Randomness Testing with Bayesian Stats

According to LessWrong, one Bayesian statistician poses a challenge: if Bayesian methods are truly superior, shouldn't they handle everything classical statistics can do? She decides to test this with a concrete problem—determining if a random number generator is biased toward ones or zeros. Classical statistics reaches for p-values. The Bayesian approach uses a likelihood ratio instead. Rather than testing against a single suspected bias, it assigns equal probability to all possible biases and lets the data do the learning. The mathematics works out elegantly. After observing the bit sequence, the likelihood ratio reveals whether the generator passes or fails. And remarkably, this approach is not only correct—it's simpler and more intuitive than the classical method. The technique scales naturally to harder problems, too: block frequencies, runs, multi-bit patterns, autocorrelation. All follow the same logic. The upshot: Bayesian statistics doesn't just match frequentist methods. Often, it surpasses them in clarity and elegance.

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