Md. Asif Uddin

    Chapter 2 VIII.2

    Problem Formulation

    A research question becomes tractable when it is written as an estimand: a quantity, on a population, under a condition.

    A question becomes tractable when it is written as an estimand.

    How this chapter is built

    M1Definitional

    Mathematics defines, and stops there. At most three displayed equations, no derivations.

    basics2/6what the words mean
    concept2/2what to picture
    theory0/1why it works, and when it does not
    mathematics0/4derive it, then compute it
    practice0/5build 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

    Most projects fail before any model is trained, because the question was never stated precisely enough to be answered. Writing it as an estimand is what exposes that.

    A model as a parameterised functionAn input enters a box marked f of x semicolon theta and an output leaves it. A second arrow enters the box from below carrying the parameters theta, drawn as a stack of adjustable values. The input arrives from the world; the parameters are chosen by training.the world suppliesthe model returnsxinputf( x ; θ )fixed formŷpredictionθ — the parameters, and the only thing training may change
    Fig. 2 — A model as a function of two arguments. The input comes from the world; the parameters are the only part training is allowed to change.

    What this chapter covers

    • Identifying a problem
    • Defining the research question
    • Hypothesis
    • Assumptions
    • Baselines
    • Evaluation

    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.

    Estimators, bias and variance 0.ST.01

    Notation

    • 𝔼Expectation
    • θ̂An estimate, as against the quantity it estimates
    • θAll parameters of a model, taken together

    Propositions

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

    Worked problems

    0/1 problems0/1 variants0/3 exercisesowes 4 more

    Not yet written. At M1 this chapter owes 1 worked problems across 1 distinct variants, and 3 exercises, every one with a published solution. The build enforces that from the day the chapter is marked published.