  Stochastic reduced models are an important tool in climate systems whose many
spatial and temporal scales cannot be fully discretized or underlying physics
may not be fully accounted for. One form of reduced model, the linear inverse
model (LIM), has been widely used for regional climate predictability studies -
typically focusing more on tropical or mid-latitude studies. However, most LIM
fitting techniques rely on point estimation techniques deriving from
fluctuation-dissipation theory. In this methodological study we explore the use
of Bayesian inference techniques for LIM parameter estimation of sea surface
temperature (SST), to quantify the skillful decadal predictability of Bayesian
LIM models at high latitudes. We show that Bayesian methods, when compared to
traditional point estimation methods for LIM-type models, provide better
calibrated probabilistic skill, while simultaneously providing better point
estimates due to the regularization effect of the prior distribution in
high-dimensional problems. We compare the effect of several priors, as well as
maximum likelihood estimates, on (1) estimating parameter values on a perfect
model experiment and (2) producing calibrated 1-year SST anomaly forecast
distributions using a pre-industrial control run of the Community Earth System
Model (CESM). Finally, we employ a host of probabilistic skill metrics to
determine the extent to which a LIM can forecast SST anomalies at high
latitudes. We find that the choice of prior distribution has an appreciable
impact on estimation outcomes, and priors that emphasize physically relevant
properties enhance the model's ability to capture variability of SST anomalies.
