Predicting Parkinson's Disease (PD) progression is crucial, and voice biomarkers offer a non-invasive method for tracking symptom severity (UPDRS scores) through telemonitoring. Analyzing this longitudinal data is challenging due to within-subject correlations and complex, nonlinear patient-specific progression patterns. This study benchmarks LMMs against two advanced hybrid approaches: the Generalized Neural Network Mixed Model (GNMM) (Mandel 2021), which embeds a neural network within a GLMM structure, and the Neural Mixed Effects (NME) model (Wortwein 2023), allowing nonlinear subject-specific parameters throughout the network. Using the Oxford Parkinson's telemonitoring voice dataset, we evaluate these models' performance in predicting Total UPDRS to offer practical guidance for PD research and clinical applications.

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.

First, there are often pathologies in LMMs that hinder efficient HMC sampling.

Linear mixed models are widely used for clustered data, but their reliance on parametric forms limits flexibility in complex and high-dimensional settings. In contrast, gradient boosting methods achieve high predictive accuracy through nonparametric estimation, but do not accommodate clustered data structures or provide uncertainty quantification. We introduce Gradient Boosted Mixed Models (GBMixed), a framework and algorithm that extends boosting to jointly estimate mean and variance components via likelihood-based gradients. In addition to nonparametric mean estimation, the method models both random effects and residual variances as potentially covariate-dependent functions using flexible base learners such as regression trees or splines, enabling nonparametric estimation while maintaining interpretability. Simulations and real-world applications demonstrate accurate recovery of variance components, calibrated prediction intervals, and improved predictive accuracy relative to standard linear mixed models and nonparametric methods. GBMixed provides heteroscedastic uncertainty quantification and introduces boosting for heterogeneous random effects. This enables covariate-dependent shrinkage for cluster-specific predictions to adapt between population and cluster-level data. Under standard causal assumptions, the framework enables estimation of heterogeneous treatment effects with reliable uncertainty quantification.

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating embeddings as latent random effects within a variational autoencoder framework, our method substantially decreases the number of parameters -- from the conventional embedding approach of cardinality $\times$ embedding dimension, which quickly becomes infeasible with large cardinalities, to a significantly smaller, cardinality-independent number determined primarily by the encoder architecture. This reduction dramatically mitigates overfitting and computational burden in high-cardinality settings. Extensive experiments on simulated and real datasets, encompassing collaborative filtering and tabular regression tasks using varied architectures, demonstrate that MMbeddings consistently outperforms traditional embeddings, underscoring its potential across diverse machine learning applications.

It appears that individuals experience different numbers of small and large growth spurts that differ in magnitude and timing.

Hierarchical data with multiple observations per group is ubiquitous in empirical sciences and is often analyzed using mixed-effects regression. In such models, Bayesian inference gives an estimate of uncertainty but is analytically intractable and requires costly approximation using Markov Chain Monte Carlo (MCMC) methods. Neural posterior estimation shifts the bulk of computation from inference time to pre-training time, amortizing over simulated datasets with known ground truth targets. We propose metabeta, a transformer-based neural network model for Bayesian mixed-effects regression. Using simulated and real data, we show that it reaches stable and comparable performance to MCMC-based parameter estimation at a fraction of the usually required time.

The ability to infer what others are looking at is a critical component of a theory of mind that underpins natural human-AI interaction. We characterized this skill in 111 Vision Language Models (VLMs) and human participants (N = 65) using photos taken with manipulated difficulty and variability. We found that 94 of the 111 VLMs were not better than random guessing, while humans achieved near-ceiling accuracy. VLMs respond with each choice almost equally frequently. Are they randomly guessing? At least for five top-tier VLMs, their performance was above chance, declined with increasing task difficulty, but barely varied across different prompts and scene objects. These behavioral patterns cannot be explained by considering VLMs as random guessers. Instead, they likely utilize head orientation but not eye appearance to infer gaze direction, such that their performance is imperfect, subject to the task difficulty, but robust to superficial perceptual variations. This suggests that VLMs, lacking effective gaze inference skills, have yet to become technologies that can naturally interact with humans, but the potential remains.