Intensity estimation on geometric networks with penalized splines

In the past decades growing amount of network data lead to many novel statistical models. this paper we consider so-called geometric networks. Typical examples are road networks or other infrastructure Nevertheless, neurons blood vessels in a human body can also be interpreted as embedded three-dimensional space. A network-specific metric, rather than Euclidean is usually used all these applications, making analyses challenging. We network-based point processes, and our task estimate intensity (or density) process which allows us detect high- low-intensity regions underlying stochastic processes. Available routines that tackle problem commonly based on kernel smoothing methods. This uses penalized spline extends toward smooth estimation Furthermore, approach easily incorporating covariates, enabling respect geometry regression model framework. Several simulation study show spline-based numerically stable efficient tool. it estimating linear covariate effects, distinguishing from already existing methodologies.