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Despite decades of research, large multi-model uncertainty remains about the Earth’s equilibrium climate sensitivity to carbon dioxide forcing as inferred from state-of-the-art Earth system models (ESMs). Statistical treatments of multi-model uncertainties are often limited to simple ESM averaging approaches. Sometimes models are weighted by how well they reproduce historical climate observations. Here, we propose a novel approach to multi-model combination and uncertainty quantification. Rather than averaging a discrete set of models, our approach samples from a continuous distribution over a reduced space of simple model parameters. We fit the free parameters of a reduced-order climate model to the output of each member of the multi-model ensemble. The reduced-order parameter estimates are then combined using a hierarchical Bayesian statistical model. The result is a multi-model distribution of reduced-model parameters, including climate sensitivity. In effect, the multi-model uncertainty problem within an ensemble of ESMs is converted to a parametric uncertainty problem within a reduced model. The multi-model distribution can then be updated with observational data, combining two independent lines of evidence. We apply this approach to 24 model simulations of global surface temperature and net top-of-atmosphere radiation response to abrupt quadrupling of carbon dioxide, and four historical temperature data sets. Our reduced order model is a 2-layer energy balance model. We present probability distributions of climate sensitivity based on (1) the multi-model ensemble alone and (2) the multi-model ensemble and observations. [ABSTRACT FROM AUTHOR]