We consider a Bayesian Additive Regression Trees (BART) model that accounts for skewed error distributions with heavy-tailed error distributions. These characteristics are commonly observed in empirical datasets and often violate the Gaussian distribution error assumption typically assumed in regression modeling. To address this limitation, we propose SkT-BART, a novel extension of the BART model that incorporates a skew-t error distribution. The proposed model retains the flexibility of BART in capturing complex nonlinear relationships and interaction effects, while providing enhanced robustness to asymmetry and heavy tails in the data. For posterior computation, we develop a Metropolis-within-Gibbs sampler that combines data augmentation for the skew-t error distribution with joint Metropolis-Hastings updates for tree structures and terminal-node parameters. In each tree update, a candidate tree structure is generated using standard BART-style local proposals, and the associated terminal-node parameters are proposed from Laplace-based independence proposals. The proposed tree-leaf state is then accepted or rejected jointly through a Metropolis-Hastings correction The performance of SkT-BART is evaluated through extensive simulation studies under varying degrees of skewness and tail heaviness. While results show that SkT-BART consistently outperforms existing BART variants under heavy-tailed or outlier-contaminated scenarios, yielding lower root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), it underperforms simpler Gaussian-based models when errors approach normality. Additionally, under non-Gaussian settings, the model achieves higher log pseudo marginal likelihood (LPML), reflecting better model fit. Finally, the practical utility and robustness of SkT-BART are extensively validated across 17 benchmark datasets, demonstrating its effectiveness and flexibility in capturing complex distributional patterns in practical applications.
Detecting spatial change boundaries that separate regions with different regression relationships is important for the analysis of spatially heterogeneous data. We develop three residual-based procedures for detecting spatial change boundaries in linear regression models: a spatial path scanning procedure, a local block discrepancy procedure, and an integrated strip scanning procedure. The first and third procedures apply cumulative sum (CUSUM) statistics to one-dimensional sequences induced by spatial orderings, whereas the second procedure compares residual averages over neighboring local blocks. The asymptotic properties of the proposed procedures are established under a regular-lattice framework, while irregularly sampled designs are treated as computational extensions and evaluated through simulation. Simulation studies under different boundary configurations, sampling designs, and spatial dependence structures reveal complementary strengths and limitations of the proposed procedures in detecting and localizing spatial change boundaries. Comparisons with residual-based Point Wombling and the spatially clustered coefficient regression method based on a minimum spanning tree (SCC-MST) further illustrate the relative strengths and limitations of the proposed procedures. A Boston Housing application provides a real-data illustration of the spatial boundary patterns produced by the proposed methods.
Computer simulations are invaluable for understanding complex scientific and engineering phenomena, but their use in statistical inference can be prohibitively expensive. Emulators provide computationally tractable approximations to such simulators, yet in practice multiple emulators of differing fidelity and complexity may be available, making model selection non-trivial. In this work, we investigate multifidelity emulation for inverse problems, namely parameter inference from data, after defining the model fidelities as hierarchical approximations to a ‘gold-standard’ simulator, that is, as low- and high-fidelity emulators. We show, both theoretically and empirically, that low-fidelity emulators of multivariate simulator outputs can, despite being less accurate than their high-fidelity counterparts from a forward-prediction perspective, yield more accurate parameter inference at lower computational cost. Thus, we propose a novel multifidelity inference framework that adaptively switches between, or combines, high- and low-fidelity emulators using a classifier that identifies regions of parameter space in which each fidelity is expected to provide more accurate inference. We further introduce a combined multifidelity strategy incorporating both mechanisms and demonstrate that it can outperform inference based on single (high-) fidelity emulators.
This paper proposes efficient covariance and correlation matrix measures using high-frequency data. The proposed matrix measures are the multivariate extension of the Parkinson volatility measure that incorporates High, Low, Open and Close price information distinct from the classical approaches based solely on one information type such as closing price information when constructing the sample covariance matrices. The proposed novel matrix measures facilitate new developments for multivariate time series modelling of dependence structures, including the extension of volatility models such as Conditional Autoregressive Range models to multivariate settings. Model results will provide important risk measures to practitioners for portfolio or investment strategies that deal with a large number of stock assets. Through simulation studies, the proposed matrix measures are shown to perform well under heteroskedastic variance conditions and are positive semi-definite. A demonstration is provided for hypotheses testing applying the estimated variance-covariance matrices to various one and two samples tests. Results show that the proposed matrix measures outperform the classical single source of information based sample covariance and correlation matrix measures.
