  In this article we perform an asymptotic analysis of parallel Bayesian
logspline density estimators. Such estimators are useful for the analysis of
datasets that are partitioned into subsets and stored in separate databases
without the capability of accessing the full dataset from a single computer.
The parallel estimator we introduce is in the spirit of a kernel density
estimator introduced in recent studies. We provide a numerical procedure that
produces the normalized density estimator itself in place of the sampling
algorithm. We then derive an error bound for the mean integrated squared error
of the full dataset posterior estimator. The error bound depends upon the
parameters that arise in logspline density estimation and the numerical
approximation procedure. In our analysis, we identify the choices for the
parameters that result in the error bound scaling optimally in relation to the
number of samples. This provides our method with increased estimation accuracy,
while also minimizing the computational cost.
