Fig. 3From: Bayesian mendelian randomization with study heterogeneity and data partitioning for large studiesJoint posterior distributions of causal effects of X1 on Y1 (\(\hat {\beta }_{1}\), horizontal axis) and X2 on Y2 (\(\hat {\beta }_{2}\), vertical axis) obtained from 2-dimensional Gaussian kernel density estimation in Bayesian Mendelian randomisation when the true causal effects β1=β2=0.3. Results were based on full data (red), 5 subsets with equal sample size (orange) and 50 subsets with equal sample size (blue). α: instrument strengthBack to article page