Classical and Bayesian Parameter Estimation under Varying Sample Sizes and Data Conditions

Parameter estimation is central to empirical statistical analysis, yet researchers often face uncertainty about whether classical or Bayesian inference offers the most reliable interpretation of unknown model parameters. This study comparatively evaluates classical and Bayesian parameter estimation under controlled simulation settings and two applied empirical cases. Classical inference is represented by maximum likelihood logistic regression, ordinary least squares regression, standard errors, and confidence intervals. Bayesian inference uses weakly informative normal priors, posterior mode estimation, approximate posterior covariance, and credible intervals. The simulation component evaluates mean absolute bias, mean squared error, interval width, and coverage across small, medium, and large sample sizes under clean and contaminated data conditions. The main empirical application uses a credit-risk binary outcome with 30,000 observations, while a continuous insurance-cost application provides a robustness case for linear parameter estimation. The simulation results show that the two approaches converge closely in large samples when the model is correctly specified, while weak Bayesian regularization modestly stabilizes estimates in small samples. Under label contamination, both approaches lose interval coverage, indicating that robust data-generating assumptions are as important as the inferential paradigm. In the credit-risk case, classical and Bayesian logistic estimates produced nearly identical out-of-sample performance, with an area under the receiver operating characteristic curve (ROC-AUC) of approximately 0.716 and accuracy of approximately 0.809. The insurance-cost robustness case produced similar predictive accuracy for classical and Bayesian linear estimation. The findings support a practical interpretation: Bayesian methods add uncertainty representation and regularization, while classical methods remain efficient when sample size is large, and assumptions are reasonable.

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