Classical experiments have shown that sensory neurons carry information about ongoing decisions during random-dot motion discrimination tasks [1, 2]. These conclusions are based on the receiver-operating-characteristic (ROC) applied to single-cell recordings, which assumes the presence of a second hypothetical "anti-neuron". Furthermore, ROC analysis is by definition a measure of the average correlation between neuronal activity and stimulus/decisions. These limitations make ROC analysis unsuitable to study information about stimuli and decisions in neuronal populations on a trial by trial basis. In this study, using Poisson-like decoders, we inferred the information that a pair of motion selective MT neurons carries about the direction of motion of a random-dot stimulus presented to a monkey and about the ongoing formation of the decision of the animal. We found that Poisson-like decoders outperformed ROC analysis in both predicting stimulus and decision, with the predictive power of the Poisson-like decoders being twice that of the ROC analysis when decoding decisions. Because our framework is fully Bayesian, we could also detect signals that correspond to the belief that the animals have about their decisions, and track the time evolution of those signals. Our theory explains well-known behaviors in the meta-cognition literature such as underconfidence in easy trials, and sets a basis to study decision confidence in decision making using multielectrode recordings.