Comparison of the Sparse Instrumental Variable approach (SPIV) with Likelihood-based Causality Model Selection (LCMS) and Mendelian Randomization (MR).

1By observation noise we mean variations between true and observed biomarkers, and their different treatment in the underlying models.
2Model selection implies probabilistic model comparison based on likelihood scores that can be used, for example, to infer the direction of causality. Note that while the classic MR can be used to compute p-values for causal and reverse models Timpson et al. (2011), it cannot be easily used to assess relative value of causal vs reverse causal explanations. In classic MR, formal and fair comparisons are further complicated by the fact that the causal and reverse models are not nested and use non-overlapping sets of instruments. The more recent Bayesian treatment of MR suggested by McKeigue et al. (2010) can in principle be used for model selection, but is limited to selecting either the conventional causal or non-causal explanation under the assumption of no pleiotropy.
3Because SPIV is Bayesian and can use prior information to break symmetries between causal and reverse models, it can be used to infer the direction of causality even if only weak instruments are available.