In this study, spatial only, and spatio-temporal Bayesian Maximum a Posteriori (MAP) methods and an another spatio-temporal method, the Kalman filter approach, are used to solve the inverse electrocardiography (ECG) problem. Training sets are used to obtain the required a priori information for all methods. Two different approaches are employed to calculate the state transition matrix (STM), which maps the epicardial potentials in two consecutive time instants in the Kalman filter method. The first one uses the training set itself to iteratively estimate the STM, and the second one uses the candidate solution obtained using the spatial only Bayesian MAP estimate. The results are quantitatively compared using the correlation coefficient, the relative difference measurement star, the computation time measures, and qualitatively compared using spatial and temporal displays of epicardial potentials.