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Model-assisted estimation combines sample survey data with auxiliary information to increase precision when estimating finite population quantities. Accurately estimating the variance of model-assisted estimators is challenging: the classical approach ignores uncertainty from estimating the working model for the functional relationship between survey and auxiliary variables. This approach may be asymptotically valid, but can underestimate variance in practical settings with limited sample sizes. In this work, we develop a connection between model-assisted estimation and the theory of U- and V-statistics. We demonstrate that when predictions from the working model for the variable of interest can be represented as a U- or V-statistic, the resulting model-assisted estimator also admits a U- or V-statistic representation. We exploit this connection to derive an improved estimator of the exact variance of such model-assisted estimators. The class of working models for which this strategy can be used is broad, ranging from linear models to modern ensemble methods. We apply our approach to the model-assisted estimator constructed with a linear regression working model, commonly referred to as the generalized regression estimator, show that it can be re-written as a U-statistic, and propose an estimator of its exact variance. We illustrate our proposal and compare it against the classical asymptotic variance estimator using household survey data from the American Community Survey.

Education is a key driver of social and economic mobility, yet disparities in attainment persist, particularly in low- and middle-income countries (LMICs). Existing indicators, such as mean years of schooling for adults aged 25 and older (MYS25) and expected years of schooling (EYS), offer a snapshot of an educational system, but lack either cohort-specific or temporal granularity. To address these limitations, we introduce the ultimate years of schooling (UYS)-a birth cohort-based metric targeting the final educational attainment of any individual cohort, including those with ongoing schooling trajectories. As with many attainment indicators, we propose to estimate UYS with cross-sectional household surveys. However, for younger cohorts, estimation fails, because these individuals are right-censored leading to severe downwards bias. To correct for this, we propose to re-frame educational attainment as a time-to-event process and deploy discrete-time survival models that explicitly account for censoring in the observations. At the national level, we estimate the parameters of the model using survey-weighted logistic regression, while for finer spatial resolutions, where sample sizes are smaller, we embed the discrete-time survival model within a Bayesian spatiotemporal framework to improve stability and precision. Applying our proposed methods to data from the 2022 Tanzania Demographic and Health Surveys, we estimate female educational trajectories corrected for censoring biases, and reveal substantial subnational disparities. By providing a dynamic, bias-corrected, and spatially disaggregated measure, our approach enhances education monitoring; it equips policymakers and researchers with a more precise tool for monitoring current progress towards education goals, and for designing future targeted policy interventions in LMICs.

Electronic flat bands associated with quenched kinetic energy and heavy electron mass have attracted great interest for promoting strong electronic correlations and emergent phenomena such as high-temperature charge fractionalization and superconductivity. Intense experimental and theoretical research has been devoted to establishing the rich non-trivial metallic and heavy fermion phases intertwined with such localized electronic states. Here, we investigate the transition metal oxide spinel LiV2O4, an enigmatic heavy fermion compound lacking localized f orbital states. We use angle-resolved photoemission spectroscopy and dynamical mean field theory to reveal a new kind of correlation-induced flat band with suppressed inter-atomic electron hopping arising from intra-atomic Hund coupling. The appearance of heavy quasiparticles is ascribed to a proximate orbital-selective Mott state characterized by fluctuating local moments as evidenced by complementary magnetotransport measurements. The spectroscopic fingerprints of long-lived quasiparticles and their disappearance with increasing temperature further support the emergence of a high-temperature bad metal state observed in transport data. This work resolves a long-standing puzzle on the origin of heavy fermion behavior and unconventional transport in LiV2O4. Simultaneously, it opens a new path to achieving flat bands through electronic interactions in d-orbital systems with geometrical frustration, potentially enabling the realization of exotic phases of matter such as the fractionalized Fermi liquids., Comment: 21 pages, 4 figures

Small area estimation using survey data can be achieved by using either a design-based or a model-based inferential approach. With respect to assumptions, design-based direct estimators are generally preferable because of their consistency and asymptotic normality. However, when data are sparse at the desired area level, as is often the case when measuring rare events for example, these direct estimators can have extremely large uncertainty, making a model-based approach preferable. A model-based approach with a random spatial effect borrows information from surrounding areas at the cost of inducing shrinkage towards the local average. As a result, estimates may be over-smoothed and inconsistent with design-based estimates at higher area levels when aggregated. We propose a unit-level Bayesian model for small area estimation of rare event prevalence which uses design-based direct estimates at a higher area level to increase accuracy, precision, and consistency in aggregation. After introducing the model and its implementation, we conduct a simulation study to compare its properties to alternative models and apply it to the estimation of the neonatal mortality rate in Zambia, using 2014 DHS data.

Accurate and precise estimates of the under-5 mortality rate (U5MR) are an important health summary for countries. However, full survival curves allow us to better understand the pattern of mortality in children under five. Modern demographic methods for estimating a full mortality schedule for children have been developed for countries with good vital registration and reliable census data, but perform poorly in many low- and middle-income countries (LMICs). In these countries, the need to utilize nationally representative surveys to estimate the U5MR requires additional care to mitigate potential biases in survey data, acknowledge the survey design, and handle the usual characteristics of survival data, for example, censoring and truncation. In this paper, we develop parametric and non-parametric pseudo-likelihood approaches to estimating child mortality across calendar time from complex survey data. We show that the parametric approach is particularly useful in scenarios where data are sparse and parsimonious models allow efficient estimation. We compare a variety of parametric models to two existing methods for obtaining a full survival curve for children under the age of 5, and argue that a parametric pseudo-likelihood approach is advantageous in LMICs. We apply our proposed approaches to survey data from four LMICs.

Over the past decade classical optical systems with gain or loss, modelled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic states is fundamentally voided by quantum-limited amplifier noise. Here, we show that second-quantised Hermitian Hamiltonians on the Fock space give rise to non-Hermitian effective Hamiltonians that generate the dynamics of corresponding creation and annihilation operators. Using this equivalence between $\mathcal{PT}$-symmetry and symplectic Bogoliubov transformations, we create a quantum optical scheme comprising squeezing, phase-shifters, and beam-splitters for simulating arbitrary non-unitary processes by way of singular value decomposition. In contrast to the post-selection scheme for non-Hermitian quantum simulation, the success probability in this approach is independent of the system size or simulation time, and can be efficiently Trotterised similar to a unitary transformation., Comment: 7 pages, 1 figure

Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible regression models that allow for nonlinearities and interactions in the covariate specification. Existing machine learning approaches that allow for spatial dependence in the residuals fail to provide reliable uncertainty estimates. In this paper, we investigate the combination of a Gaussian process spatial model with a Bayesian Additive Regression Tree (BART) model. The computational burden of the approach is reduced by combining Markov chain Monte Carlo (MCMC) with the Integrated Nested Laplace Approximation (INLA) technique. We study the performance of the method first via simulation. We then use the model to predict anthropometric responses in Kenya, with the data collected via a complex sampling design. In particular, household survey data are collected via stratified two-stage unequal probability cluster sampling, which requires special care when modeled.

When mapping subnational health and demographic indicators, direct weighted estimators of small area means based on household survey data can be unreliable when data are limited. If survey microdata are available, unit level models can relate individual survey responses to unit level auxiliary covariates and explicitly account for spatial dependence and between area variation using random effects. These models can produce estimators with improved precision, but often neglect to account for the design of the surveys used to collect data. Pseudo-Bayesian approaches incorporate sampling weights to address informative sampling when using such models to conduct population inference but credible sets based on the resulting pseudo-posterior distributions can be poorly calibrated without adjustment. We outline a pseudo-Bayesian strategy for small area estimation that addresses informative sampling and incorporates a post-processing rescaling step that produces credible sets with close to nominal empirical frequentist coverage rates. We compare our approach with existing design-based and model-based estimators using real and simulated data.

Producing subnational estimates of the under-five mortality rate (U5MR) is a vital goal for the United Nations to reduce inequalities in mortality and well-being across the globe. There is a great disparity in U5MR between high-income and Low-and-Middle Income Countries (LMICs). Current methods for modelling U5MR in LMICs use smoothing methods to reduce uncertainty in estimates caused by data sparsity. This paper includes cohort alongside age and period in a novel application of an Age-Period-Cohort model for U5MR. In this context, current methods only use age and period (and not cohort) for smoothing. With data from the Kenyan Demographic and Health Surveys (DHS) we use a Bayesian hierarchical model with terms to smooth over temporal and spatial components whilst fully accounting for the complex stratified, multi-staged cluster design of the DHS. Our results show that the use of cohort may be useful in the context of subnational estimates of U5MR. We validate our results at the subnational level by comparing our results against direct estimates., Comment: 16 pages, 6 Figures, 2 Tables

The under-5 mortality rate (U5MR), a critical health indicator, is typically estimated from household surveys in lower and middle income countries. Spatio-temporal disaggregation of household survey data can lead to highly variable estimates of U5MR, necessitating the usage of smoothing models which borrow information across space and time. The assumptions of common smoothing models may be unrealistic when certain time periods or regions are expected to have shocks in mortality relative to their neighbors, which can lead to oversmoothing of U5MR estimates. In this paper, we develop a spatial and temporal smoothing approach based on Gaussian Markov random field models which incorporate knowledge of these expected shocks in mortality. We demonstrate the potential for these models to improve upon alternatives not incorporating knowledge of expected shocks in a simulation study. We apply these models to estimate U5MR in Rwanda at the national level from 1985-2019, a time period which includes the Rwandan civil war and genocide., Comment: 59 pages