In this work, we study some computational aspects for the Bayesian analysis involving stable distributions. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, the use of a latent or auxiliary random variable facilitates to obtain any posterior distribution when being related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to daily price returns of Abbey National shares, considered in [1], and the other is the length distribution analysis of coding and non-coding regions in a Homo sapiens chromosome DNA sequence, considered in [2]. Posterior summaries of interest are obtained using the OpenBUGS software
Electrocardiography (ECG) is the process of recording the electrical activity of the heart over a period of time using electrodes placed on the skin. The time intervals between its various peaks, may contain useful information about the nature of disease afflicting the heart. In the last years, different methods have been used by the researchers to detect arrhythmias from electrocardiogram (ECG) signal. In this paper we propose an arrhythmia detection coefficient based on the coefficient of variation and on the principle of wavelet shrinkage. This coefficient is tested in RR time series from databases of the PhysioBank.
In this work, we analyze the long-range dependence parameter for a nucleotide sequence in several different transformations. The long-range dependence parameter is estimated by the approximated maximum likelihood method, by a novel estimator based on the spectral envelope theory, by a regression method based on the periodogram function, and also by the detrended fluctuation analysis method. We study the length distribution of coding and noncoding regions for all Homo sapiens chromosomes available from the European Bioinformatics Institute. The parameter of the tail rate decay is estimated by the Hill estimator ˆα. We show that the tail rate decay is greater than 2 for coding regions, while for almost all noncoding regions it is less than 2.
The presence of human-made explosions in a seismic catalog leads to errors in statistical analyses of seismicity. We proposed the Hurst estimator by the Smoothed Detrended Fluctuation Analysis method (SDFA) like an additional classification tool to discriminate between natural tectonic earthquakes and human-made explosions.
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