5.X.2. Statement of Bayes’ Theorem

Try these first

1. 1.

   What is Bayes' Theorem used for?

   Hint

   Think about how we revise our guesses when we get more information.

2. 2.

   What is the formula for Bayes’ Theorem?

   Hint

   Remember the structure: Posterior is influenced by Likelihood.

3. 3.

   What does Bayes' Theorem calculate?

   • The probability of event A
   • The prior probability
   • The posterior probability of event A based on evidence B

   Hint

   Think about how we adjust our beliefs with new findings.

4. 4.

   True or False: Bayes' Theorem can be used in machine learning.

   • True
   • False

   Hint

   Consider the contexts where probabilistic models are applied.

5. 5.

   A clinical test has a 90% sensitivity and 80% specificity. The disease prevalence is 5%. How would you compute the probability of actually having the disease after a positive test result?

   Hint

   Ensure you factor in the specificity for false positives.

6. 6.

   In a machine learning context, if a certain algorithm predicts a class with 85% accuracy, and the class prevalence is 30%, what would be the posterior probability of the class given a positive prediction?

   Hint

   Break down accuracy into its components to understand true positives vs. false positives.