A visual display device for significant features in complicated signals

Abstract

For many applications the significant features found in a data set depend on the level of resolution for which the data are considered. An excellent example of this is in climatology where the features found on scales of tens and hundreds of years, respectively, may be very different. A natural way to study such data sets is through the scale-space approach. In this paper a new scale-space method, which finds significant features in signals, is proposed. The new method, posterior smoothing, is formulated in a Bayesian framework and utilizes sampling from the posterior density. We compare the new methodology to a successful, existing scale-space technique entitled SiZer (Significant Zero crossings of derivatives). For smooth signals SiZer and the new method have similar performance. In signals containing complicated structures, posterior smoothing is preferable. This is demonstrated by applying the methods to simulated and real data sets. In particular, we show that posterior smoothing has better performance in applications taken from climatology, medical imaging, and fish industry.