Multilayer micro-perforated/slit panels (MPP/MSP) are used to achieve broadband absorption in Architectural Acoustics. Both micro-perforated and micro-slit panels can achieve a high absorption coefficient, but the frequency bandwidth is usually narrow for single-layer panels. For this reason, the multilayer design is proposed to achieve a broadband high absorption coefficient. This work applies Bayesian inference to the design of multilayered micro-perforated/-slit panels for a given design scheme. A higher level of inference, Bayesian model selection, estimates the parsimonious number of layers needed to achieve the design scheme. The lower level of inference estimates MPP/MSP parameters once the structure of the multilayer design is chosen. Once the exact parameters and the model are given, the theoretical absorption coefficient is compared with the measurement results. The causal inference is further applied to analyze the possible reasons for the deviations between the model and the experimental data. Applying the Bayesian framework and causal inference minimizes the uncertainties and inaccuracies during the manufacture and leads to a satisfactory design.