Multiple changes in Earth's climate system have been observed in past decades. Determining how likely each of these changes are to have been caused by human influence is important for decision making and policy. Here we describe an approach for deriving the probability that anthropogenic forcings have caused a given observed change which is anchored in causal counterfactual theory (Pearl 2009). Using numerical models' simulations under a factual and a counterfactual setting, an optimal index is defined by maximizing the causal evidence associated with the forcing under scrutiny, in agreement with the notion of fingerprint. This yields patterns of evolution which are both physically inconsistent with the counterfactual setting, and consistent with the factual one. The maximization is performed in the context of a Bayesian hierarchical model accounting for numerical models' uncertainty, observational uncertainty and sampling uncertainty. The approach is illustrated by focusing on the causal influence of anthropogenic forcings on the observed evolution of two distinct variables, temperature and agricultural yields, during the past five decades and at global scale.