We propose a global geomagnetic field model for the last fourteen
thousand years, based on thermoremanent records. We call the model
ArchKalMag14k. ArchKalMag14k is constructed by modifying recently
proposed algorithms, based on space-time correlations. Due to the amount
of data and complexity of the model, the full Bayesian posterior is
numerically intractable. To tackle this, we sequentialize the inversion
by implementing a Kalman-filter with a fixed time step. Every step
consists of a prediction, based on a degree dependent temporal
covariance, and a correction via Gaussian process regression. Dating
errors are treated via a noisy input formulation. Cross-correlations are
re-introduced by a smoothing algorithm and model parameters are inferred
from the data. Due to the specific statistical nature of the proposed
algorithms, the model comes with space and time dependent uncertainty
estimates. The new model ArchKalMag14k shows less variation in the large
scale degrees than comparable models. Local predictions represent the
underlying data and agree with comparable models, if the location is
sampled well. Uncertainties are bigger for earlier times and in regions
of sparse data coverage. We also use ArchKalMag14k to analyze the
appearance and evolution of the South Atlantic anomaly together with
reverse flux patches at the core mantel boundary, considering the model
uncertainties. While we find good agreement with earlier models for
recent times, our model suggests a different evolution of intensity
minima prior to 1650 CE. In general, our results suggest that prior to
6000 BCE the database is not strong enough to support global models.