In this talk I will present research on the efficient computation of EVPPI (Expected Value of Partial Perfect Information) and EVSI (Expected Value of Sample Information). I will start by explaining how the need for these arises from decision making under uncertainty, for example in deciding whether to fund medical research to reduce the uncertainty in identifying the best treatment for a particular condition. I will then outline our development of a Multilevel Monte Carlo method for the resulting nested expectation problems. This is joint work with Dr Howard Thom of the University of Bristol, and Dr Takashi Goda of the University of Tokyo. M.B. Giles, T. Goda. “Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI”. Statistics and Computing, 29(4):739-751, 2019. T. Hironaka, M.B. Giles, T. Goda, H. Thom. “Multilevel Monte Carlo estimation of the expected value of sample information”. SIAM/ASA Journal on Uncertainty Quantification, 8(3):1236-1259, 2020.