In this work, inspired by machine learning techniques, we propose a new Bayesian model for Small Area Estimation (SAE), the Fay-Herriot model with Spectral Clustering (FH-SC). Unlike traditional approaches, clustering in FH-SC is based on spectral clustering algorithms that utilize external covariates, rather than geographical or administrative criteria. A major advantage of the FH-SC model is its flexibility in integrating existing SAE approaches, with or without clustering random effects. To enable benchmarking, we leverage the theoretical framework of posterior projections for constrained Bayesian inference and derive closed form expressions for the new Rao-Blackwell (RB) estimators of the posterior mean under the FH-SC model. Additionally, we introduce a novel measure of uncertainty for the benchmarked estimator, the Conditional Posterior Mean Square Error (CPMSE), which is generalizable to other Bayesian SAE estimators. We conduct model-based and data-based simulation studies to evaluate the frequentist properties of the CPMSE. The proposed methodology is motivated by a real case study involving the estimation of the proportion of households with internet access in the municipalities of Colombia. Finally, we also illustrate the advantages of FH-SC over existing Bayesian and frequentist approaches through our case study.

Personal health data, often derived from personal devices such as wearables, are distinguished by their multi-dimensional, continuous and longitudinal measurements that capture granular observations of physiology and behavior in-situ rather than in a clinical setting. Research studies have highlighted the significant health impacts of physical activity and sleep patterns, emphasizing the potential for wearable-derived data to reveal personalized health insights and promote positive behavior changes [1, 4, 30, 46, 47]. For example, individuals with a device-measured Physical Activity Energy Expenditure (PAEE) that is 5 kJ/kg/day higher had a 37% lower premature mortality risk [47]. Those with frequent sleep disturbances were associated with an increase in risk of hypertension, diabetes and cardiovascular diseases [9, 30]. A large meta-analysis suggests that activity trackers improve physical activity and promote weight loss, with users taking 1800 extra steps per day [16]. Despite these gross benefits, using wearable data to derive intelligent responses and insights to personal health queries is non-trivial. These data are usually collected without clinical supervision and users often do not have access to the expertise that could aid in data interpretation. For example, a common question of wearable device users is "How can I get better sleep?". Though a seemingly straightforward question, arriving at an ideal response would involve performing a series of complex, independent analytical steps across multiple irregularly sampled time series such as: checking the availability of recent data, deciding on metrics to optimize (e.g.