Automatic transaction of signal via statistical modeling

The statistical information processing can be characterized by the likelihood function defined by giving an explicit form for an approximation to the true distribution. This mathematical representation, which is usually called a model, is built based on not only the current data but also prior knowledge on the object and the objective of the analysis. Akaike^2,3) showed that the log-likelihood can be considered as an estimate of the Kullback-Leibler (K-L) information which measures the similarity between the predictive distribution of the model and the true distribution. Akaike information criterion (AIC) is an estimate of the K-L information and makes it possible to evaluate and compare the goodness of many models objectively. In consequence, the minimum AIC procedure allows us to develop automatic modeling and signal extraction procedures. In this article, we give a simple explanation of statistical modeling based on the AIC and demonstrate four examples of applying the minimum AIC procedure to an automatic transaction of signals observed in the earth sciences. Genshiro, Kitagawa, Ph.D.: He is a Professor in the Department of Prediction and Control at the Institute of Statistical Mathematics. He is currently Deputy Director of the Institute of Statistical Mathematics and Professor of Statistical Science at the Graduate University for Advanced Study. He obtained his Ph.D. from the Kyushu University in 1983. His primary research interests are in time series analysis, non-Gaussian nonlinear filtering, and statistical modeling. He has published over 50 research papers. He was awarded the 2nd Japan Statistical Society Prize in 1997. Tomoyuki Higuchi, Ph.D.: He is an Associate Professor in the Department of Prediction and Control at the Institute of Statistical Mathematics. He is currently an Associate Professor of Statistical Science at the Graduate University for Advanced Study. He obtained his Ph.D. from the University of Tokyo in 1989. His research interests are in statistical modeling of space-time data, stochastic optimization techniques, and data mining. He has published over 30 research papers.