B-spline data models are a powerful way to represent scientific data sets with a functional approximation that admit analytical formulas for computing function values, derivatives, and box-aligned integrals. However, computing line integrals of these models is only efficient when the path of integration is aligned with a Cartesian direction. In many scientific disciplines, it is necessary to quickly and repeatedly compute line integrals along rays with high accuracy. Here, we demonstrate a new method for quickly integrating B-spline models along straight-line (but not axis-aligned) paths. We show that our method operates roughly an order of magnitude more efficiently than standard approximations with the trapezoidal rule for two dimensional data. The efficiency of the method is also studied in three dimensions. In three dimensions, we find the method is less efficient, yet still comparable with traditional approaches.
In this article, we present an empirical-based parameter estimation method called Search via Simulation. Using a hierarchical simulation procedure, surrogate data is propagated and selected based on its ability to mimic the inherent behavior of the observed data via the Kolmogorov-Smirnov distance. This method can be easily applied to probability distributions that do not have a density, distribution or characteristic function in closed form. We define strong Kolmogorov-Smirnov continuity for the assumed parameter estimator. The performance of this method is compared to established estimation methods using a simulation study which includes an execution on stable distributions. We also demonstrate the comparative performance of the Search via Simulation method in fitting stable distributions to CRSP excess returns data typically characterized by heavy tails. This research opens a new global and effective simulation-based inference approach to parameter estimation in accordance with current advances in data science and computational technology.
Temporal point process data arise in many applications, such as neuroscience and finance, where the focus is on the timing of sequential events. In many settings, however, observations are collected under an event-driven stopping mechanism, where recording terminates upon the occurrence of a fixed number of events, resulting in a stochastically stopped temporal point process. This leads to sequential event-time data with a random terminal time and no information beyond the last observed event, inducing a constrained event-time space with temporal ordering and a stochastic boundary that is not adequately captured by standard multivariate approaches. In this paper, we propose a novel product depth for event-time data observed up to the first k events, providing a principled tool for measuring centrality and ranking such temporal trajectories. The proposed depth integrates a marginal component that captures the overall duration through the terminal event and a conditional component that characterizes the relative structure of inter-arrival times. We establish its key theoretical properties and demonstrate its practical utility through simulation studies and real data applications.
Missing data are common in environmental mixture studies and can bias inference if not properly addressed. This study evaluates how different imputation strategies influence variable selection performance in six mixture modeling frameworks: Weighted Quantile Sum (WQS), Bayesian WQS (BWQS), Quantile g-computation (Q-gcomp), Bayesian Kernel Machine Regression (BKMR), Elastic Net, and Least Absolute Shrinkage and Selection Operator (LASSO). Using Monte Carlo simulations (MCS), we generated multivariate normal (MVNORM) and multivariate t- (MVT) distributed exposures under linear and nonlinear outcome structures. Missingness was introduced at 25% for exposure and outcome variables, and at 5%-25% under both missing-at-random (MAR) and missing-not-at-random (MNAR) mechanisms. The study compares single imputation (SI) methods (mean, median, and k-nearest neighbors [KNN]) with multiple imputation approaches [MI] (MICE and Amelia) based on sensitivity (SE), specificity (SP), and false discovery rate (FDR). Across simulations, MI consistently improved variable selection performance under MAR, whereas SI and listwise deletion increased variability and reduced accuracy. Under MNAR, performance declined across all methods, with greater instability observed in flexible models such as BKMR and WQS. Q-gcomp demonstrated the most consistent balance across SE, SP, and FDR and remained relatively robust to violations of the MAR assumption. Additional analyses highlight the importance of imputation model specification: excluding relevant covariates (e.g. income) from the imputation process increased variability and reduced stability, particularly for flexible models and binary outcomes. Application to NHANES 2007-2014 data (n = 8,233) showed that MI improved the stability of variable importance estimates, with BWQS and Q-gcomp yielding more reproducible exposure rankings. Overall, results demonstrate that both the missingness mechanism and the choice and specification of imputation strategy substantially influence variable selection in mixture models, underscoring the importance of carefully designed imputation procedures in environmental epidemiology.
Near real time change detection is important for a variety of Earth monitoring applications and remains a high priority for remote sensing science. Data sparsity, subtle changes, seasonal trends, and the presence of outliers make detecting actual landscape changes challenging. Adams and MacKay introduced Bayesian Online Changepoint Detection (BOCPD), a computationally efficient, exact Bayesian method for change detection. Incorporation of prior information allows for relaxed dependence on dense data and an extensive stable period, making this method applicable to short time series and multiple changepoint detection. In this paper, we conduct BOCPD with a multivariate linear regression framework that supports seasonal trends and outlier robustness. We adapt BOCPD to introduce Robust Online Bayesian Monitoring (roboBayes), which includes a mechanism to make BOCPD robust against occasional outliers, such as corrupted images, without compromising the computational efficiency of an exact posterior change distribution nor the detection latency. Without this robustness feature, the change detection algorithm cannot be employed autonomously without an inflated false positive rate. We show via simulations that the method effectively detects change in the presence of outliers. The method is applied to monitor deforestation in Myanmar where we show superior performance compared to current online changepoint detection methods.
