A visual display device for significant features in complicated signals

Bayesian multiscale analysis for time series data

“…This is a comparison with Godtliebsen and ]igård (2005), who suggested a Wiener-process as the prior model. In such a model the derivatives do not exist, so finite difference alternatives had to be applied.…”

“…In this paper we reconsider the approach taken by Godtliebsen and ]igård (2005) and suggest numerous important improvements in the model, the algorithms and how to display the results. The changes are as follows:…”

“…Although SiZer has proven very successful in a large set of applications, it is clear that it has weaknesses for complicated signals, see Godtliebsen and ]igård (2005) where a new Bayesian multiscale method was introduced. The new method turned out to be very successful for exploratory analysis of structures in applications where the observed signal contains complicated and rapidly changing structures.…”

“…Hence the costs are linear in the length of the time series. The simulation based approach using MCMC, taken by Godtliebsen and ]igård (2005), is both costly in comparison to an exact algorithm and does not provide reliable estimates when the smoothing is severe. This is due to slow convergence.…”

“…By doing this one can, in contrast to SiZer, do meaningful inference also at very small scales. In Godtliebsen and ]igård (2005), scale was introduced through a smoothing parameter in the prior distribution of the true underlying curve. Samples from the posterior distribution were drawn using Markov Chain Monte Carlo (MCMC).…”