The use of hydrogen peroxide as an oxidizing agent becomes increasingly important in chemistry. The example of vegetable oil epoxidation is an excellent illustration of the potential of such an agent. This reaction is traditionally performed by Prileschajew oxidation, i.e., by the in situ production of percarboxylic acids. Drawbacks of this approach are side reactions of ring-opening and thermal runaway reactions due to percarboxylic acid instability. One way to overcome this issue is the direct epoxidation by hydrogen peroxide by using γ-alumina. However, the reaction mechanism is not elucidated: does hydrogen peroxide decompose with alumina or oxidize the hydroxyl groups at the surface? The kinetics of hydrogen peroxide consumption with alumina in homogeneous liquid and heterogeneous liquid-liquid systems was investigated to reply to this question. Bayesian inference was used to determine the most probable models. The results obtained led us to conclude that the oxidation mechanism is the most credible for the heterogeneous liquid-liquid system.