MAS8384: Bayesian Methodology

Clement Lee

2024-09-16

Icebreaker

  • A 40-year-old woman has a mammogram (screening) as a routine checkup.

  • Her test result is abnormal.

  • What is the probability she actually has breast cancer?
    • 10% of women get abnormal results (whether cancer is present or not).
    • 80% of breast cancer patients get abnormal results.

 

source: https://breastcancersupport.org.uk/

Icebreaker

  • A 40-year-old woman has a mammogram (screening) as a routine checkup.

  • Her test result is abnormal.

  • What is the probability she actually has breast cancer?
    • 10% of women get abnormal results (whether cancer is present or not).
    • 80% of breast cancer patients get abnormal results.
    • 0.4% of women have breast cancer.

 

source: https://breastcancersupport.org.uk/

Bayes rule

  • \(0.004 \times 0.8 / 0.1 = 0.032\)

  • Prior knowledge: breast cancer prevalence

  • Data: abnormal mammogram (for the woman)

  • Outcome: breast cancer probability (for the woman)

  • Counterintuitive:

    • If breast cancer \(\rightarrow\) high chance of abnormal result (80%)
    • If abnormal result \(\rightarrow\) low chance of breast cancer (3.2%)

 

Another example

In this module

  • Same goal: obtain the posterior
    • that combines data & prior knowledge
  • More complex models and data
    • with the help of computational statistics
    • Markov chain Monte Carlo
  • Want to know more?

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