Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

van Lieshout, M. N. M.

doi:10.1007/s10463-023-00890-6

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…From a computational point of view, (3) is more costly than (4). The practical efficacy of both techniques for a range of point process models is investigated by Van Lieshout (2023).…”

Section: T (H; X I ) − |W || Between the Volume Of W And The Test Fun...mentioning

confidence: 99%

Discussion of ‘Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks’ by Matthias Eckardt and Mehdi Moradi

van Lieshout

2024

JABES

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We congratulate Professors Eckardt and Moradi on their fine paper in which they survey the state of the art of summary statistics for marked point processes. The authors focus on non-stationary point processes and distinguish between discrete, real-valued and objectvalued marks. The case of point processes in an Euclidean space with discrete marks is by far the most well studied. Here, centre stage is taken by the cross K , H and J statistics. After a brief detour into the frequency domain, the authors consider point processes on linear networks. The concept of intensity-reweighted moment pseudo-stationarity (IRMPS) is introduced and used to define counterparts of the cross statistics just mentioned.From a measure-theoretic point of view, point processes are counting measures. It is therefore interesting to note that the cross K , H and J statistics have been generalised to multivariate random measures as well (Van Lieshout 2018). The basic ideas are to replace λ (m) in (3) by p m , the m-point coverage function, and to let the role of the generating functional be taken over by the Laplace transform. For example,under coverage-reweighted moment stationarity assumptions that are satisfied, for instance, by the lognormal random field models of Ballani et al. (2012) for which

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“…From a computational point of view, (3) is more costly than (4). The practical efficacy of both techniques for a range of point process models is investigated by Van Lieshout (2023).…”

Section: T (H; X I ) − |W || Between the Volume Of W And The Test Fun...mentioning

confidence: 99%

Discussion of ‘Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks’ by Matthias Eckardt and Mehdi Moradi

van Lieshout

2024

JABES

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Exploring Seismic Hazard in the Groningen Gas Field Using Adaptive Kernel Smoothing

Lieshout¹,

Z.²

2023

Math Geosci

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The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards, though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state-of-the-art rate-and-state models for the prediction of seismic hazard fail to capture inter-event interaction in the earthquake catalogue. Based on these findings, we suggest a modified rate-and-state model that also takes into account changes in gas production volumes and uncertainty in the pore pressure field.

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Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

Cited by 2 publications

References 26 publications

Discussion of ‘Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks’ by Matthias Eckardt and Mehdi Moradi

Discussion of ‘Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks’ by Matthias Eckardt and Mehdi Moradi

Exploring Seismic Hazard in the Groningen Gas Field Using Adaptive Kernel Smoothing

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