Uses likelihood ratios instead of p-values, integrating over all possible biases with a uniform prior?

Uses likelihood ratios instead of p-values, integrating over all possible biases with a uniform prior

Closed-form solution derived for likelihood ratio of biased vs perfect RNG given count of ones?

Closed-form solution derived for likelihood ratio of biased vs perfect RNG given count of ones

For n=1000, ratio strongly favors bias at extremes (e.g., 0 or 1000 heads) and neutral near 500 heads

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LessWrong AI June 27, 2026

⚡One integral replaces infinite p-values in randomness tests

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Key Points

Uses likelihood ratios instead of p-values, integrating over all possible biases with a uniform prior
Closed-form solution derived for likelihood ratio of biased vs perfect RNG given count of ones
For n=1000, ratio strongly favors bias at extremes (e.g., 0 or 1000 heads) and neutral near 500 heads

Bayesian hypothesis testing offers a principled alternative to p-values for RNG validation and beyond.