

c. The patient has symptom S3. D1 0.833 and D2 0.166 (3 pts)

d. For a patient with symptom S1 in part (a), we also find symptom S3. The posterior probabilities are: D1 0.4839 and D2 0.5161 (3 pts)

An example:

$\displaystyle P(D1|S1)=\frac{P(S1|D1)P(D1)}{P(S1)}=\frac{P(S1|D1 )P(D1)}{P(S1|D1)P(D1)+P(S1|D2)P(D2)}$ $\displaystyle =\frac{0.25\times 0.5}{0.25\times 0.5+0.1\times 0.5}=0.714$

But your exact question still escapes us.

CB

6. ## Bayesian Theory

Dear CB,
I've used the Bayes theory formula to complete the answers however, I don't seem to understand it. I've used excel to complete it and unfortunately don't land on the right answer. Any help is much appreciated it.

7. Originally Posted by ANDS!
I still don't understand the question. Are you simply meant to find the Probability a person has Symptoms 1, 2 and 3?

Dear Ands,
I'm trying to find the probability of symptons for S2 for patient D1 and D2 and S3 for patient D1 and D2.
I also need to find the prior probability for patient with sympton S1 and sympton S3?

If you can possibly help me, I would appreciate it.

thank you.

8. Can someone please help me with the Bayes Theory? I'm having issues solving it. I thought I had it right but I don't

9. Originally Posted by desire150
Can someone please help me with the Bayes Theory? I'm having issues solving it. I thought I had it right but I don't
You've clearly made an attempt, so show your working please.

10. Originally Posted by desire150
Dear Ands,
I'm trying to find the probability of symptons for S2 for patient D1 and D2 and S3 for patient D1 and D2.
I also need to find the prior probability for patient with sympton S1 and sympton S3?

If you can possibly help me, I would appreciate it.

thank you.
Oh ok. Well that makes quite a bit more sense. Remember what Bayes says (paraphrased and in non-legalese):

If I have a collection of events, we can call them A1, A2, A3. . .An that cover an entire space, and further we have a collection of sub-events, B1, B2, B3. . .Bn - then the P(of B occurring) = P(A1)P(B|A1)+. . .P(An)P(B|An).

How about an example: Say I know (I don't know) that in the United States, 54% of the population are females and 46% of the population are males. I further know that among females, 2% have cancer, and among males it is 3%. How would I go about finding the probability that someone has cancer in the United States?

Looking at Bayes I know my exhaustive events (the events that cover the entire sample space) are P(M) and P(F). I also know that the sub-event is the P(Cancer|Male) as well as for females. Using Bayes Theorem, I can find out what P(Cancer) is. Try it.