Complementary analysis to MR, which uses Bayesian statistics and model fitting algorithms to construct the most optimum networks that describe relationships between variables. Including genetic variants within such models allows for the plausible network space to be reduced and improves causal inference.

Generally, Bayesian networks describe relationships between variables. Causal Bayesian networks extend this framework to infer causality in such relationships, under a few key assumptions that are similar to those assumptions made in MR analyses. These causal Bayesian network assumptions are that (1) a variable is independent of all other variables except for its immediate descendants, conditional on its causal ascendants (known as the "causal Markov assumption"); (2) the network structure and causal Markov relationships represent all conditional relationships amongst all variables (known as the "causal faithfulness assumption"); and (3) there are no external variables that cause two or more variables within the model, all variables are included in the data and model and there is no unobserved confounding (known as the "causal sufficiency assumption"). A further assumption is that there is no measurement error. In these Bayesian network analyses, the most plausible relationships between variables (i.e., depicted by a complete directed acyclic graph (DAG)) given the data and included variables is inferred using a set of developed algorithms. The use of genetic variants within these analyses creates a framework such that the number of possible DAGs reduces and improves the ability to identify the most well-fitting DAG.

## References

## Other terms in 'Pleiotropy-robust two-sample MR methods':

- Bayes MR
- Bayesian implementation of the MR-Egger Estimator (BMRE)
- Bayesian multi-instrument Mendelian randomization (MIMR)
- Causal Analysis Using Summary Effect estimates (MR-CAUSE)
- Contamination mixture models
- Generalized Summary MR (GSMR)
- Genetic Instrumental Variable (GIV)
- Hierarchical joint Analysis of Marginal summary statistics (hJAM)
- Inverse variance weighted (IVW) random effects model
- Iterative Mendelian Randomization and Pleiotropy (IMRP)
- Leave-one-out analysis
- Median-based estimate
- Mode-based estimate
- MR accounting for Correlated and Idiosyncratic Pleiotropy (MRCIP)
- MR accounting for Linkage Disequilibrium and Pleiotropy (MR-LDP)
- MR Lasso
- MR Mixture (MRMix)
- MR using Robust regression (MR Robust)
- MR with penalized weights
- MR with regularization
- MR-Clust
- MR-Egger regression and extensions
- MR-Link
- MR-Path
- Multivariable MR (MVMR) and extensions
- Welch-weighted Egger regression (WWER)