Abstract

When a logistic regression dataset contains a large number of observations with estimated probabilities very close to 0 or 1, the Maximum Likelihood Estimation (MLE) method often encounters difficulties in parameter estimation and may produce unstable estimates with large errors. In this context, the Bayesian approach is considered an effective alternative because it allows prior information to be combined with the observed data. However, the performance of Bayesian methods depends substantially on the selection of appropriate prior distributions for the model parameters. In this paper, we propose a new Bayesian method to reduce estimation errors in logistic regression models. First, a parameter acceptance–rejection algorithm is employed to construct prior information based on the similarity between simulated data and observed data. The resulting prior information is then combined with the likelihood function to establish the posterior distribution of the parameters. Subsequently, the Metropolis–Hastings (MH) algorithm is applied to generate a stationary Markov chain and estimate the model parameters. The performance of the proposed method is evaluated through simulation studies and a real-world dataset. The results demonstrate that the proposed Bayesian approach improves the accuracy of parameter estimates and reduces estimation errors compared with both the MLE method and Bayesian methods that employ non-informative priors.