This paper presents a novel direction-of-arrival (DOA) estimation method for sound that utilizes sparse Bayesian estimation with a two-dimensional spatiotemporal spectrum as a transfer function. The proposed method is designed for compact microphone arrays, such as those embedded in smartphones, enabling the accurate estimation of multiple sound-source DOAs. This method leverages the sparsity of the spatiotemporal spectrum to enhance robustness and accuracy, addressing the limitations of conventional approaches based on steering vectors. Computational simulations were conducted to explore the optimal parameter settings of the method and evaluate its performance in comparison with that of a traditional method. The results showed that the proposed approach achieved higher accuracy and maintained robust performance in noisy environments. These findings highlight the potential of the method for real-world applications, including sound-source separation and noise suppression for compact devices.