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Statistical sample

As explained in Causal AI

A random sample is a dataset formed by repeatedly selecting individuals from a population according to a random sampling mechanism.

A statistical sample is a dataset formed by repeatedly selecting individuals from a population through a random sampling mechanism. Each selection follows the same procedure, and selections are independent when the sample is IID. section 2.3.1

Treat a sample as IID when:

  • Every data point is sampled in the same way. section 2.3.1
  • Whether one individual is selected does not affect another selection. section 2.3.1
  • All observations come from the same population distribution. section 2.3.1

Generating an IID sample

A probabilistic model can represent the population process and then generate repeated observations from it. In Pyro, pyro.plate("IID", 10) marks ten conditionally repeated samples; pgmpy can generate a requested sample size. section 2.3.1

How Causal AI covers it

How deep it goes
Defines random sampling and IID conditions, then connects them to stochastic data-generation code without developing sampling theory.
Examples
Uses population-selection diagrams, pgmpy generation, and a ten-observation Pyro Bernoulli sample.
What it assumes
Assumes population and probability-distribution concepts while defining sampling and IID conditions explicitly.
What you can do after
Apply it via pgmpy or Pyro to generate repeated observations from a probabilistic population model.
How it connects
Connects sampling with populations, probability distributions, independent and identically distributed data, and data-generating processes.
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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.