Where \ hat m ( \ mathbf { s } _ 0 ) is the fitted deterministic part, \ hat e ( \ mathbf { s } _ 0 ) is the interpolated residual, \ hat \ beta _ k are estimated deterministic model coefficients ( \ hat \ beta _ 0 is the estimated intercept ), \ lambda _ i are kriging weights determined by the spatial dependence structure of the residual and where e ( \ mathbf { s } _ i ) is the residual at location { \ mathbf { s } } _ i.
32.
:: I'll add ( from a different perspective ) that random phenomena is a bad direction in which to start searching for free will . free will is not random ( in fact, there is no decent analytical definition of what free will means, and so there is no possibility of testing for or measuring it ) . when a scientist uses a random model to study human / cognitive behavior it's not because he necessarily thinks there is or isn't anything random about human / cognitive behavior, it's only because human / cognitive behavior is too subtle and complex to be handled accurately using a deterministic model under current empirical limitations .-- Ludwigs 2 07 : 10, 11 July 2010 ( UTC)
