Bayesian Model Selection for the Glacial–Interglacial Cycle

Abstract

A prevailing viewpoint in palaeoclimate science is that a single palaeoclimate record contains insufficient information to discriminate between most competing explanatory models. Results we present here suggest the contrary. Using SMC 2 combined with novel Brownian bridge type proposals for the state trajectories, we show that even with relatively short time series it is possible to estimate Bayes factors to sufficient accuracy to be able to select between competing models. The results show that Monte Carlo methodology and computer power have now advanced to the point where a full Bayesian analysis for a wide class of conceptual climate models is now possible. The results also highlight a problem with estimating the chronology of the climate record prior to further statistical analysis, a practice which is common in palaeoclimate science. Using two datasets based on the same record but with different estimated chronologies results in conflicting conclusions about the importance of the orbital forcing on the glacial cycle, and about the internal dynamics generating the glacial cycle, even though the difference between the two estimated chronologies is consistent with dating uncertainty. This highlights a need for chronology estimation and other inferential questions to be addressed in a joint statistical procedure. * Email: Jake.Carson@warwick.ac.uk 1

Accelerating pseudo-marginal MCMC using Gaussian processes

“…The IS and SMC approaches have been extended to allow for unbiased likelihood estimators to be used (see Chopin et al (2013), Tran et al (2014), Duan and Fulop (2015) and Drovandi and McCutchan (2016)). The IS and SMC methods are of additional interest as they produce also an estimate of the evidence, which can be used for fully Bayesian model comparisons; see, for example, Drovandi and McCutchan (2016) and Carson et al (2017).…”

Estimating model evidence using ensemble‐based data assimilation with localization – The model selection problem

“…() and Carson et al . (). In the present article, we focus on the use of DA for this purpose, following and expanding the work of Carrassi et al .…”

“…Several metrics for model version selection have been defined in the literature (Akaike, 1974;Schwarz, 1978;Burnham and Anderson, 2002). In the present article, we focus on model evidence as the metric of choice (Särkkä, 2013;Elsheikh et al 2014aElsheikh et al , 2014bOtsuka and Miyoshi, 2015;Reich and Cotter, 2015;Carson et al, 2018). Let us define the ideal set of observations over an infinite past as y k∶ = {y k , y k−1 , … , y 1 , y 0 , … , y −∞ }.…”

“…; Otsuka and Miyoshi, ; Reich and Cotter, ; Carson et al . ). Several of these approaches advocate the use of the marginal likelihood of the data – also called model evidence – for model selection.…”

“…Some attempts to analytically address the model or model version selection problem have been successful (e.g., Winiarek et al 2011), but only under specific assumptions that may not be realistic for large-dimensional geoscientific applications. Numerical methodologies that may be computationally affordable for high-dimensional problems have also been proposed in recent years (Särkkä, 2013;Elsheikh et al, 2014aElsheikh et al, , 2014bOtsuka and Miyoshi, 2015;Reich and Cotter, 2015;Carson et al, 2018). Several of these approaches advocate the use of the marginal likelihood of the data -also called model evidence -for model selection.…”