Challenge 2: Bayes' Theorem
In the world of probability and statistics, Bayesian thinking offers a framework for understanding the probability of an event based on prior knowledge. It contrasts with the frequentist approach, which determines probabilities based on the long-run frequencies of events. Bayes' theorem is a fundamental tool within this Bayesian framework, connecting prior probabilities and observed data.
Swipe to start coding
Imagine you are a data scientist working for a medical diagnostics company. Your company has developed a new test for a rare disease. The prevalence of this disease in the general population is 1%. The test has a 99% true positive rate (sensitivity) and a 98% true negative rate (specificity).
Your task is to compute the probability that a person who tests positive actually has the disease.
Given:
- P(Disease) = Probability of having the disease =
0.01 - P(Positive|Disease) = Probability of testing positive given that you have the disease =
0.99 - P(Negative|No\ Disease) = Probability of testing negative given that you don't have the disease =
0.98
Using Bayes' theorem:
P(Disease|Positive) = P(Positive|Disease) * P(Disease) / P(Positive)
Where P(Positive) can be found using the law of total probability:
P(Positive) = P(Positive|Disease) * P(Disease) + P(Positive|No Disease) * P(No Disease)
Compute P(Disease|Positive), the probability that a person who tests positive actually has the disease.
Lösning
Byt till skrivbordet för praktisk övningFortsätt där du är med ett av alternativen nedanTack för dina kommentarer!
Byt till skrivbordet för praktisk övningFortsätt där du är med ett av alternativen nedan