Simulation of nonhomogeneous poisson processes by thinning
Abstract
A simple and relatively efficient method for simulating one‐dimensional and two‐dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.
Citing Literature
Number of times cited according to CrossRef: 367
- Boris I. Godoy, Victor Solo, Syed Ahmed Pasha, Truncated Hawkes point process modeling: System theory and system identification, Automatica, 10.1016/j.automatica.2019.108733, 113, (108733), (2020).
- S. V. Buldyrev, F. Pammolli, M. Riccaboni, H. E. Stanley, , The Rise and Fall of Business Firms, 10.1017/9781316798539, (2020).
- Jingru Ji, Donghua Wang, Dinghai Xu, Chi Xu, Combining a self-exciting point process with the truncated generalized Pareto distribution: An extreme risk analysis under price limits, Journal of Empirical Finance, 10.1016/j.jempfin.2020.03.003, (2020).
- Wu Changye, Christian P. Robert, Markov Chain Monte Carlo Algorithms for Bayesian Computation, a Survey and Some Generalisation, Case Studies in Applied Bayesian Data Science, 10.1007/978-3-030-42553-1_4, (89-119), (2020).
- Tadashi Dohi, Junjun Zheng, Hiroyuki Okamura, Data-driven software reliability evaluation under incomplete knowledge on fault count distribution, Quality Engineering, 10.1080/08982112.2020.1757705, 32, 3, (421-433), (2020).
- Ran Xiao, Duc Do, Cheng Ding, Karl Meisel, Randall J. Lee, Xiao Hu, Generalizability of SuperAlarm via Cross-Institutional Performance Evaluation, IEEE Access, 10.1109/ACCESS.2020.3009667, 8, (132404-132412), (2020).
- M. Mohammadi, S. Rezakhah, N. Modarresi, Semi-Lévy driven continuous-time GARCH process, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2020.124855, 557, (124855), (2020).
- Le-Minh Kieu, Nicolas Malleson, Alison Heppenstall, Dealing with uncertainty in agent-based models for short-term predictions, Royal Society Open Science, 10.1098/rsos.191074, 7, 1, (191074), (2020).
- Ernesto Berríos-Caro, Danna R. Gifford, Tobias Galla, Competition delays multi-drug resistance evolution during combination therapy, Journal of Theoretical Biology, 10.1016/j.jtbi.2020.110524, (110524), (2020).
- Zane Z. Chou, Gene J. Yu, Theodore W. Berger, Generation of Granule Cell Dendritic Morphologies by Estimating the Spatial Heterogeneity of Dendritic Branching, Frontiers in Computational Neuroscience, 10.3389/fncom.2020.00023, 14, (2020).
- Chenchen Ma, Yongming Qu, Haoda Fu, Analysis of recurrent hypoglycemic events, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2020.1765370, (1-9), (2020).
- Deborshee Sen, Matthias Sachs, Jianfeng Lu, David B Dunson, Efficient posterior sampling for high-dimensional imbalanced logistic regression, Biometrika, 10.1093/biomet/asaa035, (2020).
- Andreia Monteiro, Raquel Menezes, Maria Eduarda Silva, Modelling informative time points: an evolutionary process approach, TEST, 10.1007/s11749-020-00722-2, (2020).
- R. Bowden, H. P. Keeler, A. E. Krzesinski, P. G. Taylor, Modeling and analysis of block arrival times in the Bitcoin blockchain, Stochastic Models, 10.1080/15326349.2020.1786404, (1-36), (2020).
- Aydar Uatay, A Stochastic Modelling Framework for Single Cell Migration: Coupling Contractility and Focal Adhesions, Symmetry, 10.3390/sym12081348, 12, 8, (1348), (2020).
- Haixu Wang, Jiguo Cao, Estimating time-varying directed neural networks, Statistics and Computing, 10.1007/s11222-020-09941-x, (2020).
- James P Roney, Jeremy Ferlic, Franziska Michor, Thomas O McDonald, ESTIpop: a computational tool to simulate and estimate parameters for continuous-time Markov branching processes, Bioinformatics, 10.1093/bioinformatics/btaa526, (2020).
- David J. Walwark, John K. Grey, Steady-State Fluorescence Signatures of Intramolecular Singlet Fission from Stochastic Predictions, The Journal of Physical Chemistry A, 10.1021/acs.jpca.0c06966, (2020).
- Flavio F. M. Sabatti, Stephen M. Goodnick, Marco Saraniti, Particle-Based Modeling of Electron–Phonon Interactions, Journal of Heat Transfer, 10.1115/1.4045137, 142, 1, (2019).
- Ting Wang, Matthew Schofield, Mark Bebbington, Koji Kiyosugi, Bayesian modelling of marked point processes with incomplete records: volcanic eruptions, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12380, 69, 1, (109-130), (2019).
- Xiao Liu, Rong Pan, Analysis of Large Heterogeneous Repairable System Reliability Data With Static System Attributes and Dynamic Sensor Measurement in Big Data Environment, Technometrics, 10.1080/00401706.2019.1609584, 62, 2, (206-222), (2019).
- Manon Michel, Xiaojun Tan, Youjin Deng, Clock Monte Carlo methods, Physical Review E, 10.1103/PhysRevE.99.010105, 99, 1, (2019).
- Caner Canyakmaz, Süleyman Özekici, Fikri Karaesmen, An inventory model where customer demand is dependent on a stochastic price process, International Journal of Production Economics, 10.1016/j.ijpe.2019.01.039, (2019).
- Wilhelm Braun, André Longtin, Interspike interval correlations in networks of inhibitory integrate-and-fire neurons, Physical Review E, 10.1103/PhysRevE.99.032402, 99, 3, (2019).
- Arijeet Ghosh, Iti Saha Misra, undefined, 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), 10.23919/URSIAP-RASC.2019.8738431, (1-2), (2019).
- Pierre Monmarché, A Short Introduction to Piecewise Deterministic Markov Samplers, Stochastic Dynamics Out of Equilibrium, 10.1007/978-3-030-15096-9_11, (375-390), (2019).
- Dongmin Li, Qingpei Hu, Lujia Wang, Dan Yu, Statistical Inference for M/G/Infinity Queueing Systems Under Incomplete Observations, European Journal of Operational Research, 10.1016/j.ejor.2019.06.055, (2019).
- Nina Gunkelmann, Dan Serero, Aldo Glielmo, Marina Montaine, Michael Heckel, Thorsten Pöschel, Stochastic Nature of Particle Collisions and its Impact on Granular Material Properties, Particles in Contact, 10.1007/978-3-030-15899-6, (565-590), (2019).
- Chun Tung Chou, Designing Molecular Circuits for Approximate Maximum a Posteriori Demodulation of Concentration Modulated Signals, IEEE Transactions on Communications, 10.1109/TCOMM.2019.2913864, 67, 8, (5458-5473), (2019).
- Arne Pommerening, Pavel Grabarnik, Arne Pommerening, Pavel Grabarnik, Spatial and Individual-Based Modelling, Individual-based Methods in Forest Ecology and Management, 10.1007/978-3-030-24528-3, (199-252), (2019).
- Shinichiro Shirota, Sudipto Banerjee, Scalable inference for space‐time Gaussian Cox processes, Journal of Time Series Analysis, 10.1111/jtsa.12457, 40, 3, (269-287), (2019).
- Sambit Kumar Ghosh, Santanu Das, Somak Bhattacharyya, undefined, 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), 10.23919/URSIAP-RASC.2019.8738642, (1-4), (2019).
- Kris V Parag, On Signalling and Estimation Limits for Molecular Birth-Processes, Journal of Theoretical Biology, 10.1016/j.jtbi.2019.07.007, (2019).
- K. Giesecke, G. Schwenkler, Simulated likelihood estimators for discretely observed jump–diffusions, Journal of Econometrics, 10.1016/j.jeconom.2019.01.015, (2019).
- Ali Noroozian, Reza Baradaran Kazemzadeh, Enrico Zio, Seyed Taghi Akhavan Niaki, Importance analysis considering time‐varying parameters and different perturbation occurrence times, Quality and Reliability Engineering International, 10.1002/qre.2542, 35, 8, (2558-2578), (2019).
- Mi Zhang, Shujie Han, Patrick P. C. Lee, SimEDC: A Simulator for the Reliability Analysis of Erasure-Coded Data Centers, IEEE Transactions on Parallel and Distributed Systems, 10.1109/TPDS.2019.2921551, 30, 12, (2836-2848), (2019).
- Arijeet Ghosh, Iti Saha Misra, Anindita Kundu, Coverage and rate analysis in two‐tier heterogeneous networks under suburban and urban scenarios, Transactions on Emerging Telecommunications Technologies, 10.1002/ett.3648, 30, 12, (2019).
- William A. Muir, Stanley E. Griffis, Judith M. Whipple, A Simulation Model Of Multi‐Echelon Retail Inventory With Cross‐Channel Product Returns, Journal of Business Logistics, 10.1111/jbl.12209, 40, 4, (322-338), (2019).
- Proloy Das, Behtash Babadi, Multitaper Spectral Analysis of Neuronal Spiking Activity Driven by Latent Stationary Processes, Signal Processing, 10.1016/j.sigpro.2019.107429, (107429), (2019).
- Yan Qu, Angelos Dassios, Hongbiao Zhao, Efficient simulation of Lévy-driven point processes, Advances in Applied Probability, 10.1017/apr.2019.44, 51, 4, (927-966), (2019).
- R. Ozgur Doruk, Kechen Zhang, Adaptive Stimulus Design for Dynamic Recurrent Neural Network Models, Frontiers in Neural Circuits, 10.3389/fncir.2018.00119, 12, (2019).
- Ran Liu, Michael E. Kuhl, Yunan Liu, James R. Wilson, Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes, INFORMS Journal on Computing, 10.1287/ijoc.2018.0828, (2019).
- Hannah L Payne, Ranran L French, Christine C Guo, TD Barbara Nguyen-Vu, Tiina Manninen, Jennifer L Raymond, Cerebellar Purkinje cells control eye movements with a rapid rate code that is invariant to spike irregularity, eLife, 10.7554/eLife.37102, 8, (2019).
- Rodrigo Saul Gaitan, Keh-Shin Lii, The first and second order moment structure of an inhomogeneous gamma point process, Communications in Statistics - Theory and Methods, 10.1080/03610926.2019.1639746, (1-12), (2019).
- Resat Ozgur Doruk, Laila Abosharb, Estimating the Parameters of Fitzhugh–Nagumo Neurons from Neural Spiking Data, Brain Sciences, 10.3390/brainsci9120364, 9, 12, (364), (2019).
- Behzad Tabibian, Utkarsh Upadhyay, Abir De, Ali Zarezade, Bernhard Schölkopf, Manuel Gomez-Rodriguez, Enhancing human learning via spaced repetition optimization, Proceedings of the National Academy of Sciences, 10.1073/pnas.1815156116, (201815156), (2019).
- Christian Furrer, Experience rating in the classic Markov chain life insurance setting, European Actuarial Journal, 10.1007/s13385-019-00190-5, (2019).
- Changye Wu, Christian P. Robert, Coordinate sampler: a non-reversible Gibbs-like MCMC sampler, Statistics and Computing, 10.1007/s11222-019-09913-w, (2019).
- Jinmeng Bi, Changsheng Jiang, Comparison of Early Aftershock Forecasting for the 2008 Wenchuan MS8.0 Earthquake, Pure and Applied Geophysics, 10.1007/s00024-019-02192-6, (2019).
- Chenlong Li, Zhanjie Song, Wenjun Wang, Xu (Sunny) Wang, Mining periodic patterns and cascading bursts phenomenon in individual e-mail communication, Journal of Applied Statistics, 10.1080/02664763.2019.1605340, (1-24), (2019).
- undefined, Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining - WSDM '18, 10.1145/3159652.3159734, (324-332), (2018).
- Le Minh Kieu, Chen Cai, Stochastic collective model of public transport passenger arrival process, IET Intelligent Transport Systems, 10.1049/iet-its.2018.0085, 12, 9, (1027-1035), (2018).
- D. T. Koops, M. Saxena, O. J. Boxma, M. Mandjes, Infinite-server queues with Hawkes input, Journal of Applied Probability, 10.1017/jpr.2018.58, 55, 3, (920-943), (2018).
- Paul C. Bressloff, Bhargav R. Karamched, Doubly Stochastic Poisson Model of Flagellar Length Control, SIAM Journal on Applied Mathematics, 10.1137/16M110811X, 78, 2, (719-741), (2018).
- Hongmin Li, Guoqi Li, Luping Shi, Super-resolution of spatiotemporal event-stream image, Neurocomputing, 10.1016/j.neucom.2018.12.048, (2018).
- Luca Gonzato, Carlo Sgarra, Estimation of a Self-Exciting Jump Diffusion Model for Oil Price by a Particle Markov Chain Monte Carlo Method, SSRN Electronic Journal, 10.2139/ssrn.3245915, (2018).
- R. Ozgur Doruk, Kechen Zhang, Fitting of dynamic recurrent neural network models to sensory stimulus-response data, Journal of Biological Physics, 10.1007/s10867-018-9501-z, 44, 3, (449-469), (2018).
- Chetan D. Pahlajani, Indrajeet Yadav, Herbert G. Tanner, Ioannis Poulakakis, Decision-Making Accuracy for Sensor Networks with Inhomogeneous Poisson Observations, Distributed Autonomous Robotic Systems, 10.1007/978-3-319-73008-0_13, (177-190), (2018).
- Hafiz Attaul Mustafa, Ali Riza Ekti, Muhammad Zeeshan Shakir, Muhammad Ali Imran, Rahim Tafazolli, Intracell Interference Characterization and Cluster Interference for D2D Communication, IEEE Transactions on Vehicular Technology, 10.1109/TVT.2018.2850820, 67, 9, (8536-8548), (2018).
- Joris Bierkens, Alexandre Bouchard-Côté, Arnaud Doucet, Andrew B. Duncan, Paul Fearnhead, Thibaut Lienart, Gareth Roberts, Sebastian J. Vollmer, Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains, Statistics & Probability Letters, 10.1016/j.spl.2018.02.021, 136, (148-154), (2018).
- Vo Hong Thanh, Luca Marchetti, Federico Reali, Corrado Priami, Incorporating extrinsic noise into the stochastic simulation of biochemical reactions: A comparison of approaches, The Journal of Chemical Physics, 10.1063/1.5016338, 148, 6, (064111), (2018).
- Lorenzo Duso, Christoph Zechner, Selected-node stochastic simulation algorithm, The Journal of Chemical Physics, 10.1063/1.5021242, 148, 16, (164108), (2018).
- Arne Gollin, Volker Dürr, Estimating Body Pitch from Distributed Proprioception in a Hexapod, Biomimetic and Biohybrid Systems, 10.1007/978-3-319-95972-6_20, (187-199), (2018).
- Michael F. Faulkner, Liang Qin, A. C. Maggs, Werner Krauth, All-atom computations with irreversible Markov chains, The Journal of Chemical Physics, 10.1063/1.5036638, 149, 6, (064113), (2018).
- Christèle Etchegaray, Nicolas Meunier, Crawling migration under chemical signalling: A stochastic model, Mathematical Methods in the Applied Sciences, 10.1002/mma.5145, 41, 18, (8799-8815), (2018).
- Woonghee Tim Huh, Jaywon Lee, Heesang Park, Kun Soo Park, The potty parity problem: Towards gender equality at restrooms in business facilities, Socio-Economic Planning Sciences, 10.1016/j.seps.2018.11.003, (2018).
- David O. Lignell, Victoria B. Lansinger, Juan Medina, Marten Klein, Alan R. Kerstein, Heiko Schmidt, Marco Fistler, Michael Oevermann, One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application, Theoretical and Computational Fluid Dynamics, 10.1007/s00162-018-0465-1, 32, 4, (495-520), (2018).
- Indrajeet Yadav, Chetan D. Pahlajani, Herbert G. Tanner, Ioannis Poulakakis, Information-sharing and decision-making in networks of radiation detectors, Autonomous Robots, 10.1007/s10514-018-9716-7, 42, 8, (1715-1730), (2018).
- Chenhao Li, Simon J. Godsill, undefined, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 10.1109/ICASSP.2018.8462457, (2856-2860), (2018).
- Somayeh Moazeni, Boris Defourny, Optimal control of energy storage under random operation permissions, IISE Transactions, 10.1080/24725854.2017.1401756, 50, 8, (668-682), (2018).
- J. Scharcanski, C.T.J. Dodson, R. T. Clarke, Nonwoven Structure Statistics: Simulation of Effects of Fiber Crimp, Flocculation, Density and Orientation, International Nonwovens Journal, 10.1177/1558925002OS-01100107, os-11, 1, (1558925002OS-01), (2018).
- Frederic Paik Schoenberg, Marc Hoffmann, Ryan J. Harrigan, A recursive point process model for infectious diseases, Annals of the Institute of Statistical Mathematics, 10.1007/s10463-018-0690-9, (2018).
- K. J. Falconer, J. Lévy Véhel, Self-stabilizing processes, Stochastic Models, 10.1080/15326349.2018.1521726, (1-26), (2018).
- Renato Pagliara, Deborah M. Gordon, Naomi Ehrich Leonard, Regulation of harvester ant foraging as a closed-loop excitable system, PLOS Computational Biology, 10.1371/journal.pcbi.1006200, 14, 12, (e1006200), (2018).
- Bruno M. C. Martins, Amy K. Tooke, Philipp Thomas, James C. W. Locke, Cell size control driven by the circadian clock and environment in cyanobacteria, Proceedings of the National Academy of Sciences, 10.1073/pnas.1811309115, (201811309), (2018).
- G. Avlogiaris, A. C. Micheas, K. Zografos, A Criterion for Local Model Selection, Sankhya A, 10.1007/s13171-018-0126-x, (2018).
- J. Chen, A. G. Hawkes, E. Scalas, M. Trinh, Performance of information criteria for selection of Hawkes process models of financial data, Quantitative Finance, 10.1080/14697688.2017.1403140, 18, 2, (225-235), (2017).
- Vincent Lemaire, Michèle Thieullen, Nicolas Thomas, Exact Simulation of the Jump Times of a Class of Piecewise Deterministic Markov Processes, Journal of Scientific Computing, 10.1007/s10915-017-0607-4, 75, 3, (1776-1807), (2017).
- Flávio B. Gonçalves, Dani Gamerman, Exact Bayesian inference in spatiotemporal Cox processes driven by multivariate Gaussian processes, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 10.1111/rssb.12237, 80, 1, (157-175), (2017).
- Yongqiang Tang, Algorithms for imputing partially observed recurrent events with applications to multiple imputation in pattern mixture models, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2017.1333999, 28, 3, (518-533), (2017).
- Paul C. Bressloff, Sean D. Lawley, Hybrid colored noise process with space-dependent switching rates, Physical Review E, 10.1103/PhysRevE.96.012129, 96, 1, (2017).
- Angelos Dassios, Hongbiao Zhao, Efficient Simulation of Clustering Jumps with CIR Intensity, Operations Research, 10.1287/opre.2017.1640, 65, 6, (1494-1515), (2017).
- Joris Bierkens, Andrew Duncan, Limit theorems for the zig-zag process, Advances in Applied Probability, 10.1017/apr.2017.22, 49, 3, (791-825), (2017).
- Thomas O. McDonald, Franziska Michor, SIApopr: a computational method to simulate evolutionary branching trees for analysis of tumor clonal evolution, Bioinformatics, 10.1093/bioinformatics/btx146, 33, 14, (2221-2223), (2017).
- Natalia Y. Ermolova, Olav Tirkkonen, Interference Analysis in Wireless Networks Operating over Arbitrary Fading Channels with Heterogeneous Poisson Fields of Transmitters and Interferers, IEEE Signal Processing Letters, 10.1109/LSP.2017.2729664, 24, 9, (1388-1392), (2017).
- A. Mignan, M. Broccardo, S. Wiemer, D. Giardini, Induced seismicity closed-form traffic light system for actuarial decision-making during deep fluid injections, Scientific Reports, 10.1038/s41598-017-13585-9, 7, 1, (2017).
- Thomas Monks, Rudabeh Meskarian, undefined, 2017 Winter Simulation Conference (WSC), 10.1109/WSC.2017.8248000, (2752-2763), (2017).
- Edwin F. Boza, Cristina L. Abad, Monica Villavicencio, Stephany Quimba, Juan Antonio Plaza, undefined, 2017 IEEE Second Ecuador Technical Chapters Meeting (ETCM), 10.1109/ETCM.2017.8247460, (1-6), (2017).
- D. T. Koops, O. J. Boxma, M. R. H. Mandjes, Networks of $$\cdot /G/\infty $$ · / G / ∞ queues with shot-noise-driven arrival intensities, Queueing Systems, 10.1007/s11134-017-9520-7, 86, 3-4, (301-325), (2017).
- D.S. Harte, Probability distribution of forecasts based on the ETAS model, Geophysical Journal International, 10.1093/gji/ggx146, 210, 1, (90-104), (2017).
- Julien Chevallier, Mean-field limit of generalized Hawkes processes, Stochastic Processes and their Applications, 10.1016/j.spa.2017.02.012, 127, 12, (3870-3912), (2017).
- Lorenzo Donatiello, Gustavo Marfia, Models and performance evaluation of event goodput in sensor platforms, Computer Networks, 10.1016/j.comnet.2017.05.015, 123, (119-136), (2017).
- Michael E. Kuhl, undefined, 2017 Winter Simulation Conference (WSC), 10.1109/WSC.2017.8247791, (231-242), (2017).
- María I. Restrepo, Bernard Gendron, Louis-Martin Rousseau, A two-stage stochastic programming approach for multi-activity tour scheduling, European Journal of Operational Research, 10.1016/j.ejor.2017.04.055, 262, 2, (620-635), (2017).
- Christian Backhage, César Ojeda, Rafet Sifa, Circadian Cycles and Work Under Pressure: A Stochastic Process Model for E-learning Population Dynamics, Data Science – Analytics and Applications, 10.1007/978-3-658-19287-7, (13-18), (2017).
- Zhen Qin, Christian R. Shelton, Event Detection in Continuous Video: An Inference in Point Process Approach, IEEE Transactions on Image Processing, 10.1109/TIP.2017.2745209, 26, 12, (5680-5691), (2017).
- Xiaobei Shen, Zoie Shui-Yee Wong, Man Ho Ling, David Goldsman, Kwok-Leung Tsui, Comparison of algorithms to simulate disease transmission, Journal of Simulation, 10.1057/s41273-016-0003-3, 11, 3, (285-294), (2017).
- Yosihiko Ogata, Statistics of Earthquake Activity: Models and Methods for Earthquake Predictability Studies, Annual Review of Earth and Planetary Sciences, 10.1146/annurev-earth-063016-015918, 45, 1, (497-527), (2017).
- Guangyuan Sun, John C. Hewson, David O. Lignell, Evaluation of stochastic particle dispersion modeling in turbulent round jets, International Journal of Multiphase Flow, 10.1016/j.ijmultiphaseflow.2016.10.005, 89, (108-122), (2017).
- Jing Chen, Alan G Hawkes, Enrico Scalas, Mailan Trinh, Performance of Information Criteria for Selection of Hawkes Process Models of Financial Data, SSRN Electronic Journal, 10.2139/ssrn.3040511, (2017).
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