<![CDATA[Conventional estimation of presidential approval ratings relies on face-to-face surveys that excel in population representativeness (probability sampling) but suffer from significant time lag between data collection and publication. Conversely, social media monitoring (SMM) provides real-time data but is often biased toward active digital platform demographics. This study proposes a hybrid model based on Bayesian Dirichlet-Multinomial (BDM) to integrate survey data as prior belief with SMM data as likelihood to generate more dynamic and accurate posterior estimates. Prior data were drawn from the Indikator Politik Indonesia national survey of October 2025 (n=1,220, MoE ±2.9%), indicating a public approval rate of 77.7%. Update data were collected from the X (Twitter) platform during November 2025 through crawling and scraping techniques, yielding 2.5 million raw data points processed through Named Entity Recognition (NER), text normalization, and Transformer-based classification (IndoBERT v2.0). After deduplication, 310,000 unique accounts were retained with 120 million total impressions. Sentiment distribution showed 61% positive, 15% negative, and 24% neutral. Bayesian updating produced a corrected public approval estimate of 68.4% (a 9.3 percentage point decline from the survey prior), detecting pockets of dissatisfaction on food price issues underrepresented in conventional surveys. Model validation using Leave-One-Out Cross-Validation (LOO-CV) produced an Expected Log-Pointwise Predictive Density (ELPD) of -127.4, superior to the single-survey baseline model (-148.9). This model offers a new framework as a public opinion early warning system that is responsive to current issue dynamics without sacrificing the statistical validity of traditional survey methods.]]>
