Independent and identically distributed

As explained in Causal AI

Independent and identically distributed data are observations that are mutually independent and share the same probability distribution.

IID data form a random sample when each observation is sampled from the same population distribution and each selection occurs independently of the others. section 2.3.1

The assumption separates two properties:

• Identically distributed means every observation is sampled in the same way from the same population distribution. section 2.3.1
• Independent means selecting one observation does not affect whether another observation is selected. section 2.3.1
• Generating observations from a population model can emulate IID sampling, although machine-learning data is often not IID. section 2.3.1

Generating IID observations

In Pyro, pyro.plate marks repeated IID sampling: with pyro.plate("IID", 10), the model samples ten Bernoulli observations conditioned on the same generated quantity. section 2.3.1

Figure 2.19 Creating a random sample by random selection from a population. Individuals are randomly selected from the population such that the sample distribution resembles the population distribution. The sample is identically and independently distributed (IID), meaning that sample members are selected the same way, and whether an individual is selected doesn’t depend on whether another individual was selected.

Visualizes random selection from a population and shows how identical sampling and independent selection produce an IID sample. section 2.3.1

How Causal AI covers it

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 it assumes

Assumes familiarity with populations and probability distributions while defining sampling and IID structure explicitly.

What you can do after

Apply it via pgmpy or Pyro to generate IID samples from a probabilistic model.

How it connects

Connects sampling, probability distributions, stochastic processes, data-generating processes, causal modeling, and statistical independence tests.

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Also explained in

• 

  liveBookmanning.com
  Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIThe IID principle is the assumption that observations are independently sampled and follow the same probability distribution.
• 

  liveBookmanning.com
  Experimentation for EngineersThe iid assumption states that measurements are independent of one another and drawn from the same probability distribution.

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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.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.