Seminar by Dr. Kwangmin Lee

【Date&Time】
12 August, 2026 (Wednesday) 11:00-12:00
Admission Free, No Booking Necessary
【Place】
D208, The Institute of Statistical Mathematics
【Speaker】
Kwangmin Lee (Chonnam National University)
【Title】
Bayesian Signal-Shape Testing in Sparse Mixture Models
【Abstract】
Scientific experiments often generate data in which a signal of interest is embedded in a dominant background. A motivating example is random circuit sampling for quantum supremacy, where the ideal-circuit component may be obscured by samples produced by noisy or faulty circuit executions. When the signal proportion is small, inference on the　signal component becomes statistically delicate. We study this problem through a sparse two-component mixture model in which a known background distribution is mixed with an unknown signal distribution. Our goal is to test whether the irreducible signal component has a prescribed target shape. Because the signal component may be weak, non-rejection of a conventional goodness-of-fit null can be misleading: it may indicate either genuine agreement with the target signal shape or simply insufficient information to distinguish alternatives. We formalize this limitation by deriving an oracle information boundary governed by the effective amount of signal information, determined jointly by the sample size and the signal proportion. This boundary separates two regimes: one in which the signal shape can in principle be identified from the data, and one in which it cannot, regardless of the procedure used. Motivated by this limitation, we propose a Bayesian test based on the log Bayes factor. Unlike a conventional level-α test, which must choose one of the two hypotheses, the log Bayes factor provides a continuous measure of relative evidence. Values close to zero indicate that the data provide insufficient evidence to distinguish the hypotheses. Our asymptotic analysis makes this interpretation precise: the log Bayes factor remains bounded in probability in the regime identified by the oracle information boundary as intrinsically unresolvable, while it diverges in the correct direction in the complementary resolvable regime. We illustrate the method using random circuit sampling data from a quantum supremacy experiment.