Purchase Solution

Bayes Analysis Problem

Not what you're looking for?

Ask Custom Question

Assume that a patient is believed to have one of two diseases, denoted by D1 and D2 with P(D1)=0.40 and P(D2)=0.60 and that medical research has determined the probability associated with each symptom that may accompany the diseases. Suppose that given diseases D1 and D2, the probabilities that the patient will have symptom S1, S2 or S3 are as sollows:

Symptoms
S1 S2 S3
D1 0.15 0.10 0.15
D2 0.80 0.15 0.03

After a certain symtom is found to be present, the medical diagnosis will be aided by finding the revised probability of each disease. Compute the posterior probability of each disease given the following medical findings:

a. The patient has symptom S1
b. The patient has symptom S2
c. The patient has symptom S3
d. For the patient with symptom S1 in part a), supposed we also find symptom S2. What are the revised probabilities of D1 and D2?
e. If the probabilities for D1 and D2 are 0.25 and 0.75, respectively, compute the revised probability in part d).

Purchase this Solution
Solution Summary

This Solution contains calculations to aid you in understanding the Solution to these questions.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

View More Free Quizzes
Related BrainMass Solutions

  • Decision Making

    True False In a decision problem where we wish to use Bayes' theorem to calculate posterior probabilities, we should always begin our analysis with the assumption that all states of nature are equally likely, and use the sample information

  • Quantitative Methods: Multiple Choice Questions

    Sensitivity analysis information in computer output is based on the assumption of: A. no coefficient change B. one coefficient change C. two coefficient change D. all coefficients change Answer: B. one coefficient change For sensitivity analysis

  • Bayes' Theorem for Probability Revision

    144567 Bayes' Theorem for Probability Revision Set up a short problem related to your work environment to calculate the probability(ies) of an event happening. Then use Bayes' Theorem to revise the probability. Show all your work.

  • Bayesian Probability Theory

    An analysis is given to determine whether this is feasible.

  • Probability - Bayes' Theorem

    (Assume that men and women occur in equal numbers) Now if we have to solve using Bayes' Theorum, how are we supposed to set the problem up and represent them as variables? Solution.

  • Bayesian Statistics

    What is the difference between Bayes' and Empirical Bayes' approaches? Suppose I would like to determine my "true" free-throw percentage.

  • Probability : Bayes' Rule

    |smoker) Therefore we will have: P(smoker|ectopic)= P(ectopic|smoker)*0.32/(P(ectopic|smoker)*0.32+1/2P(ectopic|smoker)*0.68) or: P(smoker|ectopic)= 0.32/(0.32+0.68/2)= 0.32/0.66= 0.48 ---> 48% Bayes' rule is used to solve a probability problem

  • Decision Under Uncertainty - Bayes' Theorem

    The problem can be understood as follows Pr (Bus)= Pr(Car)= Pr(train)= 1/3 Pr (late | car)= 0.5 Pr (late | train)= 0.01 Pr (late | train)= 0.2 We have to find out Pr(car| late).

  • Problems: Probability, Markov Chain, Baye's Theorem

    269039 Problems: Probability, Markov Chain, Bayes' Theorem 1. A bag contains 10 red, 12 green, and 8 yellow marbles.

  • Bayes's theorem

    Bayes' theorem (also known as Bayes' rule or Bayes' law) is a result in probability theory that relates conditional probabilities. If A and B denote two events, P(A|B) denotes the conditional probability of A occurring, given that B occurs.

View More Related Solutions