Machine Learning: Make Your Own Recommender System (Machine Learning From Scratch Book 3) by Oliver Theobald

Author:Oliver Theobald [Theobald, Oliver]
Language: eng
Format: epub
Publisher: Scatterplot Press
Published: 2018-06-20T00:00:00+00:00

There are two elements to consider for P(B):

1) True-positives: a woman that tests positive (99%) who is pregnant (5%), and

2) False-positives: a woman that tests positive (1%) who isn’t pregnant (95%)

P(B) = (0.99 * 0.05 + 0.01 * 0.95)

Let’s now add P(B) to the equation to solve for P(A|B):

(0.05 * 0.99) / (0.99 * 0.05 + 0.01 * 0.95)

0.0495 / (0.0495 + 0.0095)

0.0495 / 0.059

= 0.8389

Using Bayes’ theorem, we’ve found that the probability of pregnancy given a positive test result P(A|B) is 83.89%, which is significantly lower than the accuracy rate (99%) when only considering pregnant women P(B|A).

This outcome crystalizes when we consider the number of false-positives in respect to the number of true-positives. If we test 1,000 women, we can expect 950 not to be pregnant (95%) and 50 who are pregnant (5%). Among the 950 women who are not pregnant, we can anticipate 9.5 false positives (950 x 0.01). Simultaneously, among the 50 women who are pregnant, 49.5 women are expected to test positive (50 x 0.99). Thus, of the 59 (9.5 + 49.5) women who test positive, 49.5/59 or 83.89% women are actually pregnant.

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