10th World Congress in Probability and Statistics

Contributed Session (live Q&A at Track 1, 11:30AM KST)

Contributed 29

Spatial Data Analysis

11:30 AM — 12:00 PM KST
Jul 20 Tue, 10:30 PM — 11:00 PM EDT

Wild bootstrap for high-dimensional spatial data

Daisuke Kurisu (Tokyo Institute of Technology)

This study establishes a high-dimensional CLT for the sample mean of p-dimensional spatial data observed over irregularly spaced sampling sites in R^d, allowing the dimension p to be much larger than the sample size n. We adopt a stochastic sampling scheme that can flexibly generate irregularly spaced sampling sites and include both pure increasing domain and mixed increasing domain frameworks. To facilitate statistical inference, we develop the spatially dependent wild bootstrap (SDWB) and justify its asymptotic validity in high dimensions by deriving error bounds that hold almost surely conditionally on the stochastic sampling sites. Our dependence conditions on the underlying random field cover a wide class of random fields such as Gaussian random fields and continuous autoregressive moving average random fields. Through numerical simulations and a real data analysis, we demonstrate the usefulness of our bootstrap-based inference in several applications, including joint confidence interval construction for high-dimensional spatial data and change-point detection for spatio-temporal data.

Lifting scheme for streamflow data in river networks

Seoncheol Park (Chungbuk National University)

In this presentation, we suggest a new multiscale method for analyzing water pollutant data located in river networks. The main idea of the proposed method is to adapt the conventional lifting scheme, reflecting the characteristics of streamflow data in the river network domain. Due to the complexity of the data domain structure, it is difficult to apply the lifting scheme to the streamflow data directly. To solve this problem, we propose a new lifting scheme algorithm for streamflow data that incorporates flow-adaptive neighborhood selection, flow proportional weight generation, and flow-length adaptive removal point selection. A nondecimated version of the proposed lifting scheme is also suggested. We will provide a simulation study and a real data analysis of water pollutant data observed on the Geum-River basin in South Korea.

Optimal designs for some bivariate cokriging models

Subhadra Dasgupta (Indian Institute of Technology Bambay-Monash Research Academy)

This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices a linear dependency criterion is identified, which allows the best linear unbiased estimator of the primary variable in a bivariate collocated cokriging setup to reduce to a univariate kriging estimator. Exact optimal designs for efficient prediction for such simple and ordinary reduced cokriging models, with one dimensional inputs are determined. Designs are found by minimizing the maximum and integrated prediction variance, where the primary variable is an Ornstein-Uhlenbeck process. For simple and ordinary cokriging models with known covariance parameters, the equispaced design is shown to be optimal for both criterion functions. The more realistic scenario of unknown covariance parameters is addressed by assuming prior distributions on the parameter vector, thus adopting a Bayesian approach to the design problem. The equispaced design is proved to be the Bayesian optimal design for both criteria. The work is motivated by designing an optimal water monitoring system for an Indian river.

Q&A for Contributed Session 29

This talk does not have an abstract.

Session Chair

Yaeji Lim (Chung-Ang University)

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