Objective This study aims to address the challenge of complex calculations for the posterior distribution function in the factor analysis model. Methods Initially the variational Bayes VB method is employed to estimate the parameters of the factor analysis model where the factors follow an exponential distribution. The VB method utilizes the coordinate ascent variational inference CAVI algorithm for iterative parameter solving. Subsequently a comparison is made with the MCMC Makov Chain Monte Carlo method. Through random simulations the effectiveness of both the VB and MCMC methods is evaluated when the sample size is 300. The ELBO plot is used to assess the convergence of the VB method while the parameter trace plot and autocorrelation plot are used to determine the convergence of the MCMC method. The performance of the two methods is judged based on the deviation between the predicted and true values.Finally an empirical analysis is carried out on an actual dataset with a sample size of 713. Results Simulation and empirical analyses indicate that both methods converge with the absolute deviations being less than 0. 1. Nevertheless the VB method outperforms the MCMC method in terms of estimation accuracy computational complexity and running time. The advantages of the VB method become more prominent when dealing with large sample sizes. Conclusion In the factor analysis model assuming that factors follow an exponential distribution can be a reasonable option. Compared to the MCMC method the variational Bayes method effectively reduces the computational burden associated with the posterior distribution function of the factor analysis model and provides more accurate parameter estimates. The VB method offers three key advantages First it simplifies calculations as it avoids the integration of complex posterior distributions. Second being based on an approximate distribution the VB method significantly reduces running time especially for large-scale samples compared to the MCMC method. Third the VB method demonstrates higher estimation accuracy than the MCMC method.