Convergence assessment and burnin estimation are central concepts in Markov chain Monte Carlo algorithms. Studies on eects, statistical properties, and comparisons between dierent convergence assessment methods have been conducted during the past few decades. However, not much work has been done on the eect of convergence diagnostic on posterior distribution of tree parameters and which method should be used by researchers in Bayesian phylogenetics inference. In this study, we propose and evaluate two novel burnin estimation methods that estimate burnin using all parameters jointly. We also consider some other popular convergence diagnostics, evaluate them in light of parallel chains and quantify the eect of burnin estimates from various convergence diagnostics on the posterior distribution of trees. We motivate the use of convergence diagnostics to assess convergence and estimate burnin in Bayesian phylogenetics inference and found out that it is better to employ convergence diagnostics rather than remove a xed percentage as burnin. We concluded that the last burnin estimator using eective sample size appears to estimate burnin better than all other convergence diagnostics.