Semi-parametric Markov models for multi-type point patterns

2025-10-13

AI Summary

In spatial point pattern analysis with multiple event types, unobserved spatial confounding biases estimates of interaction effects and covariate effects. To address this, we propose a novel semiparametric Markov point process model that augments conventional parametric interaction structures with a nonparametric spatial factor term, enabling identifiable separation of interaction and covariate effects by flexibly absorbing latent confounding. We develop estimation within a conditional pseudolikelihood framework, integrating spline-based smoothing techniques to balance computational feasibility and statistical efficiency. We establish theoretical consistency and asymptotic normality of the resulting estimators. Empirical application to spatial clustering data of two bank types in France demonstrates substantially improved estimation accuracy and interpretability. The proposed method provides a robust modeling framework for ecological, epidemiological, and social science applications where unmeasured spatial confounding is present.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates. However, estimation of interaction and covariate effects may be seriously biased in the presence of unobserved spatial confounders. In this paper we introduce a new class of semi-parametric Markov point processes that adjusts for spatial confounding through a non-parametric factor that accommodates effects of latent spatial variables common to all types of points. We introduce a conditional pseudo likelihood for parameter estimation and show that the resulting estimator has desirable asymptotic properties. Our methodology not least has great potential in studies of industry agglomeration and we apply it to study spatial patterns of locations of two types of banks in France.

Problem

• Modeling multi-type point patterns with interactions and covariate effects
• Addressing estimation bias from unobserved spatial confounders
• Developing semi-parametric Markov models for latent spatial variables

Innovation

• Semi-parametric Markov models adjust spatial confounding
• Non-parametric factor accommodates latent spatial variables
• Conditional pseudo likelihood enables parameter estimation