B1008
Title: An instrumental variable method for point processes: Generalized Wald estimation based on deconvolution
Authors: Zhichao Jiang - Harvard University (United States)
Peng Ding - University of California, Berkeley (United States)
Shizhe Chen - University of California, Davis (United States) [presenting]
Abstract: Point processes are probabilistic tools for modeling event data such as neural spike trains, natural disasters, and crimes. While there exists a fast-growing literature studying the relationships between point processes, it remains unexplored how such relationships connect to causal effects. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumental variable. We extend the traditional Wald estimation for point process treatment and outcome, and show that it should be performed after a Fourier transform and thus takes the form of deconvolution. We term this as the generalized Wald estimation and propose an estimation strategy based on well-established deconvolution methods. The proposed estimation strategy is applicable under many commonly-used models without requiring distributional assumptions on the unmeasured confounders. We apply the proposed methodology to analyze the data from an experiment on mouse neuron activities.
