梁埈豪 Junho Yang

Modeling dependent data in time and space

Broadly speaking, my main research focuses on the estimation and inference of random objects with dependent structures and their applications. Below, I will describe two of my main research contributions in detail.

Firstly, together with Prof. Suhasini Subba Rao and Akihiko Inoue, we developed a new method to solve the Wiener-Hopf (WH) equations and quantify the approximation errors of finite-section WH solutions. Specifically, I used linear prediction techniques to transform the half-convolution equation of the WH system into a “full” convolution equation. Furthermore, by employing series expansion techniques, I derived sharp bounds for the approximation errors. Applications of WH systems are prevalent in applied mathematics and engineering, including Kalman filtering, control theory, and queuing theory. Additionally, the optimal filter coefficients arising in WH systems are widely used in signal denoising and image reconstruction.

Secondly, I have also devoted my research to event data in space and time. In collaboration with Lin Zhu and Profs. Mikyoung Jun and Scott Cook, we developed new inferential methods for multivariate spatial point processes. The proposed method is computationally efficient, and the asymptotic covariance matrix of the estimator provides insights into the selection of optimal tuning parameters in the contrast measure. Applications of these methods include analyzing multivariate spatial pattern data in various disciplines, such as (1) the distribution of COVID-19 patients categorized by variants, (2) crime statistics, and (3) earthquake catalog data in Taiwan.