arXiv subjects

Mikyoung Jun

Publications and source records attributed to Mikyoung Jun.

13 recordsLinked to original sources

arXiv2026

Multivariate Spatio-Temporal Neural Hawkes Processes

We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial information into latent state evolution through learned temporal and spatial decay dynamics, enabling flexible modeling of excitation and inhibition without predefined triggering kernels. By analyzing fitted intensity functions of deep learning-based temporal Hawkes process models, we identify a modeling gap in how fitted intensity behavior is captured beyond likelihood-based performance, which motivates the proposed spatio-temporal approach. Simulation studies show that the proposed method successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns, while existing temporal neural Hawkes process approach fails to do so. An application to terrorism data from Pakistan further demonstrates the proposed model's ability to capture complex spatio-temporal interaction across multiple event types.

stat.ML↗

arXiv2024

Addressing Duplicated Data in Spatial Point Patterns

Spatial point process models are widely applied to point pattern data from various applications in the social and environmental sciences. However, a serious hurdle in fitting point process models is the presence of duplicated points, wherein multiple observations share identical spatial coordinates. This often occurs because of decisions made in the geo-coding process, such as assigning representative locations (e.g., aggregate-level centroids) to observations when data producers lack exact location information. Because spatial point process models like the Log-Gaussian Cox Process (LGCP) assume unique locations, researchers often employ ad hoc solutions (e.g., removing duplicates or jittering) to address duplicated data before analysis. As an alternative, this study proposes a Modified Minimum Contrast (MMC) method that adapts the inference procedure to account for the effect of duplicates in estimation, without needing to alter the data. The proposed MMC method is applied to LGCP models, focusing on the inference of second-order intensity parameters, which govern the clustering structure of point patterns. Under a variety of simulated conditions, our results demonstrate the advantages of the proposed MMC method compared to existing ad hoc solutions. We then apply the MMC methods to a real-data application of conflict events in Afghanistan (2008-2009).

stat.ME↗

arXiv2023

Prediction of Tropical Pacific Rain Rates with Over-parameterized Neural Networks

The prediction of tropical rain rates from atmospheric profiles poses significant challenges, mainly due to the heavy-tailed distribution exhibited by tropical rainfall. This study introduces over-parameterized neural networks not only to forecast tropical rain rates, but also to explain their heavy-tailed distribution. The prediction is separately conducted for three rain types (stratiform, deep convective, and shallow convective) observed by the Global Precipitation Measurement satellite radar over the West and East Pacific regions. Atmospheric profiles of humidity, temperature, and zonal and meridional winds from the MERRA-2 reanalysis are considered as features. Although over-parameterized neural networks are well-known for their ``double descent phenomenon," little has been explored about their applicability to climate data and capability of capturing the tail behavior of data. In our results, over-parameterized neural networks accurately predict the rain rate distributions and outperform other machine learning methods. Spatial maps show that over-parameterized neural networks also successfully describe spatial patterns of each rain type across the tropical Pacific. In addition, we assess the feature importance for each over-parameterized neural network to provide insight into the key factors driving the predictions, with low-level humidity and temperature variables being the overall most important. These findings highlight the capability of over-parameterized neural networks in predicting the distribution of the rain rate and explaining extreme values.

physics.ao-ph↗

arXiv2022

3D Bivariate Spatial Modelling of Argo Ocean Temperature and Salinity

Variables contained within the global oceans can detect and reveal the effects of the warming climate as the oceans absorb huge amounts of solar energy. Hence, information regarding the joint spatial distribution of ocean variables is critical for climate monitoring. In this paper, we investigate the spatial correlation structure between ocean temperature and salinity using data harvested from the Argo program and construct a model to capture their bivariate spatial dependence from the surface to the ocean's interior. We develop a flexible class of multivariate nonstationary covariance models defined in 3-dimensional (3D) space (longitude $\times$ latitude $\times$ depth) that allows for the variances and correlation to change along the vertical pressure dimension. These models are able to describe the joint spatial distribution of the two variables while incorporating the underlying vertical structure of the ocean. We demonstrate that the proposed cross-covariance models describe the complex vertical cross-covariance structure well, while existing cross-covariance models including bivariate Mat\'{e}rn models poorly fit empirical cross-covariance structure. Furthermore, the results show that using one more variable significantly enhances the prediction of the other variable and that the estimated spatial dependence structures are consistent with the ocean stratification.

stat.AP↗

arXiv2022

Flexible Spatio-Temporal Hawkes Process Models for Earthquake Occurrences

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space-time interactions between aftershocks with a non-separable spatio-temporal triggering structure. For model estimation, we extend the model-independent stochastic declustering (MISD) algorithm and suggest substituting its histogram-based estimators with kernel methods. We demonstrate the utility of the proposed methods by applying them to the seismicity data in regions with active seismic activities.

stat.AP↗

arXiv2022

On minimum contrast method for multivariate spatial point processes

Compared to widely used likelihood-based approaches, the minimum contrast (MC) method offers a computationally efficient method for estimation and inference of spatial point processes. These relative gains in computing time become more pronounced when analyzing complicated multivariate point process models. Despite this, there has been little exploration of the MC method for multivariate spatial point processes. Therefore, this article introduces a new MC method for parametric multivariate spatial point processes. A contrast function is computed based on the trace of the power of the difference between the conjectured $K$-function matrix and its nonparametric unbiased edge-corrected estimator. Under standard assumptions, we derive the asymptotic normality of our MC estimator. The performance of the proposed method is demonstrated through simulation studies of bivariate log-Gaussian Cox processes and five-variate product-shot-noise Cox processes.

stat.ME↗

arXiv2022

A Spatio-temporal Track Association Algorithm Based on Marine Vessel Automatic Identification System Data

Tracking multiple moving objects in real-time in a dynamic threat environment is an important element in national security and surveillance system. It helps pinpoint and distinguish potential candidates posing threats from other normal objects and monitor the anomalous trajectories until intervention. To locate the anomalous pattern of movements, one needs to have an accurate data association algorithm that can associate the sequential observations of locations and motion with the underlying moving objects, and therefore, build the trajectories of the objects as the objects are moving. In this work, we develop a spatio-temporal approach for tracking maritime vessels as the vessel's location and motion observations are collected by an Automatic Identification System. The proposed approach is developed as an effort to address a data association challenge in which the number of vessels as well as the vessel identification are purposely withheld and time gaps are created in the datasets to mimic the real-life operational complexities under a threat environment. Three training datasets and five test sets are provided in the challenge and a set of quantitative performance metrics is devised by the data challenge organizer for evaluating and comparing resulting methods developed by participants. When our proposed track association algorithm is applied to the five test sets, the algorithm scores a very competitive performance.

cs.LG↗

arXiv2022

Flexible multivariate spatio-temporal Hawkes process models of terrorism

We develop flexible multivariate spatio-temporal Hawkes process models to analyze patterns of terrorism. Previous applications of point process methods to political violence data mainly utilize temporal Hawkes process models, neglecting spatial variation in these attack patterns. This limits what can be learned from these models as any effective counter-terrorism strategy requires knowledge on both when and where attacks are likely to occur. Even the existing work on spatio-temporal Hawkes processes imposes restrictions on the triggering function that are not well-suited for terrorism data. Therefore, we generalize the structure of the spatio-temporal triggering function considerably, allowing for nonseprability, nonstatitionarity, and cross-triggering (i.e., across the groups). To demonstrate the utility of our models, we analyze two samples of real-world terrorism data: Afghanistan (2002-2013) for univariate analysis and Nigeria (2009-2017) for bivariate analysis. Jointly, these two studies demonstrate that our models outperform standard Hawkes process models, besting widely-used alternatives in overall model fit and revealing spatio-temporal patterns that are, by construction, masked in these models (e.g., increasing dispersion in cross-triggering over time).

stat.ME↗

arXiv2021

The promise and perils of point process models of political events

Event data are increasingly common in applied political science research. While these data are inherently locational, political scientists predominately analyze aggregate summaries of these events as areal data. In so doing, they lose much of the information inherent to these point pattern data, and much of the flexibility that comes analyzing events using point process models. Recognizing these advantages, applied statisticians have increasingly utilized point process models in the analysis of political events. Yet, this work often neglects inherent limitations of political event data (e.g, geolocation accuracy), which can complicate the direct application of point process models. In this paper, we attempt to bridge this divide: introducing the benefits of point process modeling for political science research, and highlighting the unique challenges political science data pose for these approaches. To ground our discussion, we focus the Global Terrorism Database, using a univariate and bivariate log-Gaussian Cox process model (LGCP) to analyze terror attacks in Nigeria during 2014.

stat.AP↗

arXiv2017

Global multivariate point pattern models for rain type occurrence

We seek statistical methods to study the occurrence of multiple rain types observed by satellite on a global scale. The main scientific interests are to relate rainfall occurrence with various atmospheric state variables and to study the dependence between the occurrences of multiple types of rainfall (e.g. short-lived and intense versus long-lived and weak; the heights of the rain clouds are also considered). Commonly in point process model literature, the spatial domain is assumed to be a small, and thus planar domain. We consider the log-Gaussian Cox Process (LGCP) models on the surface of a sphere and take advantage of cross-covariance models for spatial processes on a global scale to model the stochastic intensity function of the LGCP models. We present analysis results for rainfall observations from the TRMM satellite and atmospheric state variables from MERRA-2 reanalysis data over the tropical Eastern and Western Pacific Ocean, as well as over the entire tropical and subtropical ocean regions. Statistical inference is done through Monte Carlo likelihood approximation for LGCP models. We employ covariance approximation to deal with massive data.

stat.AP↗

arXiv2015

Covariance models on the surface of a sphere: when does it matter?

There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle distance, isotropic and positive definite functions in a Euclidean space can be used as covariance functions on the surface of a sphere. This approach, however, may result in physically unrealistic distortion on the sphere especially for large distances. We consider several classes of parametric covariance functions on the surface of a sphere, defined with either the great circle distance or the Euclidean distance, and investigate their impact upon spatial prediction. We fit several isotropic covariance models to simulated data as well as real data from NCEP/NCAR reanalysis on the sphere. We demonstrate that covariance functions originally defined with the Euclidean distance may not be adequate for some global data.

stat.AP↗

arXiv2012

Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.

stat.AP↗

arXiv2009

Nonstationary covariance models for global data

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.

stat.AP↗