The study examines gender stereotypes in STEM fields using advanced statistical techniques within a Bayesian framework. The analysis relies on a survey collected from Italian participants in 2021, investigating perceptions of STEM subjects and professional careers. By employing supervised learning for predictive analysis based on a multilevel ordinal regression model, we aim to enhance the understanding of the barriers women face in STEM, including biases and stereotypes that shape career expectations and opportunities. Additionally, we estimate the marginal effects of key predictors to quantify the impact of factors such as gender, age, education, and workplace environment on perceptions of STEM. This approach not only enhances statistical methodologies but also provides insights into real-world social challenges.