# Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach

arXiv: https://arxiv.org/abs/2306.06756 · HTML: https://mlsanity.com/paper/2306.06756/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 93 references that are in the map.
- First posted on arXiv 11 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Frequentist Consistency of Variational Bayes](https://mlsanity.com/paper/1705.03439/) (2017)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Penalising model component complexity: A principled, practical approach to constructing priors](https://mlsanity.com/paper/1403.4630/) (2014)
- [Prediction models for network-linked data](https://mlsanity.com/paper/1602.01192/) (2016)
- [Generalized Sparse Additive Models](https://mlsanity.com/paper/1903.04641/) (2019)
- [In Defense of the Indefensible: A Very Naive Approach to High-Dimensional Inference](https://mlsanity.com/paper/1705.05543/) (2017)
- [An intuitive Bayesian spatial model for disease mapping that accounts for scaling](https://mlsanity.com/paper/1601.01180/) (2016)
- [Convex and non-convex regularization methods for spatial point processes intensity estimation](https://mlsanity.com/paper/1703.02462/) (2017)
- [A Spatially Discrete Approximation to Log-Gaussian Cox Processes for Modelling Aggregated Disease Count Data](https://mlsanity.com/paper/1901.09551/) (2019)
- [Quasi-likelihood for Spatial Point Processes](https://mlsanity.com/paper/1303.0188/) (2013)
- [Inference in High Dimensions with the Penalized Score Test](https://mlsanity.com/paper/1401.2678/) (2014)
- [A Significance Test for Graph-Constrained Estimation](https://mlsanity.com/paper/1506.08339/) (2015)
- [Continuous Inference for Aggregated Point Process Data](https://mlsanity.com/paper/1704.05627/) (2017)
- [Adaptive lasso and Dantzig selector for spatial point processes intensity estimation](https://mlsanity.com/paper/2101.03698/) (2021)

## Abstract (arXiv)

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and correlation. However, existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for estimating covariate effects in doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity of the underlying intensity. Our approach is based on an approximate (discrete and deterministic) formulation of the true (continuous and stochastic) intensity function. We show that consistency and asymptotic normality of the covariate effect estimates can be achieved despite the model misspecification, and develop a covariance estimator that leads to a valid, albeit conservative, statistical inference procedure. A simulation study shows the validity of our approach under less restrictive assumptions on the data generating mechanism, and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.