The Expected Value of Perfect Partial Information (EVPPI) is adecision-theoretic measure of the ``cost” of uncertainty in decision making usedprincipally in health economic decision making. Despite having optimalproperties in terms of quantifying the value of decision uncertainty, the EVPPIis rarely used in practise. This is due to the prohibitive computational timerequired to estimate the EVPPI via Monte Carlo simulations. However, a recentdevelopment has demonstrated that the EVPPI can be estimated by non parametricregression methods, which have significantly decreased the computation timerequired to approximate the EVPPI. Under certain circumstances,high-dimensional Gaussian Process regression is suggested, but this can stillbe prohibitively expensive. Applying fast computation methods developed inspatial statistics using Integrated Nested Laplace Approximations (INLA) andprojecting from our high-dimensional input space allows us to decrease thecomputation time for fitting these high-dimensional Gaussian Processes fromaround 13 minutes to 10 seconds. We demonstrate that the EVPPI calculated usingthis new method for Gaussian Process regression is in line with the standardGaussian Process regression method and that despite the methodologicalcomplexity of this new method, R functions are available in the package R-INLAto implement it simply and efficiently.