Advances in Adaptive Data Analysis

This paper introduces a Bayesian approach to blending rainfall observations from both satellite remote sensing and ground rain gauges and to estimating errors of the blended data in terms of credible interval. The Bayesian posterior estimate (BPE) approach treats one observation as prior information and uses another observation as likelihood function information and as a correction. The BPE is an alternative to the minimum mean square estimate (MMSE) approach, also known as the least square approach. The posterior estimate outputs a probability density function (PDF), while the MMSE approach yields only an estimated mean and mean square error (MSE). When a diffusive rain rate model is assumed, the sampling errors of the Tropical Rainfall Measuring Mission (TRMM) satellite and a regular array of ground rain gauges are calculated under assumptions of idealized conditions: homogenous statistical properties of the rain rate, and flush visits of TRMM approximately twice a day. The optimal blend of the TRMM and ground gauges is determined by the optimal weight for each. The weight for the rain gauges w_g is a nonlinear function of the ratio of the space gap to the time gap. The error of the blended product increases as the gaps of time and space samplings expand, and the increase is almost linear when neither time gap nor space gap is small, but becomes strongly nonlinear when the space gap is very small. Our results are helpful in the design of appropriate sampling strategies for rainfall measurements.

A noise-assisted approach in conjunction with multivariate empirical mode decomposition (MEMD) algorithm is proposed for the computation of empirical mode decomposition (EMD), in order to produce localized frequency estimates at the accuracy level of instantaneous frequency. Despite many advantages of EMD, such as its data driven nature, a compact decomposition, and its inherent ability to process nonstationary data, it only caters for signals with a sufficient number of local extrema. In addition, EMD is prone to mode-mixing and is designed for univariate data. We show that the noise-assisted MEMD (NA-MEMD) approach, which utilizes the dyadic filter bank property of MEMD, provides a solution to the above problems when used to calculate standard EMD. The method is also shown to alleviate the effects of noise interference in univariate noise-assisted EMD algorithms which directly add noise to the data. The efficacy of the proposed method, in terms of improved frequency localization and reduced mode-mixing, is demonstrated via simulations on electroencephalogram (EEG) data sets, over two paradigms in brain-computer interface (BCI).

In the laser droplet generation process three different dripping regimes are experimentally observed in dependence on the detachment pulse power. Besides being nonlinear, the process is also inherently nonstationary. In order to consistently analyze all the dripping scenarios based on an experimental time series, time-frequency analysis by means of instantaneous frequency is used. For the calculation of instantaneous frequency, the most recent developments of the Hilbert–Huang transform are applied, i.e. ensemble empirical mode decomposition, empirical amplitude/frequency modulation decomposition, and direct quadrature. In time-frequency spectra specific patterns are associated with corresponding dripping regimes. By means of a detailed inspection of patterns, the influence of the detachment pulse power on dripping dynamics is characterized.

Empirical mode decomposition (EMD) has been established as a valuable tool in determining nonlinear signal trend. EMD decomposes a one-dimensional (1D) signal into hierarchical components known as intrinsic mode functions (IMFs) and a residue, based on the local properties of the signal. The first IMF depicts the highest local oscillations, while the residue depicts the trend of a signal/data. In each iteration of the EMD process, interpolation is applied to some local maxima and minima points to form upper and lower envelopes, respectively. But, the application of interpolation methods causes huge computation time and other artifacts in the decomposition, which limits the use of EMD for many real life signals. This paper proposes an effective method that replaces the interpolation step by direct envelope estimation using order statistics filters, which results in decreased computation time, following a similar EMD approach that has been recently proposed for two-dimensional data or image analysis. The modified EMD of this paper called pseudo EMD (P-EMD) method is particularly useful in determining, analyzing, and/or modifying the trend of various signals to obtain and/or produce some desired results/outcomes. Several synthetic and real-life signals such as speech signal and sea level pressure and temperature are tested to verify the effectiveness of the P-EMD. From the results, P-EMD has been found as a superior alternative for trend analysis of signal/data, since it results in more accurate trend compared to the other interpolation based EMD methods such as classical EMD (CEMD) and a modified EMD (MEMD), and also facilitates faster computation.

The Hilbert–Huang transform (HHT) is a novel, adaptive approach to time series analysis. It does not impose a basis set on the data or otherwise make assumptions about the data form, and so the time-frequency decomposition is not limited by spreading due to uncertainty. Because of the high resolution of the time-frequency, we investigate the possibility of the application of the HHT to the search for gravitational waves. It is necessary to determine some parameters in the empirical mode decomposition (EMD), which is a component of the HHT, and in this paper we propose and demonstrate a method to determine the optimal values of the parameters to use in the search for gravitational waves.