If a Monte Carlo copy is conditionally i.i.d. with the data given a latent variable, the empirical p-value obeys P(p_m≤α)≤2α for any finite m and no mixing assumptions.
Markov chain monte carlo significance tests
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Monte Carlo testing: non-asymptotic guarantees without joint exchangeability
If a Monte Carlo copy is conditionally i.i.d. with the data given a latent variable, the empirical p-value obeys P(p_m≤α)≤2α for any finite m and no mixing assumptions.