Bayesian multiscale analysis for time series data

SiZer Inference for Varying Coefficient Models

“…For example, Hannig and Marron (2006) proposed an improved simultaneous inference version of SiZer to reduce unexpected spurious features in the SiZer map. Bayesian scenario of SiZer has been developed as an alternative to Bayesian multiscale smoothing (Erästö and Holmström, 2005;Godtliebsen and Øigård, 2005;Øigård et al, 2006). The applications of SiZer for time series analysis have been investigated by Park et al (2004Park et al ( , 2007Park et al ( , 2009 and Rondonotti et al (2007).…”

Robust SiZer Approach for Varying Coefficient Models

“…Hannig and Marron [22] have proposed an improved simultaneous inference version of SiZer. The Bayesian scenario of SiZer has been developed by Erästö and Holmström [23], Godtliebsen and Øigård [24], and Øigård et al [25]. Ganguli and Wand [26] and Godtliebsen et al [27,28] have considered the bivariate smoothing technique in SiZer.…”

Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

“…This allows us to define a sensible range for κ, and following [17] the lower bound of κ is chosen such that ESS(κ min ) ≈ 2. The upper bound of κ is chosen such that a circle containing ESS points should not have a diameter exceeding one tenth of the smallest dimension, since the toroidal graph introduces noticeably detrimental effects at higher levels.…”

“…S 3 proceeds by viewing the image smoothed by convolutions of Gaussian kernels of varying bandwidth, and calculates gradients and curvatures that are significant above the noise level, and in this sense represents a two dimensional version of SiZer. In [16] and [17], a Bayesian approach for exploratory analysis of time series data is developed, and it is demonstrated that in certain applications it outperforms SiZer, since it can make meaningful inference on much lower levels of smoothing. In [18] Erästö and Holmström introduce a similar methodology which they refer to as BSiZer (Bayesian SiZer), for finding significant features in scatterplots, and in [19] these ideas are further developed into a tool for multiresolution analysis of random signals.…”

“…In this article a new Bayesian methodology to finding significant features in images is developed, extending the Bayesian methodology from [16] and [17] to two dimensions. The method can be seen as a Bayesian version of S 3 , and we will refer to the method as Bayesian multiscale analysis (BMulA).…”