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The seasonal autoregressive integrated moving average (SARIMA) model is one of the popular univariate time-series models in the field of short-term traffic flow forecasting. The parameters of the SARIMA model are commonly estimated using classical (maximum likelihood estimate and/or least-squares estimate) methods. In this paper, instead of using classical inference the Bayesian method is employed to estimate the parameters of the SARIMA model considered for modeling. In Bayesian analysis the Markov chain Monte Carlo method is used to solve the posterior integration problem in high dimension. Each of the estimated parameters from the Bayesian method has a probability density function conditional to the observed traffic volumes. The forecasts from the Bayesian model can better match the traffic behavior of extreme peaks and rapid fluctuation. Similar to the estimated parameters, each forecast has a probability density curve with the maximum probable value as the point forecast. Individual probability density curves provide a time-varying prediction interval unlike the constant prediction interval from the classical inference. The time-series data used for fitting the SARIMA model are obtained from a certain junction in the city center of Dublin. [ABSTRACT FROM AUTHOR]