  Bayesian hierarchical methods implemented for small area estimation focus on
reducing the noise variation in published government official statistics by
borrowing information among dependent response values. Even the most flexible
models confine parameters defined at the finest scale to link to each data
observation in a one-to-one construction. We propose a Bayesian multiresolution
formulation that utilizes an ensemble of observations at a variety of coarse
scales in space and time to additively nest parameters we define at a finer
scale, which serve as our focus for estimation. Our construction is motivated
by and applied to the estimation of $1-$ year period employment levels, indexed
by county, from statistics published at coarser areal domains and multi-year
intervals in the American Community Survey (ACS). We construct a nonparametric
mixture of Gaussian processes as the prior on a set of regression coefficients
of county-indexed latent functions over multiple survey years. We evaluate a
modified Dirichlet process prior that incorporates county-year predictors as
the mixing measure. Each county-year parameter of a latent function is
estimated from multiple coarse scale observations in space and time to which it
links. The multiresolution formulation is evaluated on synthetic data and
applied to the ACS.
