Independent and identically distributed
Independent and identically distributed describes random variables that are mutually independent and share the same probability distribution.
Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI
The IID principle is the assumption that observations are independently sampled and follow the same probability distribution.
- How it is used
- Guides assumptions about tabular rows and supports random sampling for cross-validation folds.
- How deep it goes
- Defines independence and identical distribution, gives examples, and stops short of formal mathematical derivation.
- Examples
- Uses repeated coin flips, multi-store sales, school classes, and a visual comparison of IID and non-IID sequences.
- What you can do after
- Evaluate whether tabular observations justify random sampling and randomly constructed cross-validation folds.
Causal AI
Independent and identically distributed data are observations that are mutually independent and share the same probability distribution.
- How it is used
- Models random samples from a population so generative processes can stand in for repeated sampling.
- How deep it goes
- Defines identical sampling and independent selection, then connects the assumption to generative code and notes machine-learning violations.
- Examples
- Uses random population selection, pgmpy sample generation, and Pyro's pyro.plate.
- What you can do after
- Apply it via pgmpy or Pyro to generate IID samples from a probabilistic model.
Read how Causal AI explains independent and identically distributed →
Experimentation for Engineers
The iid assumption states that measurements are independent of one another and drawn from the same probability distribution.
- How it is used
- Supports A/B-test standard-error estimation and normal z-score reasoning.
- How deep it goes
- Defines independence and identical distribution, then demonstrates repeated measurements and their false-positive consequences.
- Examples
- Uses constant and partially repeated measurement arrays produced by overly frequent sampling.
- What you can do after
- Diagnose/debug with collection audits, replication, reverse A/B tests, and holdouts before accepting experimental results.
Read how Experimentation for Engineers explains independent and identically distributed →
Related concepts
- posterior probabilityuses · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.
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