A Bayesian approach to quantum randomness is discussed which has a firm support on pragmatic grounds. First, the algebraic features of quantum randomness are introduced and its irreducibility discussed. Then, the meaning of randomness is addressed through its relation to probability theory, concluding that it refers to the coherent and adaptive arrangement of personal uncertainty. Finally, the elements comprising the structural algebraic framework of quantum information are shown to be uncertainty encoding structures with remarkable features tightly related to those of probability assignments. 

Topics covered include principals and algebraic structures of quantum theory as applied in quantum signal processing, features of quantum randomness, quantum tomography, and both the frequentism and Bayesian theories of probability.