Mendelian randomisation is well known for its weak instrument bias, which is caused by the weak genetic association with the exposure. Usually, the most significant SNP within a gene region is selected to represent the association with the exposure of interest. However, if the causal variant was not genotyped then this proxy with weaker association will be a worse instrument. Moreover, a GWAS significant proxy may not show significance in another population. In the human genome, there are many SNPs in linkage equilibrium (LD) within a gene. The correlation between the SNPs and causal variant may increase power to detect the underlying association with the exposure. My thesis will investigate whether many SNPs in LD within a gene region can provide a stronger instrument than a single proxy for the causal variant(s). The thesis will first establish the gains from having multiple SNPs in LD as instruments. Simulation of realistic LD patterns will be used to assess both classical and Bayesian approaches to the estimation of the causal effect with many dependent SNPs. A Bayesian approach to Mendelian randomisation is preferable to the classical estimation with many dependent SNPs.