Before revision:  We show that a subclass of the recently developed framework of Bayesian predictive synthesis fits within this class. Theoretical properties are examined and we show that non-linear synthesis improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions that are met in most real applications.
After revision:  We show that a subclass of BPS is the latter. With regard to expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions that are met in most real applications.