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Gervini, D. (2022), Doubly stochastic models for spatio-temporal covariation of replicated point processes. Can J Statistics, 50: 287-303. https://doi.org/10.1002/cjs.11638
Stochastic point processes in time and space have a broad range of applications, in areas as diverse as neuroscience, ecology, finance, seismology, and others. Stochastic point processes are observed when a set of points occur at random in time or space. For example, in bike-sharing systems that are now common in many cities around the world, the start-time of a bike trip can be seen as a random point in time and the destination as a random point in space. This paper proposes statistical methods to model the relationship between the spatial and temporal components of a spatio-temporal point process. For example, in bike-sharing applications, the following questions can be answered using these models: is bike demand uniformly distributed during the day, or does it peak at certain times? Is this pattern similar every day of the week or is it different on weekdays and weekends? Are trip destinations uniformly distributed in the vicinity of the bike station or do some specific locations tend to attract more trips? Are these temporal and spatial patterns related? For example, do days with an early–morning peak in bike demand also show trip destinations concentrated on a specific area, such as downtown? Answering these questions is important for an efficient administration of the bike-sharing system, because understanding the patterns of usage of each bike station helps correct imbalances in bike distribution that inevitably arise in such systems. In this paper, the author specifically analyzes the spatio-temporal patterns of usage of a bike station in the Divvy bike-sharing system of the city of Chicago.