Title: INFERENCE, PREDICTION, AND ENTROPY RATE OF CONTINUOUS-TIME, DISCRETE-EVENT PROCESSES. Abstract: The inference of models, prediction of future symbols, and entropy rate estimation of discrete-time, discrete-event processes is well-worn ground. However, many time series are better conceptualized as continuous-time, discrete-event processes. Here, we provide new methods for inferring models, predicting future symbols, and estimating the entropy rate of continuous-time, discrete-event processes. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network’s universal approximation power. Based on experiments with simple synthetic data, these new methods seem to be competitive with state-of- the-art methods for prediction and entropy rate estimation as long as the correct model is inferred.