The ability to forecast the production of power by photovoltaic (PV) systems accurately and reliably is of major importance for the appropriate management of future electrical distribution systems. Several forecasting methods have been proposed in the relevant literature, and many indices have been used to quantify the quality of the forecasts. The methods can provide either deterministic or probabilistic forecasts; the latter seem to be the most appropriate to take into account the unavoidable uncertainties of PV power production. Similarly, indices were used to quantify the quality of both deterministic and probabilistic forecasting methods, but they usually do not account for the economic consequences of forecasting errors. In this paper, two advanced probabilistic forecasting approaches based on the Bayesian inference method are applied to the short-term forecasting of PV power production. Moreover, new probabilistic indices were proposed with the aim of comparing the probabilistic forecasting methods in such way that the value of the forecast is not included only by the users in their decision-making process; instead, it is partially anticipated by the forecasters in their quality-assessment process. Numerical applications also are presented to provide evidence of the performances of the Bayesian-based approaches and the probabilistic indices that were considered.