Estimating the effect of latent time-varying count exposures using multiple lists.

A major challenge in longitudinal built-environment health studies is the accuracy of commercial business databases that are used to characterize dynamic food environments. Different databases often provide conflicting exposure measures on the same subject due to different source credibilities. As on-site verification is not feasible for historical data, we suggest combining multiple databases to correct the bias in health effect estimates due to measurement error in any 1 datasource. We propose a joint model for the time-varying health outcomes, observed count exposures, and latent true count exposures. Our model estimates the time-specific quality of sources and incorporates time dependence of true count exposure by Poisson integer-valued first-order autoregressive process. We take a Bayesian nonparametric approach to flexibly account for location-specific exposures. By resolving the discordance between different databases, our method reduces the bias in the longitudinal health effect of the true exposures. Our method is demonstrated with childhood obesity data in California public schools with respect to convenience store exposures in school neighborhoods from 2001 to 2008.

A sparse factor model for clustering high-dimensional longitudinal data.

Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and uncover underlying disease mechanisms. However, analyzing such kind of data can be difficult due to its high dimensionality, heterogeneity and computational challenges. In this article, we propose a Bayesian nonparametric mixture model for clustering high-dimensional mixed-type (eg, continuous, discrete and categorical) longitudinal features. We employ a sparse factor model on the joint distribution of random effects and the key idea is to induce clustering at the latent factor level instead of the original data to escape the curse of dimensionality. The number of clusters is estimated through a Dirichlet process prior. An efficient Gibbs sampler is developed to estimate the posterior distribution of the model parameters. Analysis of real and simulated data is presented and discussed. Our study demonstrates that the proposed model serves as a useful analytical tool for clustering high-dimensional longitudinal data.

Prediction sets adaptive to unknown covariate shift.

Predicting sets of outcomes-instead of unique outcomes-is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift-a prevalent issue in practice-poses a serious unsolved challenge. In this article, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is asymptotically probably approximately correct, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.

Measuring the impact of responsible factors on CO2 emission using generalized additive model (GAM).

The indicators of economic and sustainable development ultimately significantly depend on carbon dioxide (CO2) emissions in every country. In Bangladesh, there is an increasing trend in population, industrialization, as well as electricity demand generated from different sources, ultimately increasing CO2 emissions. This study explores the relationship between CO2 emissions and other significant relevant indicators. Moreover, the authors aimed to identify which model is effective at predicting CO2 emissions and assess the accuracy of the prediction of different models. The secondary data from 1971 to 2020, was collected from the World Bank and the Bangladesh Road Transport Authority's publicly accessible website. The generalized additive model (GAM), the polynomial regression (PR), and multiple linear regression (MLR) were used for modeling CO2 emissions. The model performance is evaluated using the Bayesian information criterion (BIC), Akaike information criterion (AIC), Root mean square error (RMSE), R-square, and mean square error (MSE). Results revealed that there are few multicollinearity problems in the datasets and exhibit a nonlinear relationship among CO2 emissions. Among the models considered in this study, the GAM model has the lowest value of RMSE = 0.008, MSE = 0.000063, AIC = -303.21, BIC = -266.64 and the highest value of R-squared = 0.996 compared to the MLR and PR models, suggesting the most appropriate model in predicting CO2 emissions in Bangladesh. Findings revealed that the total CO2 emissions and other relevant risk factors is non-linear. The study suggests that the Generalized additive model regression technique can be used as an effective tool for predicting CO2 emissions in Bangladesh. The authors believed that the findings would be helpful to policymakers in designing effective strategies in the areas of a low-carbon economy, encouraging the use of renewable energy sources, and focusing on technological advancement that reduces CO2 emissions and ensures a sustainable environment in Bangladesh.