Regularized estimation for highly multivariate log Gaussian Cox processes

Choiruddin, Achmad; Cuevas-Pacheco, Francisco; Coeurjolly, Jean‐François; Waagepetersen, Rasmus

doi:10.1007/s11222-019-09911-y

Cited by 21 publications

(14 citation statements)

References 26 publications

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“…Choiruddin et al . 2020). The intensity model chosen by CBIC coincides with the model chosen for Acalypha diversifolia by backward stepwise model selection in Guan, Jalilian & Waagepetersen (2015).…”

Section: Numerical Resultsmentioning

confidence: 99%

Information criteria for inhomogeneous spatial point processes

Choiruddin

Coeurjolly

Waagepetersen

2021

Aus NZ J of Statistics

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The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of 'sample size' needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.

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Section: Numerical Resultsmentioning

confidence: 99%

Information criteria for inhomogeneous spatial point processes

Choiruddin

Coeurjolly

Waagepetersen

2021

Aus NZ J of Statistics

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“…Saran yang diberikan pada penelitian selanjutnya mengenai analisis risiko kecelakaan lalu lintas, diantaranya adalah dengan mempertimbangkan penggunaan jenis ruas jalan sesuai dengan yang ada ditetapkan oleh dinas perencanaan tata ruang dan wilayah di Kabupaten Nganjuk, dan multi-type point pattern [13] dapat dipertimbangkan pada analisis berikutnya. Melakukan pengujian homogenitas sebaran titik lokasi kecelakaan (uji Chi-Square) menggunakan acuan uji yang lain.…”

Section: Kesimpulan Dan Saranunclassified

Analisis Risiko Kecelakaan Lalu Lintas di Jalan Raya Kabupaten Nganjuk Menggunakan Poisson Point Process on a Linear Network

Kholisatin

Choiruddin

2021

Inferensi

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Kecelakaan lalu lintas yang terjadi di Kabupaten Nganjuk dalam rentang waktu 3 tahun terakhir cukup tinggi, tercatat terdapat 2039 kecelakaan dan terdapat 1977 data lokasi kejadian yang tercatat oleh SATLANTAS Kabupaten Nganjuk dimana sebagian besar lokasi kecelakaan tersebar pada jalan arteri primer dan kolektor primer. Kejadian kecelakaan selama tahun tersebut paling sering terjadi pada Bulan Desember, hari Senin dan di jam 09.00 -10.00 pagi dan 18.00 -19.00 malam. Jumlah kecelakaan lalu lintas selama 2018 -2020 yang terjadi pada siang hari ada sebanyak dua kali lipat dibandingkan pada malam hari, selain itu jumlah kecelakaan pada jalan luar kota juga hampir dua kali lipat dari pada jalan dalam kota.. Kedua kovariat kategorik yang digunakan dijadikan sebagai marks dan masing-masing dimodelkan menggunakan model Poisson Point Process on a Linear Network. Model dengan kovariat waktu kejadian menghasilkan nilai estimasi dari intensitas kecelakaan lalu lintas di siang hari yang 62,3% lebih tinggi dibandingkan dengan intensitas kecelakaan lalu lintas pada malam hari. Sedangkan, untuk model menggunakan kovariat jenis jalan, dapat diinterpretasikan bahwa intensitas kecelakaan pada jalan luar kota dua kali lipat lebih tinggi dibandingkan dengan intensitas kecelakaan lalu lintas pada jalan dalam kota. Hasil yang didapatkan, model dengan kovariat jenis jalan menghasilkan nilai AIC yang lebih kecil.

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“…Parametric estimation of cross associations is also possible. Jalilian et al (2015), Waagepetersen et al (2016) and Choiruddin et al (2019) used parametric models of intensity and pair correlation functions, while Rajala et al (2018) specified a full multivariate Markov point process model.…”

Section: Introductionmentioning

confidence: 99%

“…Our objective in this paper is to infer the full within and between correlation structure of a multivariate point process. To do so, we adopt the parametric log Gaussian Cox process (LGCP) model for the correlation structure proposed in Waagepetersen et al (2016) and further considered in Choiruddin et al (2019). This model is flexible and has a very natural interpretation in terms of latent structures.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Semi-Parametric Inference for Multivariate Log Gaussian Cox Processes

Hessellund

Guan

et al. 2022

Journal of the Royal Statistical Society Series C: Applied Statistics

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This paper introduces a new approach to inferring the second‐order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi‐parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second‐order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross‐validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non‐parametrically.

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Regularized estimation for highly multivariate log Gaussian Cox processes

Cited by 21 publications

References 26 publications

Information criteria for inhomogeneous spatial point processes

Information criteria for inhomogeneous spatial point processes

Analisis Risiko Kecelakaan Lalu Lintas di Jalan Raya Kabupaten Nganjuk Menggunakan Poisson Point Process on a Linear Network

Second-Order Semi-Parametric Inference for Multivariate Log Gaussian Cox Processes

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