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Previous research in statistical post-processing has found systematic deficiencies in deterministic forecast guidance. As a result, ensemble forecasts of sensible weather variables often manifest biased central tendencies and anomalous dispersion. In this way, the numerical weather prediction community has largely focused on upgrades to upstream model components to improve forecast performancethat is, innovations in data assimilation, governing dynamics, numerical techniques, and various parameterizations of subgrid-scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to ensemble model output statistics. This technique directly parameterizes meteorological phenomena with probability distributions that describe the intrinsic structure of observable data. Bayesian posterior beliefs in model parameter were conditioned on previous observations and dynamical predictors available outside of the parent ensemble. An adaptive variant of the random-walk Metropolis algorithm was used to complete the inference scheme with block-wise multiparameter updates. This produced calibrated multivariate posterior predictive distributions (PPD) for 24-hour forecasts of diurnal extrema in surface temperature and wind speed. These Bayesian PPDs reliably characterized forecast uncertainty and outperformed the parent ensemble and a classical least-squares approach to multivariate multiple linear regression using both measures-oriented and distributions-oriented scoring rules.