Chapter 16 Introduction to Bayes Theorem

Question 1

P(A|B) ≠ P(B|A)
True/False P 150

Answer 1

True

Question 2

One conditional probability can be calculated using the other conditional probability. This is called Bayes Theorem, how is it formulated? P 150

Answer 2

P(A|B) = P(B|A) * P(A) / P(B)

Question 3

What is the definition of Bayes Theorem? P 150

Answer 3

Bayes Theorem: Principled way of calculating a conditional probability without the joint probability.

Question 4

It is often the case that we do not have access to the denominator directly, e.g. P(B). We can calculate it an alternative way, for example: ____This gives a formulation of Bayes Theorem that uses the alternate calculation of P(B). P 150

Answer 4

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A) P(A|B) = P(B|A) × P(A) /(P(B|A) × P(A) + P(B|not A) × P(not A))

Question 5

P(B|not A) = 1 − P(not B|not A) True/False P 150

Answer 5

True

Question 6

What are the names of the below terms, in Bayes Theorem? P 151
ˆ P(A|B)
ˆ P(A)
ˆ P(B|A)
ˆ P(B)

Answer 6

Posterior probability, Prior probability, Likelihood, Evidence

Question 7

We can also think about the calculations in the terms of a binary classifier. What are each of the below probabilities’ equivalent in terms of binary classification? P 151
ˆ P(not B|not A)
ˆ P(B|not A)
ˆ P(not B|A)
ˆ P(B|A)
ˆ P(A|B)

Answer 7

ˆ P(not B|not A): True Negative Rate or TNR (specificity). ˆ P(B|not A): False Positive Rate or FPR. ˆ P(not B|A): False Negative Rate or FNR. ˆ P(B|A): True Positive Rate or TPR (sensitivity or recall). ˆ P(A|B): Positive Predictive Value or PPV (precision).

Look at it like: P(pred 1 given ground truth 0)= FP/TN+FP= P(B| not A)= FPR
P(truth 1 given pred 1)= TP/(TP+FP)= Precision

                       B(pred)
	      	            0  1
                      0 TN FP
          A(truth)  
                      1 FN TP

Question 8

How may we re-state the calculation using these terms in terms of binary classification? P 151
P(A|B) = P(B|A) × P(A) /(P(B|A) × P(A) + P(B|not A) × P(not A))

Answer 8

P P V = T P R × P(A) /(T P R × P(A) + F P R × P(not A))