Mobile data technologies use ``actigraphs'' to furnish information on health variables as a function of a subject's movement. The advent of wearable devices and related technologies has propelled the creation of health databases consisting of human movement data to conduct research on mobility patterns and health outcomes. Statistical methods for analyzing high-resolution actigraph data depend on the specific inferential context, but the advent of Artificial Intelligence (AI) frameworks require that the methods be congruent to transfer learning and amortization. This article devises amortized Bayesian inference for actigraph time sheets. We pursue a Bayesian approach to ensure full propagation of uncertainty and its quantification using a hierarchical dynamic linear model. We build our analysis around actigraph data from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study conducted by the Fielding School of Public Health in the University of California, Los Angeles. Apart from achieving probabilistic imputation of actigraph time sheets, we are also able to statistically learn about the time-varying impact of explanatory variables on the magnitude of acceleration (MAG) for a cohort of subjects.

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these subprocesses may be inherently unknown or too computationally intensive to directly embed in the simulation model. Replacing these elements with estimated or learned approximations introduces a form of epistemic uncertainty that we refer to as submodel uncertainty. This paper investigates how submodel uncertainty affects the estimation of system performance metrics. We develop a framework for quantifying submodel uncertainty in stochastic simulation models and extend the framework to digital-twin settings, where simulation experiments are repeatedly conducted with the model initialized from observed system states. Building on approaches from input uncertainty analysis, we leverage bootstrapping and Bayesian model averaging to construct quantile-based confidence or credible intervals for key performance indicators. We propose a tree-based method that decomposes total output variability and attributes uncertainty to individual submodels in the form of importance scores. The proposed framework is model-agnostic and accommodates both parametric and nonparametric submodels under frequentist and Bayesian modeling paradigms. A synthetic numerical experiment and a more realistic digital-twin simulation of a contact center illustrate the importance of understanding how and how much individual submodels contribute to overall uncertainty.

Neural Information Processing Systems http://nips.cc/

We consider here the sparse Gaussian process regression (SGPR) approach introduced by Titsias [31], which is widely used in practice (see [1, 9] for implementations) and has been studied in many recent works [13,21,5,6,38,28,32,22,23].

Personalizing digital applications for health behavior change is a promising route to making them more engaging and effective. This especially holds for approaches that adapt to users and their specific states (e.g., motivation, knowledge, wants) over time. However, developing such approaches requires making many design choices, whose effectiveness is difficult to predict from literature and costly to evaluate in practice. In this work, we explore whether large language models (LLMs) can be used out-of-the-box to generate samples of user interactions that provide useful information for training reinforcement learning models for digital behavior change settings. Using real user data from four large behavior change studies as comparison, we show that LLM-generated samples can be useful in the absence of real data. Comparisons to the samples provided by human raters further show that LLM-generated samples reach the performance of human raters. Additional analyses of different prompting strategies including shorter and longer prompt variants, chain-of-thought prompting, and few-shot prompting show that the relative effectiveness of different strategies depends on both the study and the LLM with also relatively large differences between prompt paraphrases alone. We provide recommendations for how LLM-generated samples can be useful in practice.

We also show how second-order information can lead to more effective choices of kernel.

Uncertainty quantification (UQ) for adaptively collected data, such as that coming from adaptive experiments, bandits, or reinforcement learning, is necessary for critical elements of data collection such as ensuring safety and conducting after-study inference. The data's adaptivity creates significant challenges for frequentist UQ, yet Bayesian UQ remains the same as if the data were independent and identically distributed (i.i.d.), making it an appealing and commonly used approach. Bayesian UQ requires the (correct) specification of a prior distribution while frequentist UQ does not, but for i.i.d. data the celebrated Bernstein-von Mises theorem shows that as the sample size grows, the prior 'washes out' and Bayesian UQ becomes frequentist-valid, implying that the choice of prior need not be a major impediment to Bayesian UQ as it makes no difference asymptotically. This paper for the first time extends the Bernstein-von Mises theorem to adaptively collected data, proving asymptotic equivalence between Bayesian UQ and Wald-type frequentist UQ in this challenging setting. Our result showing this asymptotic agreement does not require the standard stability condition required by works studying validity of Wald-type frequentist UQ; in cases where stability is satisfied, our results combined with these prior studies of frequentist UQ imply frequentist validity of Bayesian UQ. Counterintuitively however, they also provide a negative result that Bayesian UQ is not asymptotically frequentist valid when stability fails, despite the fact that the prior washes out and Bayesian UQ asymptotically matches standard Wald-type frequentist UQ. We empirically validate our theory (positive and negative) via a range of simulations.