Md. Asif Uddin

    Chapter 1 VI.1

    Correlation and Causation

    The same joint distribution can be produced by different causal structures, so data alone cannot decide between them.

    The same joint distribution can come from different causal structures.

    How this chapter is built

    M2Substantive

    The derivations are the chapter. A reader who skips the algebra has not learned it.

    basics2/9what the words mean
    concept2/2what to picture
    theory0/2why it works, and when it does not
    mathematics0/9derive it, then compute it
    practice0/6build it, break it, read the papers

    Five strands, not one. Mathematics is the spine; the other four are the body. A chapter cannot pay its way out of teaching with problems, nor out of problems with teaching.

    Before you start

    The problem

    Every model in Books I to V estimates an association. A decision requires knowing what would happen under an action, and no amount of predictive accuracy answers that question. The gap has to be named before it can be closed.

    The same model on three populationsOne model evaluated on an internal held-out set, on data from a different scanner at the same hospital, and on data from another institution. The internal number is the one that appears in the abstract and the external one is the one that predicts deployment.the same weights, three populationsinternal test0.94same hospital, new scanner0.87external hospital0.71Everything upstream can be right — the split, the calibration, the augmentation — and this gap opens,because every one of those checks drew from the same distribution the model was fitted on.The only measurement that answers it is data from an institution outside the training set.
    Fig. 1 — One model on three populations. Every internal check drew from the distribution the model was fitted on.

    What this chapter covers

    • Correlation
    • Causation
    • Confounding
    • Prediction versus intervention

    Apparatus

    The mathematics this chapter leans on, held in Book 0 so it can be assumed here without being taught here. Not a gate — follow a link when a step stops making sense.

    Distributions, discrete and continuous 0.PR.01 · Bayes' rule 0.PR.04 · Conditional independence 0.PR.05

    Notation

    • X (random)A random variable
    • 𝔼Expectation
    • ⫫Statistical independence

    Propositions

    Not yet written. The topics above are the plan for this chapter; each will become a proposition with its own figure.

    Worked problems

    0/3 problems0/3 variants0/6 exercisesowes 9 more

    Not yet written. At M2 this chapter owes 3 worked problems across 3 distinct variants, and 6 exercises, every one with a published solution. The build enforces that from the day the chapter is marked published.