Abstract
<jats:p>The article employs modern methods of analyzing demographic policy in Russia and Bashkortostan, utilizing Bayesian statistics, regression modeling, and risk theory to forecast fertility scenarios and evaluate the effectiveness of support measures. Having analyzed Federal State Statistics Service data for 2007–2024 (fertility rates, infant mortality rates, life expectancy, marriage and divorce rates), a probabilistic approach was developed to interpret demographic indicators as random variables, where Bayes' theorem updates prior expectations as new data becomes available. Special emphasis is placed on modeling the impact of factors such as income, housing, and maternity capital on the probability of having a second child through logistic regression and time series analysis with interval forecasts, enabling the prediction of demographic crisis risks and the ultimate effectiveness of government programs.</jats:p>