Funded by the US National Science Foundation, grant DMS 1505780, Aug 2015 – July 2019
Project Summary
The main goal of this project is the development of statistical tools for the analysis of points that occur at random in time or space, such as the locations of street robberies in a given city or the timings of spikes of neural activity for an individual performing a certain task.
This type of data arises in many different fields, like neuroscience, ecology, finance, astronomy, seismology, criminology, and many others. The statistical methods to be developed under this project will then provide new data-analysis and inference tools for researchers and practitioners in diverse scientific fields.
In this project we will develop semiparametric methods for estimation of the intensity functions of spatial and temporal replicated point processes. These have become increasingly common in recent years, and the possibility of pooling data across replications allows for the development of more efficient statistical methods.
Acknowledgement and Disclaimer
This material is based upon work supported by the National Science Foundation under Grant Number 1505780. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Publications
- Gervini, D. (2021). Doubly stochastic models for spatio-temporal covariation of replicated point processes. To appear in The Canadian Journal of Statistics. Currently ArXiv 1903.09253.
- Technical Supplement available.
- Gervini, D. and Baur, T.J. (2020). Joint models for grid point and response processes in longitudinal and functional data. Statistica Sinica 30 1905-1924.
- Technical Supplement available.
- Gervini, D. and Khanal, M. (2019). Exploring patterns of demand in bike sharing systems via replicated point process models. Journal of the Royal Statistical Society Series C: Applied Statistics 68 585-602.
- Technical Supplement available.
- Gervini, D. (2017). Multiplicative component models for replicated point processes. ArXiv 1705.09693.
- Technical Supplement available.
- Gervini, D. (2016). Independent component models for replicated point processes. Spatial Statistics 18 474-488.
- Technical Supplement available.
Computer programs (Matlab)
Joint models for grid point and response processes in longitudinal and functional data
The zip file COVMKPP_package contains Matlab programs for estimation of the covariation models proposed by Gervini and Baur (2020).
Doubly stochastic models for spatio-temporal covariation of replicated point processes
The zip file STPP_package contains Matlab programs for estimation of the models proposed by Gervini (2021). A brief tutorial is included.
Exploring patterns of demand in bike sharing systems
The zip file Bike_programs contains Matlab programs used in Gervini and Khanal (2019).
Multiplicative Component models for replicated point processes
The zip files Temporal_MCA_package and Spatial_MCA_package contain Matlab programs for fitting temporal and spatial Multiplicative Component models of Gervini (2017). Tutorials explaining how to use the programs are included.
Independent Component models for replicated point processes
The zip files Temporal_ICAPP_package and Spatial_ICAPP_package contain Matlab programs for fitting the temporal and spatial Independent Component models of Gervini (2016). They also include tutorials explaining how to use the programs.
Talks
- Independent component models for replicated point processes. 8th International Conference of the ERCIM Working Group on Computational and Methodological Statistics, Senate House, University of London, London, UK, December 2015.
- Multiplicative component models for replicated point processes. 10th International Conference of the ERCIM Working Group on Computational and Methodological Statistics, Senate House, University of London, London, UK, December 2017.
- Functional data methods for replicated point processes. Conference on Statistical Learning and Data Science, sponsored by the ASA section on Statistical Learning and Data Science and the ASA section on Nonparametric Statistics, Columbia University, June 2018.
- Statistical methods for replicated spatio-temporal point processes. 11th International Conference of the ERCIM Working Group on Computational and Methodological Statistics, University of Pisa, Pisa, Italy, December 2018.
- Talk_London_19
Last updated: 30 Jun 2021, 21:30 hs