Here we propose an alternative approach, which addresses the issue of new introductions, requires in general smaller computational overhead and results in the estimation of the full probability distribution for R. The method is based on the probabilistic formulation of standard SIR disease transmission models analogous to the time-series SIR (TSIR) approach [33] , which simplifies the need to reconstruct transmission chains by aggregating all infectious and susceptible individuals into classes that are assumed to mix homogeneously. A Bayesian procedure is then employed to translate the time series of case numbers into a probability distribution for epidemiological parameters. The method adopts the standard assumptions made in epidemiological compartment models with homogeneously mixing classes, and benefits from their simpler computational structure allowing efficient estimation with available sparse empirical data. The estimation method developed here has been applied once before [34] to 1918 influenza pandemic death notifications time series for San Francisco, with the purpose of comparing its performance with other conventional methods for estimating R. Here we present its full derivation, provide more details and examples, include introductions from an animal reservoir and show how the method can be used to provide statistical expectations for new case predictions. We also show how case predictions with quantified uncertainty do, in turn, define possible statistical anomalies for future case numbers, which can be used to inform surveillance and logistical management in the event of a new or continuing outbreak. As an example, we apply the method to human case data of H5N1 influenza in Vietnam and Indonesia, to produce bounds on its effective reproduction number, R, and establish a basis for its continued monitoring in real time.