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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 structure. Machine learning models have been suggested in the spatial context, allowing for spatial dependence in the residuals, but fail to provide reliable uncertainty estimates. In this paper, we investigate a novel combination of a Gaussian process spatial model and 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 via simulations and use the model to predict anthropometric responses, collected via household cluster samples in Kenya.

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

We consider random forests and LASSO methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available for the sampled areas, from the survey, and for all areas, from an exterior source, and the goal is to use auxiliary variables to predict the outcome of interest. We compare areal-level random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method. Further, to measure the uncertainty of estimates obtained from random forests and the LASSO, we propose a modification of the split conformal procedure that relaxes the assumption of identically distributed data. This work is motivated by Ghanaian data available from the sixth Living Standard Survey (GLSS) and the 2010 Population and Housing Census. We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3\% of all the areas (136 out of 5019) and more than 170 potential covariates are available from both datasets. Among the four modelling methods considered, the Bayesian shrinkage performed the best in terms of bias, MSE and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation, the log consumption areal point estimates showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district gathers the richest areas., Comment: 40 pages, 10 figures

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and dependence. However, existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for estimating covariate effects in doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity of the underlying intensity. Our approach is based on an approximate (discrete and deterministic) formulation of the true (continuous and stochastic) intensity function. We show that consistency and asymptotic normality of the covariate effect estimates can be achieved despite the model misspecification, and develop a covariance estimator that leads to a valid, albeit conservative, statistical inference procedure. A simulation study shows the validity of our approach under less restrictive assumptions on the data generating mechanism, and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.

The Tutte polynomial and Derksen's $\mathcal{G}$-invariant are the universal deletion/contraction and valuative matroid and polymatroid invariants, respectively. There are only a handful of well known invariants (like the matroid Kazhdan-Lusztig polynomials) between (in terms of roughness/fineness) the Tutte polynomial and Derksen's $\mathcal{G}$-invariant. The aim of this study is to define a spectrum of generalized Tutte polynomials to fill the gap between the Tutte polynomial and Derksen's $\mathcal{G}$-invariant. These polynomials are built by taking repeated convolution products of universal Tutte characters studied by Dupont, Fink, and Moci and using the framework of Ardila and Sanchez for studying valuative invariants. We develop foundational aspects of these polynomials by showing they are valuative on generalized permutahedra and present a generalized deletion/contraction formula. We apply these results on chain Tutte polynomials to obtain new formulas for the M\"obius polynomial, the opposite characteristic polynomial, a generalized M\"obius polynomial, Ford's expected codimension of a matroid variety, and Derksen's $\mathcal{G}$-invariant., Comment: 30 pages

Condensates are a hallmark of emergence in quantum materials with superconductors and charge density wave as prominent examples. An excitonic insulator (EI) is an intriguing addition to this library, exhibiting spontaneous condensation of electron-hole pairs. However, condensate observables can be obscured through parasitic coupling to the lattice. Time-resolved terahertz (THz) spectroscopy can disentangle such obscurants through measurement of the quantum dynamics. We target $Ta_{2}NiSe_{5}$, a putative room-temperature EI where electron-lattice coupling dominates the structural transition ($T_{c}$=326 K), hindering identification of excitonic correlations. A pronounced increase in the THz reflectivity manifests following photoexcitation and exhibits a BEC-like temperature dependence. This occurs well below the $T_{c}$, suggesting a novel approach to monitor exciton condensate dynamics. Nonetheless, dynamic condensate-phonon coupling remains as evidenced by peaks in the enhanced reflectivity spectrum at select infrared-active phonon frequencies. This indicates that parametric reflectivity enhancement arises from phonon squeezing, validated using Fresnel-Floquet theory and density functional calculations. Our results highlight that coherent dynamics can drive parametric stimulated emission with concomitant possibilities, including entangled THz photon generation., Comment: 51 pages, 14 figures, 1 table

Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat band dispersions; identification of candidate platforms plays an important role in these efforts. Here, we develop a high-throughput materials search for bulk crystalline flat bands by automated construction of uniform-hopping near-neighbor tight binding models. We show that this approach captures many of the essential features relevant to identifying flat band lattice motifs in candidate materials in a computationally inexpensive manner. We apply this algorithm to 139,367 materials in the Materials Project database and identify 63,076 materials that host at least one flat band elemental sublattice. We further categorize these candidate systems into at least 31,635 unique flat band crystal nets and identify candidates of interest from both lattice and band structure perspectives. This work expands the number of known flat band lattices that exist in physically realizable crystal structures and classifies the majority of these systems by the underlying lattice, providing new insights for familiar (e.g. kagome, pyrochlore, Lieb, and dice) as well as previously unknown motifs., Comment: 29 pages, 8 figures, 2 tables