  The Macdonald process is a stochastic process on the collection of partitions
that is a $(q,t)$-deformed generalization of the Schur process. In this paper,
we approach the Macdonald process identifying the space of symmetric functions
with a Fock representation of a Heisenberg algebra. By using the free field
realization of operators diagonalized by the Macdonald symmetric functions, we
propose a method of computing several correlation functions with respect to the
Macdonald process. It is well-known that expectation value of several
observables for the Macdonald process admit determinantal expression. We find
that this determinantal structure is apparent in free field realization of the
corresponding operators and, furthermore, it has a natural interpretation in
the language of free fermions at the Schur limit. We also propose a generalized
Macdonald measure motivated by recent studies on generalized Macdonald
functions whose existence relies on the Hopf algebra structure of the
Ding--Iohara--Miki algebra.
