MAP's geostatistical models are based on Gaussian processes.
Gaussian processes (GPs) are probability distributions for functions. In this webpage, the statement 'random function 
has a GP distribution with mean 
and covariance 
' is denoted
The input space is usually obvious from context; in geostatistics, it is either a subset of the earth's surface, or the Cartesian product of such a region and a time interval. The term `Gaussian process' is often applied, in this webpage and elsewhere, to both the probability distribution of 
and the random variable 
itself.
With these definitions, the definition of the GP above is that, for any finite vector 
, whose elements are all in the domain 
of 
,
where 
evaluates to a vector and 
evaluates to a square, symmetric matrix. That is, if the function 
is regarded as a random vector in a possibly infinite-dimensional vector space, all of its finite-dimensional marginals are multivariate normal random variables.
The mean vectors and covariance matrices of these marginal distributions are obtained by evaluating the mean and covariance of 
. Because the covariance matrices must all be positive semidefinite, the covariance 
must have the property that 
is positive semidefinite for any 
. Such covariances are called `positive definite functions'.
Prevalences, such as Plasmodium falciparum prevalence, take values between 0 and 1. Gaussian processes can easily be used to construct priors for such fields using link functions, for example:
