An integrated Bayesian least-squares-support-vector-machine factorial-analysis (B-LSVM-FA) method is developed through integrating techniques of Bayesian inference, least squares support vector machine (LSVM), and factorial analysis (FA) into a general framework. B-LSVM-FA has advantages in: (i) capturing the complicated nonlinear relationship between input factors and streamflow, (ii) optimizing the key parameters of LSVM through a maximum posterior density estimation, and (iii) quantifying the contributions of individual and interactive effects of multiple factors to streamflow variation. B-LSVM-FA is then applied to inferring the changes in inflow from the Amu Darya to the Aral Sea (named as IATA). Results obtained cannot only identify the key impact factors reducing IATA during the period of 1960–2015, but also predict future trends in IATA for 2020–2050. Comparing to the conventional ANN, SVM and LSVM, the proposed method performs better in describing the IATA changes with anthropogenic, hydrometeorological, and ecological factors in terms of NSE, RMSE, and PBS. Results disclose that the major factors affecting IATA at annual/seasonal scale are upstream streamflow, agricultural water use in Uzbekistan, reservoir water storage, and evapotranspiration. The significant differences in the contributions of main factors to IATA at seasonal scale are observed because each season has unique characteristics of human activities, meteorological conditions, and vegetation coverages. In order to seek the feasible strategies of recovering the IATA level in the future, 162 scenarios based on ensemble prediction are analyzed. Results indicate that the IATA would restore to its 1970s condition if the drip irrigation rate reaches 50% at the end of 2050, and the reservoir water storage level reduces to the average value of 1960–1970. The findings can provide valuable suggestions for decision makers to increase IATA, and thus ameliorating the ecological crisis within the Aral Sea Basin.