  We present a Bayesian hierarchical modeling approach to paleoclimate
reconstruction using borehole temperature profiles. The approach relies on
modeling heat conduction in solids via the heat equation with step function,
surface boundary conditions. Our analysis includes model error and assumes that
the boundary conditions are random processes. The formulation also enables
separation of measurement error and model error. We apply the analysis to data
from nine borehole temperature records from the San Rafael region in Utah. We
produce ground surface temperature histories with uncertainty estimates for the
past 400 years. We pay special attention to use of prior parameter models that
illustrate borrowing strength in a combined analysis for all nine boreholes. In
addition, we review selected sensitivity analyses.
