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==== 3.2.2 Other Probabilistic Approaches ====

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Considering the difficulty in accounting for climate modelling uncertainties in the regression-based approaches, [[#Ribes--2017|Ribes et al. (2017)]] introduced a new statistical inference framework based on an additivity assumption and likelihood maximization, which estimates climate model uncertainty based on an ensemble of opportunity and tests whether observations are inconsistent with internal variability and consistent with the expected response from climate models. The method was further developed by [[#Ribes--2021|Ribes et al. (2021)]] , who applied it to narrow the uncertainty range in the estimated human-induced warming. [[#Hannart--2018|Hannart and Naveau (2018)]] , on the other hand, extended the application of standard causal theory ( [[#Pearl--2009|Pearl, 2009]] ) to the context of detection and attribution by converting a time series into an event, and calculating the probability of causation, an approach which maximizes the causal evidence associated with the forcing. On the other hand, [[#Schurer--2018|Schurer et al. (2018)]] employed a Bayesian framework to explicitly consider climate modelling uncertainty in the optimal regression method. Application of these approaches to attribution of large-scale temperature changes supports a dominant anthropogenic contribution to the observed global warming.

Climate change signals can vary with time and discriminant analysis has been used to obtain more accurate estimates of time-varying signals, and has been applied to different variables such as seasonal temperatures ( [[#Jia--2012|Jia and DelSole, 2012]] ) and the South Asian monsoon ( [[#Srivastava--2014|Srivastava and DelSole, 2014]] ). The same approach was applied to separate aerosol forcing responses from other forcings (X. [[#Yan--2016|]] [[#Yan--2016|]] [[#Yan--2016|Yan et al., 2016]] ) and results using climate model output indicated that detectability of the aerosol response is maximized by using a combination of temperature and precipitation data. [[#Paeth--2017|Paeth et al. (2017)]] introduced a detection and attribution method applicable for multiple variables based on a discriminant analysis and a Bayesian classification method. Finally, a systematic approach has been proposed to translating quantitative analysis into a description of confidence in the detection and attribution of a climate response to anthropogenic drivers ( [[#Stone--2016|Stone and Hansen, 2016]] ).

Overall, these new fingerprinting and other probabilistic methods for detection and attribution as well as efforts to better incorporate the associated uncertainties have addressed a number of shortcomings in previously applied detection and attribution techniques. They further strengthen the confidence in attribution of observed large-scale changes to a combination of external forcings as assessed in the following sections.

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