A data-generating process is the physical mechanism that creates observed data, together with the uncertainty represented by its data-generating distribution. Its laws usually remain unknown, so observed samples provide only an empirical approximation. section 1.5.1
Coin tosses and empirical evidence
A coin-toss process may have an unknown probability p of heads. Five tosses yielding H, H, T, T, T produce an empirical distribution assigning probabilities 2/5 and 3/5; larger samples tend toward the generating distribution. section 1.5.1
Use the distinction between generating and empirical distributions to:
- Identify variables involved in the data-generation process before drawing a causal graph, consulting domain experts to reduce omitted-confounder risk. section 3.2
- Apply the adjustment formula to the empirical distribution in practice, giving each observed row weight 1/n as a finite-sample approximation. section 4.2.1
Table 1.1 Empirical distribution from a sample of H, H, T, T, T
|
Outcome
|
Probability
|
|---|---|
|
H
|
2/5
|
|
T
|
3/5
|
Compare observed frequencies with the empirical probabilities produced by five coin tosses. section 1.5.1
