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Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution. As this tag is ambiguous, please consider [survey-sampling] for the former and [monte-carlo] or [simulation] for the latter. For questions regarding creating random samples from known distributions, please consider using the [random-generation] tag.
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A non-i.i.d observations in a Bayesian inference problem
Suppose we have a simple Bayesian network which has two variables $x$ and $y$, $x$ is the parent of $y$. We sample $M$ $x$s independently based on $P(x)$, named $x_1,\ldots,x_M$, and for every $x_i$, …