Markov chain for gibbs sampler applied in electromagnetic scattering by 2D rough surface

The study of electromagnetic scattering by twodimensional rough surface remains a challenging subjects for scientists due to its bidirectional scattering field computation. In this paper, Gibbs Sampler approach is applied to study electromagnetic scattering by twodimensional rough surface. This work consists of generating a two-dimensional random rough surface. From that bivariate random distribution data generated, Gibbs Sampler method is applied to iteratively draw samples from the full conditional distribution. As we are dealing with a bivariate data two conditional probabilities distribution will be determined. They are respectively the probability distribution of x given y (P(x/y)) and the probability distribution y given x (P(y/x)). If sampling from those conditional distributions is possible then we can use Gibbs sampling method. For our study we consider a situation where it can be sampling from those two conditional distribution. Thepurpose of this samplingmethod is to estimate the marginal distributions P(X) and P(Y). And these marginal distributions are employed to compute the scattering field inx direction and in y direction. As results, a very high-frequency fluctuation is observed on scattering coefficient. Comparing with other works that exist literature this technique of Gibbs sampling shows an agreement.