Stochastic Interpolation of Spatial Random Fields by BF/MCF-ISM

In the past, interpolation of random fields was successfully treated by Kriging methods for Gaussian fields, and by conditional simulation techniques for a class of non-Gaussian translation fields. Recently, bootstrap filter/Monte Carlo filter (BF/MCF) is extensively used for interpolation of general non-Gaussian fields. However, while BF/MCF is a versatile tool to interpolate non-Gaussian fields, that is an algorithm of generating a set of sample realizations of both a predicted state vector and a filtered state vector, the computational cost is expensive due to the required sample size. In order to reduce the required sample size, an importance sampling function derived from the updating theory of Gaussian fields is applied to the ordinary BF/MCF. Interpolation of spatial fields is first demonstrated by using numerically simulated data, and the BF/MCF incorporated with importance sampling technique (BF/MCF-ISM) for the state estimation of conditional non-Gaussian fields is performed with respect to its efficiency in variance reduction.