5. Implement an MCMC algorithm to sample the posterior distribution of the ef- in the tective population size Ne given the tree simulated previous step. The proposal kernel should be a uniform random walk on the parameter Ne, so that 6Unif-10,10) and NNe 6. The lower boundary of zero can be treated by reflection or rejection. The target distribution is the coalescent likelihood: k(k 1)tk k-2 where tk is the time duration that the tree T has k lineages Plot the posterior distribution of Ne from an MCMC chain of length 10,000 steps Comment on how you would get a better estimate of the effective population size 5. Implement an MCMC algorithm to sample the posterior distribution of the ef- in the tective population size Ne given the tree simulated previous step. The proposal kernel should be a uniform random walk on the parameter Ne, so that 6Unif-10,10) and NNe 6. The lower boundary of zero can be treated by reflection or rejection. The target distribution is the coalescent likelihood: k(k 1)tk k-2 where tk is the time duration that the tree T has k lineages Plot the posterior distribution of Ne from an MCMC chain of length 10,000 steps Comment on how you would get a better estimate of the effective population size