Скачать или смотреть Understanding R's set.seed() and Random States: Can Different Seeds Share Randomness?

Explore how R's random seed system works and whether different seeds can produce overlapping random states or identical random numbers. Learn best practices for simulation reproducibility.
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Introduction

When running simulations in R, it's common to control randomness using set.seed(), often setting a new seed for each simulation run. For example:

[[See Video to Reveal this Text or Code Snippet]]

An alternate approach is setting one seed and running multiple repetitions:

[[See Video to Reveal this Text or Code Snippet]]

A natural question arises: Can different seeds lead to partially identical random states or random number overlap?



Do Different Seeds Produce Overlapping Random States?

Different seeds initialize the random number generator (RNG) state uniquely.

It is highly unlikely that two distinct seeds produce the exact same RNG state.

However, identical random numbers may appear coincidentally across sequences generated from different seeds. RNGs produce deterministic but pseudorandom sequences.

Example (hypothetical):

[[See Video to Reveal this Text or Code Snippet]]

Here the numbers 0.276 and 0.58 appear in both sequences, but this is by chance, not because the RNG states overlap.



Why Sequential Seeds May Not Yield Independent Runs

A common pitfall is generating multiple simulation values using sequential seeds, like:

[[See Video to Reveal this Text or Code Snippet]]

This approach:

Does not guarantee independence between generated numbers.

May violate assumptions in analysis, e.g., when calculating confidence intervals, which typically assume independent samples.

In contrast, using a single seed and generating all random variates in one sequence:

[[See Video to Reveal this Text or Code Snippet]]

produces values that pass standard independence tests.



Best Practices for Simulation Reproducibility

Avoid setting a new seed for each random number in a loop. Instead, set the seed once before running a simulation.

If you need reproducible access to individual runs:

Run simulations sequentially from one seed.

To replicate a particular outcome, you can store RNG states (.Random.seed) periodically.

To reproduce the kth simulation:

Restore the closest saved RNG state before k.

Advance the RNG state by running the simulation fewer times instead of resetting seeds repeatedly.

Note: The RNG state in R is relatively large (~2500 bytes), so storing many states requires significant space.



Summary

Different set.seed() values create unique RNG states with minimal risk of overlap.

Identical random numbers appearing with different seeds are coincidental, not due to shared RNG states.

Repeatedly setting sequential seeds for simulations can lead to undesirable dependencies.

The recommended way is to use one seed, generate all random numbers in sequence, and save RNG states if intermediate reproducibility is needed.

This approach ensures the statistical independence needed for valid inference and the reproducibility vital for simulation work.