  The main result of the paper is a construction of a five-parameter family of
new bases in the algebra of symmetric functions. These bases are inhomogeneous
and share many properties of systems of orthogonal polynomials on an interval
of the real line. This means, in particular, that the algebra of symmetric
functions is embedded into the algebra of continuous functions on a certain
compact space Omega, and under this realization, our bases turn into orthogonal
bases of weighted Hilbert spaces corresponding to certain probability measures
on Omega. These measures are of independent interest --- they are an
infinite-dimensional analogue of the multidimensional q-Beta distributions. Our
construction uses the big q-Jacobi polynomials and an extension of the
Knop-Okounkov-Sahi multivariate interpolation polynomials to the case of
infinite number of variables.
