A systematic Bayesian framework is developed for physics constrained parameter inference of stochastic differential equations (SDE) from partial observations. Physical constraints are derived for stochastic climate models but are applicable for many fluid systems. A condition is derived for global stability of stochastic climate models based on energy conservation. Stochastic climate models are globally stable when a quadratic form, which is related to the cubic nonlinear operator, is negative definite. A new algorithm for the efficient sampling of such negative definite matrices is developed and also for imputing unobserved data which improve the accuracy of the parameter estimates. The performance of this framework is evaluated on two conceptual climate models.

Abstract. We present statistical methods to determine climate regimes for the last glacial period using three temperature proxy records from Greenland: measurements of δ 18

We present statistical methods to systematically determine climate regimes for the last glacial period using three temperature proxy records from Greenland: measurements of δ¹⁸O from the Greenland Ice Sheet Project 2 (GISP2), the Greenland Ice Core Project (GRIP) and the North Greenland Ice Core Project (NGRIP). By using Bayesian model comparison methods we find that, in two out of three data sets, a model with 3 states is very strongly supported. We interpret these states as corresponding to: a gradual cooling regime due to iceberg influx in the North Atlantic, sudden temperature decrease due to increased freshwater influx following ice sheet collapse and to the Dansgaard-Oeschger events associated with sudden rebound temperature increase after the thermohaline circulation recovers its full flux. We find that these models are far superior to those that differentiate between states based on absolute temperature differences only, which questions the appropriateness of defining stadial and interstadial climate states. We investigate the recurrence properties of these climate regimes and find that the only significant periodicity is within the Greenland Ice Sheet Project 2 data at 1450 years in agreement with previous studies

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