The paper compares Bayesian and maximum-likelihood (ML) inference methods for estimating population genetic parameters, such as population sizes and migration rates, using coalescent theory. Both methods were implemented in the program MIGRATE, which uses a Markov chain Monte Carlo algorithm. The Bayesian method generally performs better in accuracy and coverage than the ML approach, although they are sometimes equal in performance. The ML method can fail on sparse data and produce non-conservative support intervals, while the Bayesian method with appropriate prior distributions can remedy these issues. The MIGRATE program was extended to allow both ML and Bayesian inference. Both methods estimate the same parameters under the same population model and assumptions, facilitating comparisons. The Bayesian approach uses a prior distribution to estimate parameters, while the ML approach maximizes the likelihood function. The Bayesian method incorporates prior distributions, which can improve the accuracy of parameter estimates, especially for small population sizes and low migration rates. The performance of the methods was tested on simulated datasets for four populations with unidirectional migration patterns. The Bayesian method produced more accurate estimates of population sizes and migration rates, particularly for small population sizes and low migration rates. The ML method had difficulty recovering true values, especially for small population sizes, and produced wider confidence intervals. The Bayesian method had better coverage, with true values falling within the 95% credibility interval more frequently. The paper concludes that the Bayesian approach is preferable for estimating population genetic parameters, especially when dealing with low-variability datasets. The ML method is less reliable in such cases, and the Bayesian method provides more accurate and reliable estimates. The study highlights the importance of using appropriate prior distributions in Bayesian inference to improve the accuracy of population genetic parameter estimates.The paper compares Bayesian and maximum-likelihood (ML) inference methods for estimating population genetic parameters, such as population sizes and migration rates, using coalescent theory. Both methods were implemented in the program MIGRATE, which uses a Markov chain Monte Carlo algorithm. The Bayesian method generally performs better in accuracy and coverage than the ML approach, although they are sometimes equal in performance. The ML method can fail on sparse data and produce non-conservative support intervals, while the Bayesian method with appropriate prior distributions can remedy these issues. The MIGRATE program was extended to allow both ML and Bayesian inference. Both methods estimate the same parameters under the same population model and assumptions, facilitating comparisons. The Bayesian approach uses a prior distribution to estimate parameters, while the ML approach maximizes the likelihood function. The Bayesian method incorporates prior distributions, which can improve the accuracy of parameter estimates, especially for small population sizes and low migration rates. The performance of the methods was tested on simulated datasets for four populations with unidirectional migration patterns. The Bayesian method produced more accurate estimates of population sizes and migration rates, particularly for small population sizes and low migration rates. The ML method had difficulty recovering true values, especially for small population sizes, and produced wider confidence intervals. The Bayesian method had better coverage, with true values falling within the 95% credibility interval more frequently. The paper concludes that the Bayesian approach is preferable for estimating population genetic parameters, especially when dealing with low-variability datasets. The ML method is less reliable in such cases, and the Bayesian method provides more accurate and reliable estimates. The study highlights the importance of using appropriate prior distributions in Bayesian inference to improve the accuracy of population genetic parameter estimates.