Simulation study has become an essential part of most statistical research. It allows us to study and assess new methodologies in modelling, estimation and inference. Hence it gives potential users of these new methods a good idea of their performance on real data. In most situations, researchers need to generate many long realisations with pre-specified distributional property in a short time.

This talk is divided into three parts. In the first part, I will discuss limitations on some existing simulation methods and introduce the Circulant Embedding Simulation Method, which is a fast and exact simulation method for simulating scalar-valued stationary Gaussian random fields. This method employs the idea of embedding a symmetric (nested/block) Toeplitz covariance matrix for the required stationary Gaussian processes into a symmetric (nested/block) circulant matrix with highly composite dimension. The square root of this circulant matrix is then computed efficiently using the fast Fourier transform. In the second and third parts of this talk, I will discuss how to extend this idea to simulate vector-valued stationary Gaussian random fields and fractional Brownian motions respectively.

Related Publications

Chan, G. and Wood, A.T.A. (1997a). An Algorithm for Simulating Stationary Gaussian Random Fields. Applied Statistics, 46, 171-181.

Chan, G. and Wood, A.T.A. (1997b). Simulation of Stationary Gaussian Vector Fields. Statistics and Computing, submitted.

Wood, A.T.A. and Chan, G. (1994). Simulation of Stationary Gaussian Processes in [0,1]^d. Journal of Computational and Graphical Statistics, 3, 409-432.