Bayes’ Theorem Flashcards
What is Bayes’ theorem used for?
Bayes’ theorem is used to calculate the probability of an event based on prior knowledge of conditions and new information that might be related to the event.
Can be used in Predictive Analytics models.
In Bayes’ theorem, what does P(A|B) represent?
P(A|B) represents the conditional probability of event A given event B.
Said another way: conditional probability of A in the face of evidence B.
What is the formula for Bayes’ theorem?
P(A|B) = (P(B|A) * P(A)) / P(B)
This form is used when there is only 1 predictor.
Generalized form is more complex. E = evidence, ie any number of predictors, and Dj is the set of all diseases - this is from lecture 4D-1 slide 12:
Which of the following is not an assumption of Bayes’ Theorem?
A. One predictor can only explain one outcome.
B. Diseases are predictors, and patient findings are outcomes.
C. There is no relationship between different predictors for a given outcome.
B. (It is written backwards)
Assumptions of Bayes’ theorem:
-Mutual exclusivity of conditions = one predictor can only explain one outcome
-Commonly used in diagnostic models = patient findings are predictors, and diseases diagnosed are outcomes.
-Conditional independence of predictors = no relationship between different predictors for a given outcome.
Note that these assumptions are often not true in the real world.
Which of the following is a limitation of Bayesian statistics for diagnosis?
A. Findings in a disease are usually not conditionally independent.
B. Diseases are mutually exclusive.
C. When multiple findings are important for a diagnosis, the computations become simpler.
Answer: A. Findings in a disease are usually not conditionally independent.
B. Is wrong because diseases are often not mutually exclusive
C. Is wrong because the computations become more complex with multiple predictors.
