As the first approximation, irregular sea waves are expressed as the superposition of infinite number of infinitesimal waves having various frequencies and prop
agation directions. However, nonlinear effect can not be negligible in shallow or intermediate water depth.
　In this report, I deal with the second order weakly nonlinear, quasi-Gaussian irregular sea waves. First, I introduce the concept of the second order nonlinear
kernel function which expresses the second order nonlinear effect between two component free waves, and second, I propse a new method to estimate it from measured wave data by a Bayesian approach. The proposed method is examined for numerical simulation data, and the validity of the method is discussed. Some examples of the nonlinear kernel function estimated from field wave data are also shown in this report.