We analyzed the absorption spectrum of a Cu₂O thin film sandwiched by paired MgO plates with the Metropolis algorithm of Bayesian estimation to estimate the energy shift of a yellow excitonic band gap. In the absorption spectrum, discrete excitonic resonant transitions with homogeneous and inhomogeneous widths are superimposed upon the tail parts of excitonic continuum and band-to-band absorption bands. On the basis of the Metropolis samplings with 2.5 million steps after sufficient burn-in steps, the spectral parameters of the excitonic resonant transitions can be estimated satisfactorily with a high degree of accuracy. In particular, we demonstrated that the yellow excitonic band gap in the Cu₂O thin film shifts to the lower energy side than that of Cu₂O bulk crystals. This result is consistent with the stress relaxation model for such Cu₂O thin films, which was reported in Eur. Phys. J. B 86, 194 (2013).