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Uncovering the distribution of magnitudes and arrival times of aftershocks isa key to comprehend the characteristics of the sequence of earthquakes, whichenables us to predict seismic activities and hazard assessments. However,identifying the number of aftershocks immediately after the main shock ispractically difficult due to contaminations of arriving seismic waves. Toovercome the difficulty, we construct a likelihood based on the detected dataincorporating a detection function to which the Gaussian process regression(GPR) is applied. The GPR is capable of estimating not only the parameters ofthe distribution of aftershocks together with the detection function but alsocredible intervals for both of the parameters and the detection function. Aproperty that distributions of both the Gaussian process and aftershocks areexponential functions leads to an efficient Bayesian computational algorithm toestimate the hyperparameters. After the validations through numerical tests,the proposed method is retrospectively applied to the catalog data related tothe 2004 Chuetsu earthquake towards early forecasting of the aftershocks. Theresult shows that the proposed method stably estimates the parameters of thedistribution simultaneously their credible intervals even within three hoursafter the main shock.

Forecasting temporal variation of aftershocks immediately after a main shock using Gaussian process regression